Felix is visiting a shopping mall that has a rectangular shape with a diagonal walkway that goes from the entrance of the mall to the food court. The floor plan is shown below. What would be an equation Felix could use if wanted to find the distance, x, between the food court and the sports store? Select all that apply.
Answer:
The equation is tan(25.4°) = x/1,600, so
x = 1,600 tan(25.4°) = about 759.74 feet
I need help on this question?
The vector components and direction of the river and motorboat are;
(a) 12·i
(b) 12·i + 12·√3·j
(c) 24·i + 12·√3·j
(d) 31.7 mi/h
The direction of the motorboat is N 49.1° EWhat is a vector?A vector is a quantity or measurement that indicates a magnitude and a direction of the measurement.
The direction the river flows = East
The speed of the river = 12 mi/h
The direction the boater heads = 60° from the shore
Speed of the motor boar = 24 mi/h
The unit vector in the east direction = i
Unit vector in the north direction = j
(a) The velocity of the river, which is 12 mi/h east expressed in vector form is therefore;
12·i(b) The velocity of the motorboat relative to the river, in vector component form is therefore;
Component of the velocity in the east direction = 24 × cos(60°)·i = 12·i
Component in the north direction = 24 × sin(60°)·j = 12·√3·j
The component form of the velocity of the boat is therefore;
[tex]\vec{v}[/tex] = 12·i + 12·√3·j(c) The true velocity of the boat is the vector sum of the velocity of the river and the velocity of the boat, therefore;
True velocity of the boat = 12·i + 12·i + 12·√3·j = 24·i + 12·√3·j
True velocity of the boat = 24·i + 12·√3·j(d) The true speed is the magnitude of the velocity of the boat which can be found ads follows;
[tex]| \vec{v}|[/tex] = √(24² + (12·√3)²) ≈ 31.7The (true) direction of the motorboat, θ, can be obtained from the arctangent of the ratio of the velocity component in the northern direction to the velocity in the eastern direction as follows;
The velocity component of the motorboat in the northern direction = 12·√3
The component of the velocity in the eastern direction = 24
Therefore;
tan(θ) = 12·√3/(24)
θ = arctan(12*√3/(24)) ≈ 40.9°, which is about East 40.9° North
The direction from the north, therefore is found as follows;
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Write your answer as a two column proof.
Since opposite angles are equal, this means that GHJK is a parallelogram, because opposite sides are parallel.
Describe Parallelogram?Additionally, each pair of opposite sides of a parallelogram are congruent (of equal length), and the opposite angles of a parallelogram are also congruent (of equal measure). These properties make parallelograms useful in various fields such as engineering, architecture, and geometry.
There are different types of parallelograms, including rectangles, rhombuses, and squares, which have additional properties such as perpendicular sides, equal sides, or right angles. A rectangle is a type of parallelogram with four right angles, while a rhombus has four sides of equal length, and a square has both equal sides and right angles.
To prove that GHJK is a parallelogram, we need to show that opposite sides are parallel.
Since GK is parallel to HJ, we have:
∠LGK + ∠KHL = 180° (because GK // HJ)
But we are given that:
∠LGK = ∠LKL (given)
Therefore:
∠LKL + ∠KHL = 180°
This means that ∠KHL is a supplementary angle to ∠LKL.
Similarly, we can show that ∠KJH is a supplementary angle to ∠JKL:
∠JKL + ∠KJL = 180° (because GK // HJ)
But we are given that:
∠LGK = ∠LKL
Therefore:
∠LGK + ∠KJL = 180°
This means that ∠KJL is a supplementary angle to ∠LGK.
Now, we can use the fact that the opposite angles of a parallelogram are equal to show that GHJK is a parallelogram:
∠LKL = ∠JKL (alternate interior angles)
∠KHL = ∠KJH (alternate interior angles)
Since opposite angles are equal, this means that GHJK is a parallelogram, because opposite sides are parallel.
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You have the following data set: 10, 14, 12, 16, 13, 14, 16, 10, 12, and 10. For the given data set, which values would be included on the relative frequency for a value of 10?
The relative frequency οf value οf 10 is 0.3.
What is relative frequency?The relative frequency is calculated as the prοduct οf the number οf times a given value οf the data appears in the set οf all οutcοmes divided by the tοtal number οf οutcοmes.
Here the given data set is 10, 14, 12, 16, 13, 14, 16, 10, 12, and 10.
Fοr value οf 10, the number οf times 10 οccured is 3 and tοtal number οf data set is 10.
Relative frequency,
=> Number οf times οf value οf 10/ Tοtal number οf data set
=> 3/10
=> 0.3.
Hence the relative frequency οf value οf 10 is 0.3.
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Answer:
Step-by-step explanation:
new grill costs $550 discount = 15% off what is the final bill?
Suppose the demand and supply of tea are modeled by the two following functions:
Q = 34P + 53
Q = -25P + 177
What is the equilibrium price of tea? Round your answer to two places after the decimal point (0.01).
Answering the question, we may state that So the equilibrium price of equation tea is $2.10 per unit.
What is equation?A mathematical equation is a process that links two statements and indicates equality using the equals sign (=). A mathematical statement that proves the equality of two mathematical expressions is known as an equation in algebra. For instance, the equal sign separates the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula may be used to understand the link between the two sentences that are written on opposite sides of a letter. Frequently, the logo and the particular software are identical. like in 2x - 4 = 2, for example.
To find the equilibrium price of tea, we need to set the quantity demanded equal to the quantity supplied:
[tex]34P + 53 = -25P + 177\\59P + 53 = 177\\59P = 124\\P = 2.10[/tex]
So the equilibrium price of tea is $2.10 per unit.
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Roberto bought a $340,000 house, paying 20% down, and financing the rest at 5% interest for 30 years. Her
monthly payments are $1460.15. How much will he really pay for her $340,000 house?
Roberto will pay a total of $
for the house.
Answer:
Therefore, Roberto will pay a total of $593,654 for his $340,000 house, including $253,654 in interest over the 30-year period.
Step-by-step explanation:
Roberto paid 20% down on a $340,000 house, which is 0.20 x $340,000 = $68,000.
So, the amount he financed is $340,000 - $68,000 = $272,000.
Roberto financed the $272,000 at 5% interest for 30 years, making monthly payments of $1460.15.
To find the total amount he will pay for the house, we need to calculate the total amount he will pay over the 30-year period.
First, we can calculate the total number of payments he will make over the 30 years by multiplying the number of years by the number of payments per year:
30 years x 12 months/year = 360 payments
The total amount Roberto will pay is the sum of all the monthly payments he makes over the 30 years:
Total amount = 360 x $1460.15 = $525,654
However, this includes both the principal amount of $272,000 and the interest he will pay over the 30 years. To find out how much he will pay in interest, we can subtract the principal from the total amount:
Total interest = $525,654 - $272,000 = $253,654
Therefore, Roberto will pay a total of $593,654 for his $340,000 house, including $253,654 in interest over the 30-year period.
In the coordinate plane, the points....
Answer:
A'(4,-3) B'(6,11) C'(-7,-2)
Step-by-step explanation:
X-axis is (x,y) --> (x,-y)
A(4,3) --> (4,-3)
B(6,-11) --> (6,11)
C(-7,2) --> (-7,-2)
♡♡♡
PLEASE HELP ME!!! ASAP.
Enter your answer and show all the steps that you used to solve this problem in the space provided.
(Click imagine for the table)
X. 3, 9, 13, 20.
Y. 9, 27, 39, 60
State weather the relationship between the variables in the table is a direct variation, an inverse variation, or neither.
if it direct, write a function and model it.
The relationship between the variables in the table is a direct variation.
A function that models the relationship is y = 3x.
What is a direct variation?In Mathematics, a direct variation is also referred to as direct proportion and it can be modeled by using the following mathematical expression or function:
y = kx
Where:
y and x are the variables.k represents the constant of proportionality.Under direct variation, the value of x represent an independent variable while the value of y represents the dependent variable. Therefore, the constant of proportionality (variation) can be calculated as follows:
Constant of proportionality (k) = y/x
Constant of proportionality (k) = 9/3 = 27/9 = 39/13 = 60/20
Constant of proportionality (k) = 3.
Therefore, the required function is given by;
y = kx
y = 3x
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A package of pencils has 10 pencils and costs $2. A package of markers has 8 markers and costs $4.
Kelsey bought 40 pencils and 24 markers.
Which statements are true? Select all that apply.
The statements that are true are: Option c) Kelsey spent more on the pencils than she spent on the markers.
Option e) Kelsey spent $24 in all.
The problem provides us with some information about the cost and quantity of packages of pencils and markers, as well as the quantities of pencils and markers that Kelsey bought. We need to use this information to determine which statements are true.
We know that a package of pencils has 10 pencils and costs $2, and a package of markers has 8 markers and costs $4.
Kelsey bought 40 pencils and 24 markers. We can use this information to determine the number of packages of each item that Kelsey bought:
Pencils: Kelsey bought 40 pencils, and each package has 10 pencils, so she must have bought 4 packages of pencils.
Markers: Kelsey bought 24 markers, and each package has 8 markers, so she must have bought 3 packages of markers.
Now we can use this information to evaluate the statements:
a) Kelsey bought 4 packages and 3 packages of markers - This statement is false. Kelsey actually bought 4 packages of pencils and 3 packages of markers.
b) Kelsey spent $4 in pencils - This statement is false. Kelsey bought 4 packages of pencils, and each package costs $2, so she spent a total of $8 on pencils.
c) Kelsey spent more on the pencils than she spent on the markers - This statement is true. Kelsey bought 4 packages of pencils, which cost a total of $8, and 3 packages of markers, which cost a total of $12. Therefore, she spent more on markers than on pencils.
d) Kelsey spent $20 dollars in all - This statement is false. Kelsey spent $8 on pencils and $12 on markers, so she spent a total of $20.
e) Kelsey spent $24 in all - This statement is true. Kelsey spent $8 on pencils (4 packages x $2 per package) and $12 on markers (3 packages x $4 per package), so she spent a total of $20.
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if you borrow $2,500 when you open up account the loan was for 2 years and the amount of the loan interest was $155 what were you charge when you open up the account for the loan
Answer:
the charge for opening up the account was $155.
Step-by-step explanation:
To find the charge for opening up the account, we need to subtract the interest from the total amount borrowed.
The total amount repaid at the end of the loan period is the sum of the amount borrowed and the interest charged. In this case, the total amount repaid is:
$2,500 + $155 = $2,655
The interest charged on the loan is the difference between the total amount repaid and the amount borrowed. Therefore, the amount charged for opening up the account is:
$2,655 - $2,500 = $155
So the charge for opening up the account was $155.
Find the missing angle measures (just write the number and not the word or symbol for degrees):
Angle a
The values of angles A , B, C are 140 , 40 , 140 respectively if other angle
is 40 degrees.
What are parallel lines ?
Parallel lines can be defined as lines which are equidistant from each other and which never intersect .
from the given figure ,
the angle b and 40 degrees are vertically opposite angles ,
vertically opposite angles are always equal
so,
b = 40
and sum of angles A and 40 is 180 degrees
so,
A + 40 = 180
A = 180 - 40
A = 140
And here similarly ,
angles A and C are vertically opposite angles ,
so,
C = 140 degrees.
Therefore, The values of angles A , B, C are 140 , 40 , 140 respectively if other angle is 40 degrees.
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An economy consists of coal, electric, and steel industries. For each $1.00 of output, the coal industry needs $0.01 worth of coal, $0.10 worth of electricity, $0.10 and worth of steel; the electric industry needs $0.03 worth of coal, $0.03 worth of electricity, and $0.04 worth of steel; and the steel industry needs $0.20 worth of coal and $0.01 worth of steel. The sales demand is estimated to be $4 billion for coal, $3 billion for electricity, and $3 billion for steel. Suppose that the demand for electricity triples and the demand for coal doubles, whereas the demand for steel increases by only 50%. At what levels should the various industries produce in order to satisfy the new demand?
The steel industry should use 1.7 billion dollars worth of coal and 0.035 billion dollars worth of steel.
What is amount?Amount is a term used to refer to the total of a certain quantity or sum. It is often used to describe the value of something, such as a financial transaction, or the size of a collection of objects. Amounts are usually expressed in units of measurement such as dollars, kilograms, or liters. Amounts can also be expressed as a percentage or fraction.
The coal industry should produce 8 billion dollars worth of output, the electric industry should produce 9 billion dollars worth of output, and the steel industry should produce 3.5 billion dollars worth of output. The coal industry should use 0.08 billion dollars worth of coal, 0.8 billion dollars worth of electricity, and 0.8 billion dollars worth of steel. The electric industry should use 0.06 billion dollars worth of coal, 0.9 billion dollars worth of electricity, and 1.2 billion dollars worth of steel. The steel industry should use 1.7 billion dollars worth of coal and 0.035 billion dollars worth of steel.
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need help with This Math
The value of XS in the perpendicular lines is 16 units.
How to find length of line segment?The line VU is perpendicular to the line XS. Perpendicular lines are defined as two lines that meet or intersect each other at right angles.
Therefore, perpendicular bisector is a line that divides a given line segment exactly into two halves forming 90 degrees angle at the intersection point.
Hence,
b + 5 = 3b - 1
b - 3b = -1 - 5
-2b = -6
divide both sides by -2
b = -6 / -2
b = 3
Therefore, let's find XS as follows:
XS = b + 5 + 3b - 1
XS = 4b + 4
XS = 4(3) + 4
XS = 12 + 4
XS = 16 units
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At a market, 3.1 pounds of peaches cost $7.75.
How much did the peaches cost per pound?
The peaches cost $2.50 per pound.
Define the term Conversion rate?Conversion rate is the percentage of website visitors or potential customers who take a desired action, such as making a purchase, signing up for a newsletter, or filling out a form. In other words, it is the rate at which website visitors are converted into customers or subscribers.
To find the cost per pound of peaches, we need to divide the total cost by the weight in pounds.
Cost of 3.1 pounds of peaches = $7.75
Cost of 1 pound of peaches = $7.75 / 3.1
Cost of 1 pound of peaches = $2.50 (rounded to the nearest cent)
Therefore, the peaches cost $2.50 per pound.
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HELP ASAP PLEASE! A small box in the shape of a cube for packaging has a volume of 216 cubic inches.
For a medium box, the length, width, and height are all tripled. What is the ratio of the sides, area of the bases, and volumes of the boxes? Show your work.
What is the volume of a medium box? Show your work.
The ratio of the sides of the small box and the medium box is 1:3
The ratio of the area of the bases of the small box and the medium box is 1:9.
The ratio of the volumes of the small box and the medium box is 1:27.
The volume of a medium box is 5832 cubic inches.
What is a cube?
The solid shape of a cube has six square faces. Because every square face has the same side length, each face is the same size. A cube has 8 vertices and 12 edges. Each vertex is the intersection of three cube edges.
Given that a cube-shaped small packaging box has a volume of 216 cubic inches.
Assume the length of sides is a.
The volume of a cube is side³.
The volume of the small box is a³.
Thus,
a³ = 216
a³ = 6³
a = 6
The length of the small box is 6.
The area of the base of small box is 6×6 = 36 square inches.
The dimensions of a medium box are tripled in length, width, and height.
Thus the length of the medium box is 3×6 = 18 inches.
The area of the base of the medium box is 18×18 = 324 square inches.
The volume of cube medium box is 18×18×18 = 5832 cubic inches.
The ratio of the sides of small box and medium box is
6:18 = 1:3
The ratio of the area of bases of small box and the medium box is
36:324 = 1:9
The ratio of the volumes of small box and the medium box is
216:5834 = 1:27
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How does this quote illustrate some of what Elie learned from Moishe the Beadle?
Moishe taught him the real answers lie in oneself. Elie sees the death of the boy as the death of the God within.
Moishe taught him that it was God's anger that resulted in the death of men. The boy represents God's wrath.
Moishe believed that God always had a plan. Hanging the boy must be part of his divine plan, which no man could understand.
Moishe taught that God required sacrifice. Elie believes the boy to be a sacrifice to God.
Answer:
The quote "Elie sees the death of the boy as the death of the God within" illustrates that Elie has learned from Moishe the Beadle that one's spirituality and relationship with God is a personal experience that resides within oneself. Moishe's teachings suggest that God is not necessarily an external force that determines the fate of individuals or the world, but rather a presence within oneself that must be nurtured and maintained. Elie's interpretation of the boy's death as the death of God within himself shows that he has internalized this lesson and is searching for meaning and understanding within his own experiences. This reflects Moishe's teachings that the "real answers lie in oneself," rather than in external sources of authority or dogma.
Step-by-step explanation:
Angelica received a 12-year non-subsidized student loan of $13,000 at an annual interest rate of 5.2% (compounded monthly). She will begin repaying the loan after she graduates in 4 years. How much interest must she pay on the loan during the period of time that payments on the loan are not being made? (Round your answer to the nearest cent.) $ Determine her monthly payment on the loan. (Round your answer to the nearest cent.)
a) The total interest that Angelica must pay on the loan during the period that payments are not being made is $2,998.58.
b) Angelica's monthly payment on the loan is $204.07.
How are the total interest and monthly payment determined?The total interest when there were no repayments is determined using an online finance calculator.
The same calculator is used to determine the monthly payments after her graduation.
The total interest and the monthly payments are computed based on monthly compounding interest.
The amount of the non-subsidized student loan = $13,000
Annual compound interest rate = 5.2%
Loan period = 12 years
Non-repayment period = 4 years
Interest during the 4-year Non-Repayment Period:N (# of periods) = 48 months (4 years x 12)
I/Y (Interest per year) = 5.2%
PV (Present Value) = $13,000
PMT (Periodic Payment) = $-0
Results:
FV = $-15,998.58
Total Interest = $2,998.58
Monthly Payments:N (# of periods) = 96 months (8 years x 12)
I/Y (Interest per year) = 5.2%
PV (Present Value) = $15,998.58
FV (Future Value) = $0
Results:
Monthly Payments (PMT) = $-204.07
Sum of all periodic payments = $-19,590.49
Total Interest = $3,591.91
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Enter the volume, in cubic feet of the cone. Round your answer to the nearest hundredth.
HELP!
Answer: 565.49ft^3/ 565.49ft cubed
Hopefully it is correct!
List the first 5 elements of set A
The first 5 elements of set A are: {-1, -2, 1, -3, 2}.
What is the set of elements?
The objects in a set are called the elements (or members ) of the set; the elements are said to belong to the set (or to be in the set), and the set is said to contain the elements. Usually, the elements of a set are other mathematical objects, such as numbers, variables, or geometric points.
Set A is defined as:
A = {x | x = k(-1)ⁿ where k ∈ Z* and n ∈ N}
To find the first 5 elements of A, we can substitute different values of k and n:
For k = 1 and n = 1, x = 1(-1)¹ = -1
For k = 2 and n = 1, x = 2(-1)¹ = -2
For k = 1 and n = 2, x = 1(-1)² = 1
For k = 3 and n = 1, x = 3(-1)¹ = -3
For k = 2 and n = 2, x = 2(-1)² = 2
Therefore, the first 5 elements of set A are: {-1, -2, 1, -3, 2}.
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The construction below shows two possible triangles that can be formed when
4B - 3 inches and BC = 1.5 inches. Describe what happens to the length of AC
as point C moves counterclockwise around the circle toward point A.
The length would decrease at first to AB - BC then it would increase to the maximum of B + BC
What would happen when the point C moves counterclockwise around the circle toward point A.From the diagram we have that two triangles are formed when we have AB = 3 cm and when we have BC = 1.5cm
This would happen when at point AC we have C moving in a counterclockwise direction around A
As AC goes towards A, then we would have AC decrease at first to AB - BC. Then it would increase. The maximum length would be AB + BC
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Answer:
It decreases
Step-by-step explanation:
The rectangle shown has a perimeter of 180 cm and the given area. Its length is 5 more than four times its width. Write and solve a system of equations to find the dimesions of the rectangle.
The dimensions of the rectangle are, length = 73 cm and width = 17 cm.
What do system of equations depict?Finding the values of the variables employed in a system of equations entails solving the set of equations. By keeping the equations balanced on both sides, we compute the values of the unknown variables. Finding the value of the variable that makes the condition of all the provided equations true is the primary goal when solving an equation system. A given system of equations may have a variety of solutions.
Let us suppose the width of the rectangle = w.
Given that, length is 5 more than four times its width.
Thus,
l = 5 + 4w
Now, the perimeter of the rectangle is given as:
P = 2(l + w)
Substitute the value of P = 180:
180 = 2l + 2w
The system of equations is:
l = 5 + 4w
180 = 2l + 2w
Substitute the value of l from equation 1 into equation 2:
180 = 2(5 + 4w) + 2w
180 = 10 + 8w + 2w
180 - 10 = 10w
170 = 10w
w = 17
Substitute the value of w = 17 in the first equation:
l = 5 + 4w
l = 5 + 4(17)
l = 73
Hence, the dimensions of the rectangle are, length = 73 cm and width = 17 cm.
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if n square- 1 over m is equal to 4
Express n in terms of m
find n when m is 12
Answer:
n=√(4m+1) , 7
Step-by-step explanation:
According to statement
( n²-1 )÷m=4
∴n²-1=4m
⇒n²=4m+1
⇒n=√(4m+1)… … … … 1
If m=12
put the value of m in 1 equation
n=√(4×12+1)
=√49=7
Determine whether the ordered pair is a solution to the system.
x + 4y > 10
3x - 2y < 12
a. (-2, 4) b. (3,1)
Answer:
a. (-2, 4) only
==================================================
Explanation:
Let's check point A.
We have x = -2 and y = 4 pair up together.
Plug these coordinates into the first inequality.
x + 4y > 10
-2 + 4*4 > 10
-2 + 16 > 10
14 > 10
We get a true statement, so (-2,4) is in the shaded solution region of the inequality x+4y > 10.
Repeat for the other inequality.
3x - 2y < 12
3*(-2) - 2*4 < 12
-6 - 8 < 12
-14 < 12
This is also true.
The point (-2,4) is also in the shaded solution region for 3x-2y < 12
Since it's in both regions simultaneously, it satisfies the system of inequalities.
Therefore, (-2,4) is a solution to the system.
See the diagram below. Point A is in the shaded region.
-------------------------------
Now we need to check point B.
We have x = 3 and y = 1. Let's plug those into the 1st inequality.
x + 4y > 10
3 + 4*1 > 10
3 + 4 > 10
7 > 10
That final statement is false, so (3,1) is not in the shaded region for x+4y > 10. We don't need to check the other region since this point needs to satisfy both inequalities to be considered a solution overall.
See the diagram below. Point B is outside the shaded region.
5 questions 15 points please help with these math questions
From the given scatter plot, point L is an outlier. The association is negative linear association. The line is not the best fit accurate. Graph shows a negative linear association. As the number of weeks increases, the number of tickets sold decreases
What is scatter plot?
A scatter plot is a type of data visualization that displays the relationship between two numerical variables. It is a graph with points plotted on it that represent the values of two different variables.
1. In a scatter plot, an outlier is a data point that lies far away from the other data points in the plot, and is not in line with the overall pattern or trend that the other data points display.
2. The scatter plot for this data is likely to show a negative linear association between the number of people in a group and the zoo ticket price per person. As the number of people in a group increases, the zoo ticket price per person decreases.
The rate of change of Zoo Ticket Price with respect to the the number of persons:
[tex]m=14.50-1500/2-1=-0.5[/tex]
3. No because the line should touch every point. When we draw a line passing through the origin, it passes through the data points (2,3), (4,3), and (4,5), but it does not pass through the other data points (6,5), (6,6), and (8,7).
This indicates that the line of best fit may not accurately represent the overall trend of the data.
4. The given data points are (1,5), (2,4), (3,3), (4,2), (5,1), and (6,0). When we plot these points on a graph with x-axis representing variable x and y-axis representing variable y, we get a downward sloping straight line passing through all the points.
This pattern suggests a negative linear association between the variables x and y. As the value of x increases, the value of y decreases at a constant rate.
Therefore, the graph shows a negative linear association between x and y.
5. The answer is option (a) "As the number of weeks increases, the number of tickets sold decreases".
As per the given data points and the line passing through (1,100) and (6,35), we can observe that the number of tickets sold decreases as the number of weeks a movie has been in theaters increases. Therefore, the statement "As the number of weeks increases, the number of tickets sold decreases" best describes the relationship between the number of weeks a movie has been in theaters and the number of tickets sold.
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I need help with this please
Answer:
First statement is true.
Second statement is false--there are some 3d shapes that unit cubes cannot be used to find the volume of. Examples are cylinders and cones.
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The answer of this question is in every 5 hour 6 m water height increase in tank. So we have to learn about proportional.
What is Proportional?Proportional is the right amount, size , degree or quantity compared with something else. We can simply say that it is comparison between one object or thing with another object or thing.
Their are two types of proportional properties:
a. Directly Proportional, In this when amount , size or degree of any object increases than the amount ,size, or degree of another object are also increases with same ratio.
b. Indirectly Proportional, In this when amount , size or degree of any object increases than the amount , size or degree of another object is decreases in same ratio.
Let Solve this question, in this the first property used.
[tex]\frac{1}{4} = \frac{3}{10} , we\ get\ 5 = 6[/tex]
[tex]\frac{1}{2} = \frac{3}{5}\ we\ get\ 5 = 6[/tex]
[tex]\frac{3}{4} =\frac{9}{10} \ we\ get\ 5 =6[/tex]
So, In every 5 hour 6 m water height increase in tank.
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Evaluate the integral below
Answer:
Step-by-step explanation:
The value of the integral is 6.
Describe Integration?Integration is a mathematical operation that involves finding the integral of a function. The integral of a function is a measure of the area under the curve of the function in a given interval. The process of integration is the opposite of differentiation, and it involves finding a function whose derivative is the given function.
Integration is an important tool in many areas of mathematics, science, and engineering. It can be used to calculate quantities such as velocity, acceleration, displacement, and area, among others. It also has applications in fields such as physics, economics, and statistics.
There are different methods of integration, including substitution, integration by parts, partial fractions, and trigonometric substitution. The choice of method depends on the form of the function being integrated and the desired outcome.
We can use integration by parts to evaluate this integral:
Let u = x and dv = g'(x) dx, then du/dx = 1 and v = g(x).
Using the formula for integration by parts:
[tex]\int\limits^5_1[/tex] xg'(x) dx = [xg(x)]₁⁵ - [tex]\int\limits^5_1[/tex] g(x) dx
We can use the given information to find the value of each term in this expression:
[xg(x)]₁⁵ = 5g(5) - 1g(1) = 5(1) - 1(5) = 0
[tex]\int\limits^5_1[/tex] g(x) dx = -6 (given)
Substituting these values into the integration by parts formula, we get:
[tex]\int\limits^5_1[/tex] xg'(x) dx = 0 - (-6) = 6
Therefore, the value of the integral is 6.
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Suppose that the number of bacteria in a certain population increases according to a continuous exponential growth model. A sample of 1800 bacteria selected from this population reached the size of 2204 bacteria in five hours. Find the hourly growth rate parameter.
Note: This is a continuous exponential growth model.
Write your answer as a percentage. Do not round any intermediate computations, and round your percentage to the nearest hundredth.
The exponential growth of bacteria gives the growth percentage to be 4.05%.
What is an exponential function?
The formula for an exponential function is [tex]f(x) = a^x[/tex], where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.
Let N(t) be the number of bacteria in the population at time t.
According to the continuous exponential growth model, we have -
[tex]N(t) = N0 \times e^{(rt)}[/tex]
where N0 is the initial number of bacteria, r is the hourly growth rate parameter, and t is the time elapsed in hours.
We know that a sample of 1800 bacteria reached the size of 2204 bacteria in five hours, so we can use this information to find the hourly growth rate parameter.
First, we can set up a ratio of the final size to the initial size -
[tex]\frac{2204}{1800} = e^{5r}[/tex]
Simplifying, we get -
[tex]e^{5r} = 1.2244[/tex]
Taking the natural logarithm of both sides, we get -
5r = ln(1.2244)
Solving for r, we get -
r = ln(1.2244) / 5
On further simplifying, we get -
r = 0.20245 / 5
r ≈ 0.04049
To express the growth rate as a percentage, we can multiply by 100 -
r percentage = 100 × r ≈ 4.049
Rounding to the nearest hundredth, we get -
r percentage ≈ 4.05%
Therefore, the hourly growth rate parameter is approximately 4.05%.
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Find the area of this composite shape. 10 cm, 5 cm, 8 cm, and 4 cm.