Find the horizontal and vertical components for a vector round to the nearest tenth
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as follows:
The horizontal component of a vector having:
[tex]\text{ a magnitude of v and a direction of }\theta\text{ = v cos }\theta[/tex]The vertical component of a vector having:
[tex]a\text{ magnitude of v and direction of }\theta\text{ = v sin}\theta[/tex]
Then, with the information above, the horizontal component of a vector having a magnitude of 15 and a direction of 210 degrees:
[tex]\begin{gathered} \text{Horizontal component = 15 x cos 210}^{\text{ 0}}=\text{ 15 x -0.8860 = -12.99}\approx\text{ -13.0 } \\ \text{Taking the absolute value, we have } \\ \text{Horizontal component = 13.0 units ( to the nearest tenth)} \end{gathered}[/tex]The vertical component of a vector having a magnitude of 15 and a direction of 210 degrees:
[tex]\begin{gathered} vertical\text{ component = 15 x sin 210}^{\text{ 0}}=\text{ 15 x -0.5 = -7.5 } \\ \text{Taking the absolute value, we have } \\ Vertical\text{component = 7.5 units ( to the nearest tenth)} \\ \\ \text{Hence the horizontal and vertical component of the vector =} \\ (\text{ 13. 0 , 7. 5 ) ( to the nearest tenth)} \end{gathered}[/tex]Braden owns a painting that is valued at $27,400. If the value of the artwork increases by 5% every year, how much will it be worth in 3 years?If necessary, round your answer to the nearest cent.
We know that the painting increase its value by 5% each year.
So, if P(1) is the value the next year and P(0) is the actual value ($27,400) we can write:
[tex]P(1)_{}=P(0)+0.05P(0)=1.05\cdot P(0)[/tex]In the same way, the following year, it will increase another 5% over its value:
[tex]P(2)=1.05P(1)=1.05(1.05\cdot P(0))=1.05^2\cdot P(0)=1.05^2\cdot27,400[/tex]We can generalize this as:
[tex]P(n)=27,400\cdot1.05^n[/tex]For n=3 (3 years) we will have a value of:
[tex]P(3)=27,400\cdot1.05^3\approx27,400\cdot1.1576\approx31,718.93[/tex]Answer: the value of the painting in 3 years is expected to be $31,718.93.
2. Mr. Cole took a walk with his wife. They walked 4.4 miles in 1.4 hours. What was their average speed inmiles per hour?
Mr. Cole took a walk with his wife.
They walked 4.4 miles in 1.4 hours.
So we have
Distance = 4.4 miles
Time = 1.4 hours
We are asked to find the average speed in miles per hour.
The average speed is given by
[tex]S=\frac{D}{t}[/tex]Where D is the distance and t is the time.
[tex]S=\frac{4.4}{1.4}=3.142[/tex]Therefore, their average speed is 3.142 miles per hour.
A cone with radius 6 feet and height 15 feet is shown.6ftEnter the volume, in cubic feet, of the cone. Round youranswer to the nearest hundredth.
EXPLANATION:
Given;
We are given a cone with the following dimensions;
[tex]\begin{gathered} Dimensions: \\ Radius=6ft \\ Height=15ft \end{gathered}[/tex]Required;
We are required to calculate the volume of the cone with the given dimensions.
Step-by-step solution;
To solve this problem, we would take note of the formula of the volume of a cone;
[tex]\begin{gathered} Volume\text{ }of\text{ }a\text{ }cone: \\ Vol=\frac{\pi r^2h}{3} \end{gathered}[/tex]We can now substitute and we'll have;
[tex]Vol=\frac{3.14\times6^2\times15}{3}[/tex][tex]Vol=3.14\times36\times5[/tex][tex]Vol=565.2[/tex]Therefore, the volume of the cone is,
ANSWER:
[tex]Volume=565.2ft^3[/tex]The picture below shows a pole and its shadow:
What is the height of the pole?
121 centimeters
220 centimeters
225 centimeters
231 centimeters
The height of the pole according to the attached image and parameters given is; 220 cm.
What is the height of the pole as required in the task content?It follows from the task content that the height of the pole is to be determined from the parameters given.
From observation, the triangle formed by the situation is a right triangle.
Hence, the height of the pole can be determined by Pythagoras theorem; where, c² = a² + b².
Therefore, we have;
221² = 21² + p²
p² = 48,841 - 21²
p² = 48,400
p = √48,400
p = 220.
On this note, the height of the pole is; 220 cm.
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A creative writing class compiled a list of their favorite superheroes. They listed each superhero's superpower and personality flaw. Fly Read minds Forgetful 6 11 Lazy 5 7 What is the probability that a randomly selected superhero is forgetful and can fly? Simplify any fractions.
The probability is given the following formula:
Probability = Favorable / total outcomes
In this case, there number of students that selected a forgetfull sperheroe that can fly is 6, the total number of outcomes is 6 + 11 + 5 + 7 = 29, then we get:
Probability = 6 / 29
Then, the probability of selecting a forgetful superheroe that can fly is 6/29
Exercise 1: What's In2.Mark’s temperature goes 1.5°C higher from the normal body temperature. What is Marks temperature now?A. 38.5°CB. 37.5°CC. 36.5°CD. 36.5C
The normal body temperature of a human is 37°C.
If Mark's temperature goes 1.5°C higher than that temperature, his new temperature will be:
[tex]\Rightarrow37+1.5=38.5°C[/tex]OPTION A is the correct option.
The first three terms of a sequence are given. Round to the nearest thousandth (if necessary). 6 36 1, 5' 25 . Find the 10th term
The first three terms of a sequence are given. Round to the nearest thousandth (if necessary)
1, 6/5, 36/25, Find the 10th term
__________________________________________________________________
1, 6/5, 36/25
(6/5)^(n-1)
n= 1
(6/5)^(1-1) = (6/5)^0 = 1
n= 2
(6/5)^(2-1) = (6/5)^1 = 6/5
n= 3
(6/5)^(3-1) = (6/5)^2 = 36/25
_______________________
n= 10
(6/5)^(10-1) = (6/5)^9 = 5. 1598
_______________________
Answer
Round to the nearest thousandth
The 10th term is 5.160
1. Mother bought 13.5 kg of sugar and then she repacked the sugar in several bags. If she put 1.5 kg in each bag, how many bags of sugar did she have? only numbers
The data for the production of number of components at an industry for three weeks are given below. Make a stem-and-leaf plot68, 91, 42, 85, 13, 96, 15, 46, 95, 46, 64, 18, 44, 83, 69
In a stem and leaf plot, the first digit is always the stem, while the other digits are the leaves.
For the data represented:
The stem = the first digit
The leaf = the second digit
In the plot:
13, 15, and 18 will be grouped together because they have the same stem (1)
42, 44, 46, 46 are grouped together because they have the same stem (4)
64, 68, 69 are grouped together because they have the same stem (6)
83, 85 are grouped together because they have the same stem (8)
91, 95 and 96 are grouped together because they have the same stem (9)
The stem-and-leaf plot is shown below:
Find the value of b if it is known that the graph of y=-3x+b goes through the point_
M(-2, 4)
Answer:
b = -2
Step-by-step explanation:
y = mx + b; (-2, 4)
y = -3x + b (x₁, y₁)
m = -3
y - y₁ = m(x - x₁)
y - 4 = -3(x -( -2))
y - 4 = -3(x + 2)
y - 4 = -3x - 6
+4 +4
------------------------
y = -3x - 2
I hope this helps!
The length that a hanging spring stretches varies directly with the weight placed at the end of the spring. If a weight of 8lb stretches a certain spring 9in., how far will the spring stretch if the weight is increased to 37lb? (Leave the variation constant in fraction form. Round off your final answer to the nearest in.)
ANSWER
L = 42in
EXPLANATION
Identify the explicit formula for the sequence given by the following recursive formula: A) f(n) = –2 + 4(n – 1)B) f(n) = –4 + 2(n – 1)C) f(n) = 4 – 2(n – 1)D) f(n) = 2 – 4(n – 1)
Given the recurssive formula;
[tex]f(n)=\begin{cases}f(1)=-2 \\ f(n)=f(n-1)+4\text{ if n>1}\end{cases}[/tex]Let's find the sequence using the recurssive formula, we have;
[tex]\begin{gathered} f(2)=f(2-1)+4 \\ f(2)=f(1)+4 \\ f(2)=-2+4 \\ f(2)=2 \\ f(3)=f(3-1)+4 \\ f(3)=f(2)+4 \\ f(3)=2+4 \\ f(3)=6 \\ f(4)=f(4-1)+4 \\ f(4)=f(3)+4 \\ f(4)=6+4 \\ f(4)=10 \end{gathered}[/tex]Thus, we have the sequence as;
[tex]-2,2,6,10,\ldots[/tex]We observed that the sequence is an arithmetic sequence with a common difference of 4 and first term of -2.
So, the recursive formula is;
[tex]\begin{gathered} f(n)=f(1)+d(n-1)_{} \\ f(n)=-2+4(n-1) \\ f(n)=-2+4n-4_{} \\ f(n)=4n-6 \end{gathered}[/tex]CORRECT OPTION: A
converting to slope intercept formmatch each equation to an equivalent equation written in slope intercept form.
Statement Problem: Match each equation to an equivalent equation written in slope-intercept form.
Solution:
A slope intercept form equation is written as;
[tex]y=mx+b[/tex](a)
[tex]2y-6=x[/tex]Add 6 to both sides of the equation;
[tex]\begin{gathered} 2y-6+6=x+6 \\ 2y=x+6 \end{gathered}[/tex]Divide each term by 2;
[tex]\begin{gathered} \frac{2y}{2}=\frac{x}{2}+\frac{6}{2} \\ y=(\frac{1}{2})x+3 \end{gathered}[/tex](b)
[tex]undefined[/tex]Which statements are true about the result of simplifying this polynomial?
To answer the question, we must simplify the following expression:
[tex]t^3(8+9t)-(t^2+4)(t^2-3t)[/tex]We expand the terms in the polynomial using the distributive property for the multiplication:
[tex]8t^3+9t^4-(t^4-3t^3+4t^2-12t)[/tex]Simplifying the last expression we have:
[tex]^{}^{}8t^4+11t^3-4t^2+12t[/tex]We see that the simplified expression:
• is quartic,
,• doesn't have a constant term,
,• has four terms,
,• is a polynomial,
,• it is not a trinomial.
Answer
The correct answers are:
• The simplified expression has four terms.
,• The simplified expression is a polynomial.
I am an even number.
I have three digits and they are all the same.
If you multiply me by 4, all of the digits in the product are 8.
What number am l?
Answer:
Step-by-step explanation:
The number is 2.
222x4=888
Hence, the number am I is [tex]888[/tex].
What is the even number?
A number that is divisible by [tex]2[/tex] and generates a remainder of [tex]0[/tex] is called an even number.
Here given that,
I am an even number. I have three digits and they are all the same.
If you multiply me by [tex]4[/tex], all of the digits in the product are [tex]8[/tex].
The number is [tex]2[/tex] sp ot would be
[tex]222[/tex]x[tex]4=888[/tex]
Hence, the number am I is [tex]888[/tex].
To kknow more about the even number
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Problem: A school has a student to teacher ratio of25:5. If there are 155 teachers at the school, howmany students are there?Mike's AnswerCarlos's Answer25 .5 1551552555x = 3875x=77525x = 775x=31There are 31 students at the school.There are 775 students at the scheel.Who is correct? Mike or Carlos? Explain the error thatwas made.
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
ratio = 25:5 (students:teachers)
teachers = 155
students = ?
Step 02:
[tex]\begin{gathered} \text{students = 155 teachers }\cdot\text{ }\frac{25\text{ students }}{5\text{ teachers}} \\ \text{students = }775\text{ } \end{gathered}[/tex]Carlos is correct.
[tex]\frac{25}{5}=\frac{x}{155}[/tex]The answer is:
There are 775 students.
Carlos is correct.
Mike set the variables to find in the wrong way.
Find the common difference of the arithmetic sequence 5,14,23
The Solution.
The given sequence is
[tex]5,14,23[/tex]The common difference of the arithmetic sequence is given by the formula below:
[tex]\text{common difference(d)=T}_2-T_1=T_3-T_2[/tex]In this case,
[tex]T_1=5,T_2=14,T_3=23[/tex]Substituting these values in the formula above, we get
[tex]\begin{gathered} \text{common difference = 14-5=23-14}=9 \\ \text{common difference}=9 \end{gathered}[/tex]So,the correct answer is 9.
Given that XY = ZY, WX = 6x-3 and WZ= 4x + 9, find ZX
In the Given Figure,
There are two right triangles, ΔWXY and ΔWZY,
So, according to Pythagoras' theorem,
XW^2 + YW^2 = XY^2
And WZ^2 + YW^2 = ZY^2
Now, Since XY = ZY, their squares are also equal
⇒XW^2 + YW^2 = WZ^2 + YW^2
⇒ XW^2 = WZ^2 ................(YW^2 is the common term on both sides)
⇒ (6x-3) ^2 = (4x + 9) ^2
⇒ 36x^2 - 36x + 9 = 16x^2 + 72x + 81
⇒36x^2 - 16x^2 - 36x + 72x = 81-9
⇒20x^2 - 108x = 72
⇒ 5x^2 - 27x = 18
⇒ 5x^2 - 27x - 18 = 0
⇒ (5x+3) (x-6) = 0
⇒ x = 6 or x = -3/5
Since, the distance cannot have a negative value,
⇒ x = 6
So, WX = 6x - 3 = 6(6) - 3 = 36-3 = 33
WZ = 4x + 9 = 4(6) + 9 = 24 + 9 = 33
ZX = WX + WZ = 33 + 33 = 66 units.
Also, since all the three sides of ΔWXY and ΔWZY are equal, ΔWXY and ΔWZY are congruent to each other.
What are Congruent Triangles?In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.Formally, two sets of points are said to be congruent if—and only if—they can be changed into one another by an isometry, which is a combination of rigid motions like translation, rotation, and reflection. This indicates that either object may be precisely aligned with the other object by moving and reflecting it, but not by resizing it. So, if we can cut out and then perfectly match up two separate plane figures on a piece of paper, they are congruent.If the matching sides and angles of two triangles are the same length, then the triangles are said to be congruent.To learn more about Congruent Triangles, refer to:
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how to calculate the amount compounded to 6 years not only one year1) $3000 deposit that earns 6% annual interest compounded quarterly for 6 years
Step 1
State the compound interest formula
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where;
[tex]\begin{gathered} A=\text{ amount} \\ P=Prin\text{cipal}=\text{\$3000} \\ r=\text{ rate= }\frac{\text{6}}{100}=0.06 \\ n=\text{ number of periods of compounding= 4} \\ t=\text{ time = 6 years} \end{gathered}[/tex]Step 2
Find the amount as required
[tex]\begin{gathered} A=3000(1+\frac{0.06}{4})^{6\times4} \\ A=3000(1+0.015)^{24} \\ A=3000(1.015)^{24} \\ A=\text{\$}4288.508436 \\ A\approx\text{ \$}4288.51 \end{gathered}[/tex]Hence the amount compounded quarterly for 6 years based on a principal of $3000 and a 6% annual interest rate = $4288.51
If the image of point J under a 180* rotation about the origin is (7, -3), what are the coordinates of point J?
Answer:
4,3 is the right answer
Step-by-step explanation:
yki10.87-2110-9--2-6-10Which system of equations is best represented by this graph?А3x – y = 240 +9y = 36B3. - y = 64x + 9y = 42- 3y = -18
System 2x2
Find slopes of k1 and k2
k1 slope = (10--2)/(4-0) = 12/4 = 3
k2 slope= (-9 -9)/ (8-0) = 8/-18 = -4/9
Now find k1, and k2 interceptions with y
k1 , interception= -2
k2 ,interception = 4
Then now, form the 2 equations
y = 3x - 2
and
y = (-4/9)x + 4
Now rewrite equations
3x - y = 2
and
9y + 4x = 36
Then now looking at options ,we find that
ANSWER IS
OPTION A)
3x - y = 2
I am going to have to send you a photo of the problem during the session because it is to large to crop here.
Direct variations have an special characteristic: they can be represented on a plane by a line paassing through the origin (0,0).
The equation of a line has the following shape:
[tex]y=mx+b[/tex]Where x is the slope, and b is the y intercept.
For direct variations, the line passes through the origin; then, the y intercept is 0, therefore b=0.
For direct variations, we can have an associated line with the following shape:
[tex]y=mx[/tex]We can find the value for m knowing 2 points of the line and calculating the slope. One point is (-1,-4); and the other is the origin (0,0).
Now we can calculate the slope by dividing y distance of the points by the x distance of the points:
[tex]m=\frac{0-(-4)}{0-(-1)}=\frac{0+4}{0+1}=\frac{4}{1}=4[/tex]We have calculated the slope to be 4, then the equation representing the direct variation is:
[tex]y=4x[/tex]Any pair of points x,y that satisfy the equation will an element of the direct variation.
Now, we can try each:
With 8,0:
[tex]\begin{gathered} 0=4\cdot8 \\ 0=16 \end{gathered}[/tex]8,0 does not satisfy, therefore it is not an element of the direct variation.
2,8:
[tex]\begin{gathered} 8=4\cdot2 \\ 8=8 \end{gathered}[/tex]2,8 is element of the dierct variation
-2,0:
[tex]\begin{gathered} 0=4\cdot(-2) \\ 0=-8 \end{gathered}[/tex]-2,0 is not part
4,-1:
[tex]\begin{gathered} -1=4\cdot4 \\ -1=16 \end{gathered}[/tex]4,-1 is not part
8,-1:
[tex]\begin{gathered} -1=4\cdot8 \\ -1=32 \end{gathered}[/tex]8,-1 is not part
-2,-8:
[tex]\begin{gathered} -8=4\cdot(-2) \\ -8=-8 \end{gathered}[/tex]-2,-8 is part.
Finally, we can say points (-4,-1), (2,8) and (-2,-8) are part of the direct variation.
im doing math and im wondering when do i switch the inequality?
Question:
Solve the following inequality:
[tex]12x+6<17[/tex]Solution:
Consider the following inequality
[tex]12x+6<17[/tex]solving for 12x, we get:
[tex]12x<17-6[/tex]this is equivalent to:
[tex]12x<11[/tex]solving for x, we get:
[tex]x<\frac{11}{12}[/tex]so that, the correct answer is:
[tex]x<\frac{11}{12}[/tex]x - 2/5 = 7 what is the value of x?write answer in simplest form.
Explanation:
x - 2/5 = 7
Collect like terms:
[tex]\begin{gathered} x\text{ = 7 + }\frac{2}{5}=\text{ }\frac{7}{1}+\frac{2}{5} \\ \text{LCM = 5} \end{gathered}[/tex][tex]\begin{gathered} x=\frac{35\text{ + 2}}{5}\text{ = }\frac{37}{5} \\ x=\text{ 7}\frac{2}{5} \end{gathered}[/tex]Riley rented folding chairs and tables for an event.• She rented a total of 56 chairs and tables.• She paid $2.25 per chair and $8.50 per table and paid a total of $176.00.Write a system of equations to model this situation.Enter your equations in the space provided. Enter only your equations.+-Х.Iyx rr fr)而
Total rented= 56 chairs and tables
Chair= $2.25 (let's consider chairs as x)
Table = $8.50 (let's consider tables as y)
Total paid= $176.00
If she rented 56 chairs and tables, then the equation for that would be:
[tex]\begin{gathered} 56=\text{ x + y } \\ 56\text{ -x= y} \end{gathered}[/tex]Then the system of equations to model this situation is:
[tex]176.00=\text{ 2.25x + 8.50\lparen56-x\rparen}[/tex]Write the standard form of the equation and the general form of the equation of the circlewith radius r and center (h.k). Then graph the circle.r= 10; (h,k) = (8,6)The standard form of the equation of this circle isThe general form of the equation of this circle is(Simplify your answer.)Graph the circle.-20 -18Click toenlargegraph
To solve this problem, we will first find the standard form of the circle equation. Given a circle of radius r and center (h,k), the standard form of the circle equation would be
[tex](x-h)^2+(y-k)^2=r^2[/tex]In our case, we have h=8 , k=6 and r=10. So the equation for the given circle would be
[tex](x-8)^2+(y-6)^2=10^2=100[/tex]The general form of the circle equation can be obtained from expanding the squares on the left side of the equality sign. Recall that
[tex](a-b)^2=a^2-2a\cdot b+b^2[/tex]So, applying this to the standard equation we get
[tex](x-8)^2=x^2-16x+64[/tex][tex](y-6)^2=y^2-12y+36[/tex]So our equation becomes
[tex]x^2-16x+64+y^2-12y+36=100[/tex]Operating on the left side, we have
[tex]x^2-16x+y^2-12y+100=100[/tex]By subtracting 100 on both sides, we get
[tex]x^2-16x+y^2-12y=0[/tex]which the general form of the equation of the given circle.
Using a graphing tool, we have that the circle's graph would be
A population of 2000 is decreasing by 4% each year. In how many years the population will be reduced in half?
the initial amount is 2000
the rate of change is 4%
t=time in years
Therefore we have the next exponential decay function
[tex]\begin{gathered} y=2000(1-0.04)^t \\ y=2000(0.96)t \end{gathered}[/tex]Half of the population is y=1000 so we need to find find the value of t
[tex]1000=2000(0.96)^t[/tex]we need to isolate the t
[tex]\frac{1000}{2000}=0.96^t[/tex][tex]\frac{1}{2}=0.96^t[/tex]Using logarithms
[tex]\begin{gathered} \ln (\frac{1}{2})=\ln (0.96^t) \\ \ln (\frac{1}{2})=t\ln (0.96^t) \end{gathered}[/tex][tex]t=\frac{\ln (\frac{1}{2})}{\ln (0.96^{})}=16.98\approx17[/tex]ANSWER
in 17 years the population will be reduced in half
Determine the shaded area. This figure is not drawn to scale.
To find:
The area of the shaded region.
Solution:
From the figure, it is clear that the length and width of the rectangle inside the circle are 75m and 40m. The diameter of the circle is 85m. The radius of the circle is 85/2m.
The shaded region is equals (area of the circle - area of the rectangle).
So, the area of the shaded region is:
[tex]\begin{gathered} A=\pi r^2-l\times w \\ A=\pi(\frac{85}{2})^2-75\times40 \\ A=\frac{22}{7}\times\frac{7225}{4}-3000 \\ A=\frac{158950}{28}-3000 \\ A=5676.79-3000 \\ A=2676.79m^2 \end{gathered}[/tex]Thus, the area of the shaded region is 2676.79 m^2.
your card gives you a bonus of 0.4%. what is your actual bonus if you charge $3,397.75 on your credit card?
Answer:
$13.591
Explanation:
To know your actual bonus, we need to find what is 0.4% of $3,397.75 as follows
[tex]3,397.75\times\frac{0.4}{100}=13.591[/tex]Therefore, your actual bonus is $13.591