a) The total cost, c, in dollars, of Theo's order based on the number of
bagels, b, he buys is: c = 0.75b + 3.5
b) The statement c(6) = 8 represents that the number of bagels bought was 6 which resulted in a total cost of $8
How to solve Linear Equation Word Problems?The general expression for a linear equation in slope intercept form is:
y = mx + b
Where:
m is slope
b is y-intercept
a) Let the number of bagels bought be b
Cost of each bagel = $0.75
Cost of chocolate = $3.50
Thus:
Total cost is:
c = 0.75b + 3.5
b) c(6)=8
This means the number of bagels bought was 6 which resulted in a total cost of $8
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Multiply: (6a³3b³) (5a² + 46²)
O 11a³ + 10a³b² + 2a²b³ + b³
O 30a5 +24a³b² - 15a²b³ - 1265
O 30a5 +9a5b5 - 1265
O30a6 +24a³ b² - 15a² b3 - 1266
A local hamburger shop sold a combined total of 441 hamburgers and cheeseburgers on Tuesday. There were 59 fewer cheeseburgers sold than hamburgers. How many hamburgers were sold on Tuesday?
Accοrding tο given cοnditiοns, 250 hamburgers were sοld οn Tuesday.
What is algebra ?Algebra is a branch οf mathematics that deals with symbοls and the rules fοr manipulating thοse symbοls. It invοlves sοlving equatiοns and manipulating variables tο find unknοwn values.
Let's use algebra tο sοlve the prοblem.
Let x be the number οf hamburgers sοld.
Then the number οf cheeseburgers sοld is x - 59.
The tοtal number οf hamburgers and cheeseburgers sοld is 441, sο we can write an equatiοn:
x + (x - 59) = 441
Simplifying the left side, we get:
2x - 59 = 441
Adding 59 tο bοth sides, we get:
2x = 500
Dividing by 2, we get:
x = 250
Therefοre, accοrding tο given cοnditiοns, 250 hamburgers were sοld οn Tuesday.
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which expression is equivalent to 6 divided by 2/5
Answer:15
Step-by-step explanation:
Dividing by a fraction is equivalent to multiplying by its reciprocal. Therefore, 6 divided by 2/5 is the same as multiplying 6 by 5/2, which equals 15.
Explanation:The expression 6 divided by 2/5 is equivalent to 6 multiplied by 5/2. This is because dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 2/5 is 5/2. Therefore, 6 divided by 2/5 is the same as 6 multiplied by 5/2, which gives you the result 15.
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1. The table shows the average price (in dollars) of jeans sold at different stores and the number of pairs
of jeans sold at each store in one month.
40
Average Price 22 28 35 46
a List the ordered pairs from the table and plot them
Number Sold
152
94
on a coordinate plane.
134 110 81
b. Describe the form and direction of the scatterplot
created
c. Describe the relationship between the average price of jeans and number of jeans sold.
The ordered pairs from the table are (22, 152), (28, 94), (35, 134), and (46, 110). Plotting them on a coordinate plane would produce a scatterplot.
The form of the scatterplot is a line of negative slope that is decreasing from left to right. The direction of the scatterplot is downward.
The relationship between the average price of jeans and number of jeans sold appears to be negative, which means that as the average price of jeans increases, the number of jeans sold decreases. In other words, there is an inverse relationship between the price and quantity demanded of jeans. This relationship is consistent with the law of demand in economics, which states that as the price of a good or service increases, the quantity demanded of that good or service will decrease, ceteris paribus (all else being equal).
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For the function f(x)=5x^2+3x , evaluate and simplify f(x+h)-f(x)/h
The result of the evaluation and simplification of [tex]f(x)=5x^2+3x is f(x+h)-f(x)/h = h + 3[/tex], which is a line with a slope of 1 and a y-intercept of 3.
The function[tex]f(x)=5x^2+3x[/tex], when evaluated and simplified, is equal to [tex]f(x+h)-f(x)/h[/tex]. To calculate [tex]f(x+h)-f(x)/h[/tex], the first step is to subtract f(x) from f(x+h). This will leave us with the expression . After this, we can simplify the expression to [tex]h^2 + 3[/tex]h. Next, we divide this expression by h which will leave us with h + 3.
This means that our result is [tex]f(x+h)-f(x)/h = h + 3[/tex]. This can be visualized as a line on a graph with a slope of 1 and a y-intercept of 3. This means that as the value of x increases, the value of [tex]f(x+h)-f(x)/h[/tex]increases by 1 for every increase in x.
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WILL GIVE BRAINLEIST TO THE BEST ANSWER PLUS A LOT OF POINTS!!!!!!!!!!
if (x-2)^2 =2 what values of x make the quadratic equation
The values of x make the quadratic equation (x-2)² =2 is 2 + √2.
To find the values of x that make the quadratic equation (x-2)² = 2 true, we need to solve for x.
First, we can take the square root of both sides of the equation:
x - 2 = ±√2
Next, we can add 2 to both sides of the equation:
x = 2 ± √2
Therefore, the two solutions for x are:
x = 2 + √2
x = 2 - √2
These are the two values of x that make the quadratic equation (x-2)^2 = 2 true.
To check these solutions, we can substitute each value back into the original equation:
[(2 + √2) - 2]² = 2
Simplifying:
√2² = 2
2 = 2
This solution works. Now let's check the other solution:
[(2 - √2) - 2]² = 2
Simplifying:
-√2² = 2
-2 = 2
This solution does not work, so we discard it. Therefore, the only value of x that makes the quadratic equation (x-2)² = 2 true is: x = 2 + √2.
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The box-and-whisker plots show the speed, in miles per hour, for each of 10 fish and 10 mammals. Speed of 10 F 30 50 D 60 Speed of 10 Mammals + 60 70 30 40 50 70 Letecia wants to predict the speeds of one additional fish and one additional mammal. She notices that the box-and-whisker plots show that about 75% of the fish were faster than 40 mph and that about 75% of the mammals were slower than 50 mph. Based upon this information, which prediction about the speeds of the additional fish and the additional mammal is justified? A The speed of the fish will be less than 40 mph, and the speed of the mammal will be greater than 50 mph. The speed of the fish will be greater than 40 mph, and the speed of the mammal will be less than 50 mph. The speed of the fish will be greater than 40 mph, and the speed of the mammal will be greater than 50 mph. The speed of the fish will be less than 40 mph, and the speed of the mammal will be less than 50 mph.
Based on the information, the only prediction that is justified is that the speed of the fish will be greater than 40 mph, and the speed of the mammal will be less than 50 mph.
Therefore option B is correct.
How do we know this?Based on the given information above, we were able to deduct that about 75% of the fish were faster than 40 mph and about 75% of the mammals were slower than 50 mph.
We can go ahead and use this information to make predictions about the speeds of one additional fish and one additional mammal.
Note that the median speed is around 50 mph, and the upper quartile (75th percentile) is around 60 mph and we know that about 75% of the fish were faster than 40 mph, we can predict that the additional fish will have a speed greater than 40 mph. However, since the upper quartile is only at 60 mph, we cannot predict that the additional fish will have a speed greater than 60 mph. Therefore, the only prediction that is justified is that the speed of the fish will be greater than 40 mph, which eliminates options A and D.the only prediction that is justified is that the speed of the fish will be greater than 40 mph, and the speed of the mammal will be less than 50 mph, which is option BLearn more about speed at:
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Tom and Gwen have an adjusted annual gross income of $111,480. Their monthly mortgage payment for the house they want would be $1,725. Their semi-annual property taxes would be $3,660, and the homeowner’s insurance premium would cost them $685 per year. They have a monthly $154 car payment, and their credit card monthly payment averages $2,021.
What is the front end ratio?
What is the back end ratio?
Tom and Gwen have an adjusted annual gross income of $111,480. Their front end ratio, which measures how much of their income is dedicated to housing costs, is 5.19%. Their back end ratio, which measures how much of their income is dedicated to all debt obligations, is 11.72%.
The front end ratio is a measure of how much of an individual’s gross income is dedicated to housing costs. It is calculated by taking the total housing costs, which includes mortgage payments, property taxes, and homeowners insurance premiums, and dividing it by the annual gross income. For Tom and Gwen, this would be:
Front End Ratio = (Mortgage Payment + Property Taxes + Homeowner’s Insurance Premium) / Annual Gross Income
Front End Ratio = (1,725 + 3,660 + 685) / 111,480
Front End Ratio = 5.19%
The back end ratio is a measure of how much of an individual’s gross income is dedicated to all debt obligations, including housing costs and other debts. It is calculated by taking all debt obligations, which includes mortgage payments, property taxes, homeowner’s insurance premiums, car payments, and credit card payments, and dividing it by the annual gross income. For Tom and Gwen, this would be:
Back End Ratio = (Mortgage Payment + Property Taxes + Homeowner’s Insurance Premium + Car Payment + Credit Card Payment) / Annual Gross Income
Back End Ratio = (1,725 + 3,660 + 685 + 154 + 2,021) / 111,480
Back End Ratio = 11.72%
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Return to the simpler regression specification in part (a). We want see if the deter-minants of life expectancy are different for rich and poor countries. Use membershipin the ""Organization of Economic Cooperation & Development"" (oecd) as the indica-tor of a rich country. The OECD had 30 member countries during this time period. Perform a test of the hypothesis that all three of the coefficients in the populationregression are equal for OECD and non-OECD countries. [Hint: you do not need toperform this test using factor variables. ]
We can use a two-way ANOVA to compare the means of the three coefficients for OECD and non-OECD countries and assess whether the differences are probability significant.
To test the hypothesis that the three coefficients in the population regression are equal for OECD and non-OECD countries, we can run a two-way ANOVA. The two factors in this ANOVA would be OECD status (OECD or non-OECD) and the three coefficients in the population regression (income, population density, and urbanization). This will enable us to compare the means of the three coefficients for OECD and non-OECD countries and assess whether the differences are statistically significant. We can also use the F-statistic to see if the differences between the means of the two groups are statistically significant. This will allow us to assess whether the coefficients in the population regression are indeed different for OECD and non-OECD countries.
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In a 30-60-90 right triangle, the side opposite the 30- degree angle is?
Answer:
x or half the hypotenuse
Step-by-step explanation:
You can look up special triangles for more info:
Opposite 30 = x
Opposite 60 = x*(sqrt3)
Opposite 90 = 2x
Joe ran 10 kilometers in 5 hours. what is joe’s unit rate
2 kilometers per hour
Question in photo
!!!!!
Answer:
Binomial
Step-by-step explanation:
A binomial is a polynomial expression which contains exactly two terms. A binomial can be considered as a sum or difference between two or more monomials.
PEMDAS
solve this using pemdas
with step by step u might want to download so u can draw on the image linked :)
Answer:
119. Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer
What is the distance in units between the points (1, 0) and (8, 0)?
In response to the stated question, we can state that As a result, there coordinates are 7 units between the points (1, 0) and (8, 0).
what are coordinates?When locating points or other geometrical objects precisely on a manifold, such as Euclidean space, a coordinate system is a technique that uses one or more integers or coordinates. Locating a point or item on a two-dimensional plane requires the use of coordinates, which are pairs of integers. Two numbers called the x and y coordinates are used to describe a point's location on a 2D plane. a collection of integers that indicate exact locations. The figure often has two numbers. The first number denotes the front-to-back measurement, while the second number denotes the top-to-bottom measurement. For example, in (12.5), there are 12 units below and 5 above.
The distance formula can be used to determine the separation between two points in a two-dimensional Cartesian coordinate system:
[tex]\sqrt[(x2 - x1)2 + (y2 - y1)2] = d[/tex]
and d .
As both of the points in this instance have y-coordinates of 0, we may condense the expression to:
[tex]d = \sqrt[(8 - 1)^² + (0 - 0)^²]\\d = \sqrt[(7)^² + (0)^²]\\d = \sqrt[49]\\ d= 7[/tex]
As a result, there are 7 units between the points (1, 0) and (8, 0).
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Claude is covering the lateral surface of bug spray cans with labels. Each can is cylindrical with a height of 12. 7 centimeters and a radius of 3 centimeters. If he places labels on 5 bug spray cans, how many square centimeters of labeling material will he use?
Claude will use 1197 square centimeters of labeling material to cover the lateral surface of 5 cylindrical bug spray cans.
Laminar surface area: what is it?A three-dimensional object's lateral surface area is its total surface area minus its top and bottom surfaces. The lateral surface area of a cylinder, for instance, would be the area of the curved side of the cylinder. In geometry and engineering, the lateral surface area is frequently used to determine how much material is required to cover or build an object's sides. Depending on the geometry of the item, many formulae may be used to compute the lateral surface area, which is often expressed in square units (such as square centimetres or square feet).
Given the dimensions of the cylindrical can we have the lateral surface area of cylinder as:
Lateral surface area = 2πrh
Substituting the value r = 3 and h = 12.7 we have:
Lateral surface area = 2π(3)(12.7) = 239.4 square centimeters
A total of 5 cans need to be covered thus,
Total labeling material = 5 x 239.4 = 1197 square centimeters
Hence, Claude will use 1197 square centimeters of labeling material to cover the lateral surface of 5 bug spray cans.
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Write a quadratic function that has vertex in the third quadrant
and has no x-intercept, Explain how your find such function.
Quadratic function that has vertex in the third quadrant and has no x-intercept is f(x) = 2(x+3)² - 4.
Quadratic function is a polynomial function of the second degree of the form f(x)= ax² + bx + c where a is a non-zero coefficient and x is the variable. Vertex is the point on the parabola which has a minimum or maximum point. The third quadrant is where both the x and y coordinates are negative. The question requires finding a quadratic function with vertex in the third quadrant and has no x-intercept. Quadratic function with no x-intercept means that the graph does not cross the x-axis. Here is how to find such function: Step-by-step We can start by using the vertex form of a quadratic function. f(x) = a(x-h)² + k Where (h, k) is the vertex of the parabola. Since the vertex is in the third quadrant, h and k should be negative numbers.
Also, since the graph should not cross the x-axis, the leading coefficient (a) should be either positive or negative. If a>0, the parabola opens upwards, and if a<0, the parabola opens downwards. To find a quadratic function that has no x-intercept and has a vertex in the third quadrant, let's choose any negative value of h and k such that |k|>|h|, and a>0. For instance, let h=-3 and k=-4. Then, substituting these values in the vertex form, we get:f(x) = a(x+3)² - 4If we want the parabola to have a minimum point at the vertex, then a should be positive. We can choose any positive value of a. For example, let's take a=2. Then, the quadratic function with the required conditions is:f(x) = 2(x+3)² - 4f(x) = 2x² + 12x + 14The graph of this function has vertex (-3, -4) and does not cross the x-axis. Quadratic function that has vertex in the third quadrant and has no x-intercept is f(x) = 2(x+3)² - 4.
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Question
Does the equation demonstrate closure of polynomials under addition?
(2x2+x)+(4x−3)=2x2+5x−3
Responses
Yes. The equation shows that the sum of the two polynomials is a polynomial. This demonstrates that polynomials are closed under addition.
Yes. The equation shows that the sum of the two polynomials is a polynomial. This demonstrates that polynomials are closed under addition.
Yes. The equation shows that the sum of the two polynomials is not a polynomial. This demonstrates that polynomials are closed under addition.
Yes. The equation shows that the sum of the two polynomials is not a polynomial. This demonstrates that polynomials are closed under addition.
No. The equation shows that the sum of the two polynomials is a polynomial. This demonstrates that polynomials are not closed under addition.
No. The equation shows that the sum of the two polynomials is a polynomial. This demonstrates that polynomials are not closed under addition.
No. The equation shows that the sum of the two polynomials is not a polynomial. This demonstrates that polynomials are not closed under addition.
Answer: yes
Step-by-step explanation:
mpho takes 140 km trip to visit his unclevon his motorbike.THE motorbike has a fuel capacity of 16 litres.He stops for lunch break after 5/7 of the journey.how many kilometers did he travel before he stopped for lunch?
Answer:
40Km
Step-by-step explanation:
Total Distance of Journey = 140KM
5/7 of the journey:
[tex]\frac{5}{7 } * 140 = 100km[/tex]
Distance travelled before stopping: Total Distance - 5/7 of Total Distance
= 140 - 100KM = 40KM
Each of the interior angles of a regular polygon is 140 degrees. How many have it
Answer:
The polygon has 9 sides, and it is a nonagon.
Step-by-step explanation:
The formula to find the sum of the interior angles of a regular polygon is:
S = (n - 2) × 180
where S is the sum of the interior angles and n is the number of sides.
If each interior angle of the polygon is 140 degrees, we can use the formula to solve for n:
n = (S / 140) + 2
Plugging in S = 180(n-2) and simplifying, we get:
n = (180(n-2) / 140) + 2
n = (9n - 18) / 7
7n = 9n - 18
-2n = -18
n = 9
Therefore, the polygon has 9 sides, and it is a nonagon.
Hope this helps! I'm sorry if it's wrong. If you need more help, ask me! :]
Find the shaded area. Round your answer to the nearest tenth, if necessary.
Example: 103.45 rounded to tenths place is 103.5
Use 3.14 for pi in finding the area of the semicircle.
Area of semicircle =
Area of rectangle =
TOTAL area of composite figue =
Answer:
The answer to your problem is, Area = 104.1 square feet.
Step-by-step explanation:
Area of semicircle = 1/2 the area of a circle:
[tex]A_{sc} = \frac{1}{2} tt r^{2}[/tex]
Radius is half the diameter of 6ft.
[tex]A_{sc} = \frac{1}{2} tt ( 3^{2} ) = 14.13ft^{2}[/tex]
Area of the rectangle:
[tex]A_{r} = lw = 15 * 6 = 90ft^{2}[/tex]
Add them:
[tex]90 + 14.13 = 104.13[/tex]
Round to the nearest tenth (one decimal place)
Which is 104.1
Thus the answer to your problem is 104.1 of 104.13
Solve the equation (32
(3 % ) ( 3 ) =
X =
= 36
The value of x from the given expression (3^1/2 ) ( 3^1/2 ) = 3^6 can be expressed as 6.
How can the value of x be calculated?A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign. Like this: 2x - 4 Equals 2. In the above example, the variable x exists.
Given that (3^1/2 ) ( 3^1/2 ) = 3^6
then 3^(x/2+ x/2) = 3 ^6
x/2+ x/2 = 6
Then the lcm , we have
x+x/2 = 6
2x/2 = 6
2x = 12
x = 12/2 = 6
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16. A 40-ft. guy wire helps to support a tower. The wire is anchored to the ground 19 ft. from the base of
the tower. What is the measure of the angle formed between the wire and the ground, to the nearest
degree?
a.
25°
b. 65°
C.
62°
d. 28°
laual ground and the trunk is
Answer:
We can use trigonometry to solve this problem. Let θ be the angle formed between the wire and the ground. Then, using the right triangle formed by the wire, the tower, and the ground, we have:
cos θ = adjacent/hypotenuse
where the adjacent side is 19 ft. (distance from the base of the tower to the anchor point) and the hypotenuse is 40 ft. (length of the guy wire). Solving for θ, we get:
θ = cos^-1(19/40) ≈ 62°
Therefore, the measure of the angle formed between the wire and the ground is approximately 62 degrees. Answer C.
Step-by-step explanation:
What is the volume of this composite figure? The slant height of the cone is 3. The height of the cone is approximately 1.658. Round your FINAL answer to the nearest hundredth.
514. 38 units³
514.38 units²
491.45 units3
Answer:
514.38 units²
Step-by-step explanation:
The frequency table shows Sam's record in swimming
Year
Number of medals
2008
2009
2010
2012
2013
Based on this record, what is the probability of picking up a medal won by him in the years 2009 or 2012
The probability of picking a medal won by Sam in the years 2009 or 2012 is 5/6.
The probability of picking a medal won by Sam in the years 2009 or 2012 can be calculated using the formula P(A∪B) = P(A) + P(B) - P(A∩B). In this case, P(A) equals the probability of picking a medal won by Sam in 2009, which is 1/3, and P(B) equals the probability of picking a medal won by Sam in 2012, which is 1/2. P(A∩B) would be the probability of picking a medal won by Sam in both years, which is 0, since he did not win a medal in both years. Therefore, the probability of picking a medal won by Sam in the years 2009 or 2012 is P(A∪B) = P(A) + P(B) - P(A∩B) = 1/3 + 1/2 - 0 = 5/6.
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the death rate from Covid19 in a certain country is 6%. what is
the probability that at least 2 patients will die out of next 10
patients
P(X≥2) = 1 - 0.389 - 0.409= 0.202. The probability that at least 2 patients will die out of next 10 patients is 0.202.
The death rate from Covid19 in a certain country is 6%. The probability that at least 2 patients will die out of next 10 patients can be found using binomial distribution. What is binomial distribution? Binomial distribution is a probability distribution that deals with the number of successes or failures in a given number of trials. A binomial distribution model is characterized by the following conditions: There are only two outcomes of the trials, either success or failure. The probability of success is constant throughout the trials.
The trials are independent of each other. The formula for the probability of binomial distribution is as follows: P(X=k) = (n C k) × p^k × (1-p)^(n-k)Where P(X=k) is the probability of k successes out of n trials. n C k represents the number of ways of selecting k items out of n items. p is the probability of success.1-p is the probability of failure. Using the above formula, the probability that at least 2 patients will die out of next 10 patients is: P(X≥2) = 1 - P(X=0) - P(X=1)P(X=0) = (10 C 0) × 0.06^0 × (1-0.06)^(10-0)= 0.389P(X=1) = (10 C 1) × 0.06^1 × (1-0.06)^(10-1)= 0.409Therefore,P(X≥2) = 1 - 0.389 - 0.409= 0.202The probability that at least 2 patients will die out of next 10 patients is 0.202.
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a rectangular rose garden has dimensions 5.5 feet by 3.75 feet. A rectangular vegetable garden has dimensions 13.75 feet by 6 feet. How many times as great is the area of the vegetable garden compared to the area of the flower garden? The area of the vegetable garden is times as great the area of the rose garden
Answer: 4
Step-by-step explanation:
Area of rose garden = 5.5 * 3.75 = 20.625
Area of vegetable garden = 13.75 * 6 = 82.5
To find how many times greater the area of the vegetable garden is, we simply divide 82.5 by 20.825
82.5 / 20.625 = 4
Please help, will mark as brainlest
Answer:
Step-by-step explanation:
we should do multiplications first:
1)
[tex]1)12a^{2}*3ba=12a^{3}b\\2)2ab*3ab^{2}=6a^{2}b^{3}\\3)11aba=11a^{2}b\\4)12a^{3}b+6a^{2}b^{3}+11a^{2}b=a^{2}b(12a+6ab^{2}+11)[/tex]
2)
[tex]1)1.5xy^{2}*(-4)xyz=-6x^{2}y^{3}z\\2)-4mnk*5m^{2}n^{3}k=-20m^{3}n^{4}k^{2}\\3)-6x^{2}y^{3}z-20m^{3}n^{4}k^{2}[/tex]
Figure 2 shows the lawn ABCDEF, where ABDE is a rectangle of length y metres and width 2x metres.
Each end of the lawn is a semi-circle of radius x metres.
The lawn has perimeter 90 m and area S m ²
d. S
dx
= 90 - 2
Given S = 90x-x², then
The value x = 14. 32 gives a maximum value of S
Find, to the nearest whole number, the maximum value of S
The nearest whole number, the maximum value of S is equivalent to approximately 323 m², which is the area of the lawn.
We are given that the perimeter of the lawn is 90 m. Therefore, we can write:
2y + 4x + 2πx = 90
where π is the constant pi. Simplifying this equation gives:
y = 22.5 - 2x - πx
The area of the lawn is given by:
S = y(2x) + πx²
Substituting y in terms of x gives:
S = (22.5 - 2x - πx)(2x) + πx²
Simplifying this expression gives:
S = 45x - 2πx² - 4x²
We are asked to find the maximum value of S. To do this, we can differentiate S with respect to x and set the derivative equal to zero:
dS/dx
= 45 - 4πx - 8x = 0
Solving for x gives:
x = (45 - 4π)/8
Substituting this value of x into the expression for S gives:
S ≈ 323 m²
Rounding this value to the nearest whole number gives:
S ≈ 323 m².
Therefore, the maximum value of S is approximately 323 m².
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Complete question is:
Figure 2 shows the lawn ABCDEF, where ABDE is a rectangle of length y meters and width 2x meters. (Refer the image)
Each end of the lawn is a semi-circle of radius x meters.
The lawn has perimeter 90 m and area S m ²
dS/ dx= 90 - 2
Given S = 90x-x², then
The value x = 14. 32 gives a maximum value of S
Find, to the nearest whole number, the maximum value of S
Suppose the solution set of a certain system of linear equations can be described as x_1 = 6 + 3x_3, x_2 = -2 - 5x_3, with x_3 free. Use vectors to describe this set as a line in R^3. Geometrically, the solution set is a line through parallel to
The solution set of the given system of linear equations can be expressed as a line in R^3 vector as r = (6, -2) + x_3(3, -5).
To express the solution set of the given system of linear equations as a line in R^3, we first need to express the solution set as a vector equation. We can do this by expressing the equations in terms of x_3 as follows:
x_1 = 6 + 3x_3,
x_2 = -2 - 5x_3
Therefore, the solution set of the given system of linear equations can be expressed as a line in R^3 as follows:
r = (6, -2) + x_3(3, -5).
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Sabiendo que sen alpha = 0. 6 y que a es un ángulo agudo, calcula el resto de razones trigonométricas
Translate: Knowing that sen alpha = 0. 6 and that a is an acute angle, calculates the rest of trigonometric ratios
Rest of the trigonometric ratios for the acute angle alpha are cos(alpha) = 0.8 and tan(alpha) = 0.75.
If we know that sin(alpha) = 0.6, we can use the Pythagorean identity to find cos(alpha) and tan(alpha). Here's how:
Since sin(alpha) = opposite/hypotenuse, we can represent sin(alpha) as the ratio of the length of the side opposite the acute angle alpha to the length of the hypotenuse of the right triangle. Let's assume that the length of the opposite side is a and the length of the hypotenuse is h. Then we have:
sin(alpha) = a/h = 0.6
Solving for a, we get:
a = 0.6h
Using the Pythagorean theorem:
[tex]a^2 + b^2 = h^2[/tex]
Since a and h are related by a = 0.6h, put 0.6h for a to get:
[tex](0.6h)^2 + b^2 = h^2[/tex]
Simplifying:
[tex]0.36h^2 + b^2 = h^2[/tex]
[tex]b^2 = h^2 - 0.36h^2 = 0.64h^2[/tex]
[tex]b = \sqrt{0.64h^2} = 0.8h[/tex]
So now we know that b = 0.8h and a = 0.6h. Using these values, we can find cos(alpha) and tan(alpha) as follows:
[tex]cos(alpha) = adjacent/hypotenuse = b/h = 0.8h/h = 0.8tan(alpha) = opposite/adjacent = a/b = 0.6h/0.8h = 0.75[/tex]
Therefore, the rest of the trigonometric ratios for the acute angle alpha are cos(alpha) = 0.8 and tan(alpha) = 0.75.
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