Answer:
$7,200
Step-by-step explanation:
r=p × n
where
r=revenue
p = price per item
n = number of items sold
A change in price changes quantity ( number sold)
Variable x changes with price, then
Let
p+x=a dollar price increase
p-x= a dollar price decrease
n+x= an increase in quantity sold
n-x= a decrease in quantity sold
Therefore,
A $2 dollar increase in price=p+2x
2 decrease in room quantity sold= n-2x
Substituting in the above equation
r=(p+2x)*(n-2x)
P=$60
n=180
Then
r=(60+2x)*(180-2x)
r=10,800-120x+360x-4x^2
r=-4x^2-240x+10,800
Solve the quadratic equation
The maximum value of x in the vertex = - b/2*a
Where
b=240
a=-4
Value of x=-240/2*(-4)
X=30
r=-4x^2-240x+10,800
=-4(30)^2-240(30)+10,800
=-4(900)-7200+10,800
=3,600-7200+10800
=$7,200
The rate that maximises revenue=$7,200
Answer:
The rate that maximizes revenue is $14,000
Step-by-step explanation:
First of all, you should know that the income equation is:
R = p * n
where:
p = price per item n = number of items soldOn the other hand, if p + x means a price increase, while n - x means a decrease in the number of an item sold.
In this case, reference is made to rooms, where 60 + 2x is the increased price and 180-2x is the decrease in rooms for rent.
So:
R=(60+2x)*(180-2x)
Expressing this in another way, applying distributive property:
R=60*180+60*(-2)x+2x*180+2x*(-2)x
R=10,800+240x-4x² equation (A)
This is a quadratic equation that is graphically represented by a parabola. If a, the coefficient that accompanies the term x², has a positive value, the parabola will be oriented upwards. On the contrary, if a has a negative value, the parabola will be oriented downwards. In this case, the value of a is -4, with the parabola facing down. The vertex is a point that is part of the parabola, which has the value as ordered minimum or maximum function. In this case, since the parabola faces downward, the vertex will be its maximum value.
The value of x in the vertex is [tex]-\frac{b}{2*a}[/tex]. In this case:
a=-4b=240Replacing:
[tex]x=-\frac{240}{2*(-4)}[/tex]
Solving:
x=40
To find the rate that maximizes income you simply replace this value in equation (A)
R=10,800+240*40-4*(40)²
R=14,000
The rate that maximizes revenue is $14,000
whats 138 divided by 2 lol
Answer:
69
Step-by-step explanation:
The solution is, 138 divided by 2 is 69.
What is division?Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.
here, we have,
138 divided by 2
i.e. 138/2
= 69
Hence, The solution is, 138 divided by 2 is 69.
To learn more on division click:
brainly.com/question/21416852
#SPJ5
Square ABCD has a side length of 4 inches. The square is dilated by a scale factor of 4 to form square A'B'C'D'. What is the side length of square A'B'C'D' ? Type a number for your answer.
We have been given that square ABCD has a side length of 4 inches. The square is dilated by a scale factor of 4 to form square A'B'C'D'. We are asked to find the side length of square A'B'C'D'.
We know that when scale factor is greater than 1, then the resulting figure would be an enlargement.
To find the side length of new square after dilation, we will multiply the original side by scale factor.
[tex]\text{New side length}=\text{Original side}\times \text{Scale factor}[/tex]
[tex]\text{New side length}=\text{4 inches}\times 4[/tex]
[tex]\text{New side length}=16\text{ inches}[/tex]
Therefore, the side length of square A'B'C'D' would be 16 inches.
. Hernandez bought 18 pens for her class. Highlighters cost $3 each, and gel pens cost $2.50 each. She spent a total of $50. Use a system of equations to find the number of highlighters and gel pens Mrs. Hernandez bought. Enter your answers in the boxes.
A circle has a radius of 2 units. Find the radian measure of a central angle that intercepts an arc length of 5.8 units. Round the radians measure to the nearest tenth.
Answer:
2.9 radians.
Step-by-step explanation:
Please kindly check the attached file for explanation.
The radian measure of a central angle intercepting an arc length of 5.8 units in a circle with a radius of 2 units is 2.9 radians when rounded to the nearest tenth.
The question deals with finding the radian measure of a central angle in a circle with a given radius and arc length. The formula for this calculation is theta = arc length / radius. Given that the circle's radius (r) is 2 units and the arc length (l) is 5.8 units, we substitute these values into the formula to find the radian measure of the central angle.
theta = l / r = 5.8 units / 2 units
This gives us theta = 2.9 radians. However, we need to round this to the nearest tenth, resulting in theta = 2.9 radians as the final answer.
Which equation represents a line that passes through (-9, -3) and has a slope of -6?
y-9=-5(x – 3)
y+9= -6(x + 3)
y-3--5(x – 9)
y+3=-6[X + 9)
Answer:
y +3 = -6(x +9)
Step-by-step explanation:
The point-slope form of the equation of a line is ...
y -k = m(x -h)
for a line with slope m through point (h, k).
You want the line with slope -6 through point (-9, -3), so its equation is ...
y -(-3) = -6(x -(-9))
y +3 = -6(x +9) . . . . . matches the last choice
A psychological study found that men who were distance runners lived, on average, five years longer than those who were not distance runners. The study was conducted using a random sample of 50 men who were distance runners and an independent random sample of 30 men who were not distance runners. The men who were distance runners lived to be 84.2 years old, on average, with a standard deviation of 10.2 years. The men who were not distance runners lived to be 79.2 years old, on average, with a standard deviation of 6.8 years. Which of the following is the test statistic for the appropriate test to determine if men who are distance runners live significantly longer, on average, than men who are not distance runners?
Answer:
C 84.2-79.2/SQRoot(10.2^2/50 + of of 6.8^2/30)
Step-by-step explanation:
Final answer:
To determine if there is a significant difference in lifespan between men who are distance runners and those who are not, a two-sample t-test test statistic is calculated as approximately 1.051 using the provided sample means, standard deviations, and sample sizes.
Explanation:
To determine if men who are distance runners live significantly longer, on average, than men who are not distance runners, we would use a two-sample t-test statistic. The test statistic formula for a two-sample t-test is:
t = (x1 - x2) / [tex]\sqrt{(s1^2/n1 + s2^2/n2)[/tex]
where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes of the two groups.
In this case, the mean age at death for men who are distance runners is 84.2, the standard deviation is 10.2, and the sample size is 50 (n1 = 50). The mean age at death for men who are not distance runners is 79.2, the standard deviation is 6.8, and the sample size is 30 (n2 = 30).
Plugging the values into the formula, we calculate the test statistic as follows:
t = (84.2 - 79.2) / [tex]\sqrt{(10.2^2/50 + 6.8^2/30)[/tex]
t = 2.0 / [tex]\sqrt{((104.04/50) + (46.24/30))[/tex]
t = 2.0 / [tex]\sqrt{(2.0808 + 1.5413)[/tex]
t = 2.0 / √3.6221
t ≈ 2.0 / 1.9032
t ≈ 1.051
This is the test statistic that you would use to determine whether there is a significant difference in lifespan between the two groups.
What is the perimeter of the parallelogram?
Answer:
36 units
Step-by-step explanation:
Split the parallelogram into 3 shapes. Two right triangles and one rectangle.
Find the length of all the sides.
Triangle one: Triangle two:
Leg 1: 8 a^2+b^2=c^2 Leg 1: 8 a^2+b^2=c^2
Leg 2: 6 8^2 + 6^2 = c^2 Leg 2: 6 8^2 + 6^2 = c^2
Hypotenuse: ? 64 + 36 = c^2 Hypotenuse: ? 64 + 36 = c^2
100=c^2 100=c^2
c=10 c=10
Hypotenuse One: 10 units
Hypotenuse Two: 10 units
Base One Length: 8 units
Base Two Length: 8 units
Add all these numbers up and your answer would be 36 units.
Nancy bought 570 crayons that came in packs of 15 how many packs of crayons did Nancy buy
Answer:
38
Step-by-step explanation:
Answer:
38 packs
Step-by-step explanation:
Which graph represents the solution set to this system of equations? –x + 2y = 6 and 4x + y = 3
Answer:
c
Step-by-step explanation:
The graph represents the solution set is attached.
The value of x is 0 and y is 3.
Given that,
Equation; [tex]-x + 2y = 6 \ and \ 4x + y = 3[/tex].
We have to determine,
Which graph represents the solution set to this system of equations?
According to the question,
Equation; [tex]-x + 2y = 6 \ and \ 4x + y = 3[/tex].
Solving both the equation,
From equation 1,
[tex]-x+2y =6\\\\2y = x+6\\\\y= \dfrac{x+6}{2}[/tex]
Substitute the value of y in equation 2,
[tex]4x+y = 3\\\\4x + \dfrac{x+6}{2} = 3\\\\\dfrac{8x+x+6} {2}= 3\\\\{9x+6} = 3\times 2\\\\9x + 6 = 6\\\\ 9x = 6-6\\\\9x =0\\\\x = \dfrac{0}{9}\\\\x = 0[/tex]
And the value of y is,
[tex]-x+2y = 6\\\\-0+2y = 6\\\\2y = 6\\\\y = \dfrac{6}{2}\\\\y = 3[/tex]
Hence, The value of x is 0 and y is 3.
For more details refer to the link given below.
rainly.com/question/16208461
Lyle went fishing for 1 hour and 30 minutes until he ran out of bait at 6:40 p.m. At what time did Lyle start fishing? *
Answer:
he started fishing by 5:10pm
Step-by-step explanation:
just subtract 1:30 from 6:40
Which of the following has the same slope as the equation Y=1/2x-10?
a
1/2x - y = 10
b
-x + 3y = 12
c
-1/2x + y = -10
d
-2x + y = -6
Answer:
c. -1/2x + y = -10
Step-by-step explanation:
[tex] - \frac{1}{2} x + y = - 10 \\ y = \frac{1}{2} x - 10[/tex]
Changing the order of the equation, you can verify the coefficient of x is the same when y is isolated.
In slope-intercept form, the coefficient of x, or the m in y=mx+b, is the slope or gradient.
After converting each given equation to the slope-intercept form, it is clear that both the original equation Y=1/2x-10 and the option c, -1/2x + y = -10, have the same slope of 1/2.
Explanation:To determine which equation has the same slope as Y=1/2x-10, we rewrite each given equation in slope-intercept form (y = mx + b), where m represents the slope.
1/2x - y = 10 can be rewritten as y = 1/2x - 10, which has a slope of 1/2.-x + 3y = 12 can be rewritten as y = 1/3x + 4, so the slope is 1/3.-1/2x + y = -10 can be rewritten as y = 1/2x - 10, which has a slope of 1/2.-2x + y = -6 can be rewritten as y = 2x - 6, indicating a slope of 2.Based on this analysis, the equations y = 1/2x - 10 and -1/2x + y = -10 both have the same slope of 1/2. Therefore, the correct answer is option c.
What are two ways to name the marked angle? *
Error Analysis- Charles claimed the function
f(x) = (3) represents exponential decay.
Explain the error Charles made.
Answer:
Answer is below
Step-by-step explanation:
Charles is wrong because 3 doesn't represent exponential decay. This is because 3 is greater than 1, so it represents exponential growth. If the number was less than 1, then it would represent exponential decay.
If this answer is correct, please make me Brainliest!
The correct answer is Charles should represent as Exponential growth instead of exponential decay
What are exponential growth and exponential decay?Exponential growth : In a function [tex]f (x) =b^{x}[/tex] where b is always greater than 1 is known as exponential growthExponential Decay :In a function [tex]f (x) =b^{x}[/tex] where b is always less than 1 is known as exponential DecayHere f(x) = 3 where 3 is greater than 1
so, It is exponential growth instead of exponential decay
Hence , Charles made an error of exponential decay instead of exponential growth.
Learn more about exponential growth and decay below
https://brainly.com/question/7920039
#SPJ2
Three men are climbing Mt. Meru, which is located in India. Mt. Meru is 6.6 kilometers tall. When the men are 150 meters from the peak of the mountain, the extreme weather forces them to stop climbing and return to the bottom. How high had the men climbed before stopping and going back down the mountain?
Answer:
.15 kilometers or 150 meters
Step-by-step explanation:
The volume of a gift box is 972 in³. The height of the gift box is 12 inches and the area of the base is 81 in². If the base shape is a square, what is the length of each side of the square base? *
Answer:
9 inches
Step-by-step explanation:
Volume is the product of cross sectional area and height.
V=Ah
Where A is area of base and h is height
Given that the base is square, the area of square is given by A=b*b
Xonsidering that the area is given as 81 square inches then
b*b=81
b is the square root of 81 which is +9 or -9
Since base must be positive interger, then base is 9 inches
Bonita has $2.95 in dimes and quarters in her pocket. If she has five more dimes than quarters, how many of each coin does she have?
Bonita have 12 dimes and 7 quarters in her pocket.
What is linear expression?
A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.
Given that;
Bonita have with dimes and quarters in pocket = $2.95
Bonita have 5 more dimes than quarters.
Now,
Let number of dimes = x
Let number of quarters = y
Since, Bonita have 5 more dimes than quarters.
x = y + 5
Here,
Bonita have with dimes and quarters in pocket = $2.95
So, we can formulate;
0.1x + 0.25y = =$2.95
Substitute the value of x in above equation, we get;
0.1 (y + 5) + 0.25y = $2.95
0.1y + 0.5 + 0.25y = $2.95
0.35y + 0.5 = $2.95
Subtract 0.5 we get;
0.35y + 0.5 - 0.5 = $2.95 - 0.5
0.35y = 2.45
Divide by 0.35 we get;
y = 7
And, x = y + 5 = 7 + 5 = 12
Thus, Bonita have 12 dimes and 7 quarters in her pocket.
Learn more about the linear expression visit:
https://brainly.com/question/28061742
#SPJ2
4. Find the value of each variable. (x and y) *
45°
Answer:
x=13 y=18
Step-by-step explanation:
The value of x and y from the given triangle are 13 and 13√2 respectively.
What are trigonometric ratios?The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
From the given triangle, Adjacent is 13 units, opposite side is x units and hypotenuse id y units.
We know that tanθ=Opposite/Adjacent and cosθ=Adjacent/Hypotenuse
tan45°=x/13
1=x/13
x=13 units
cos45°=13/y
1/√2=13/y
y=13√2
Therefore, the value of x and y from the given triangle are 13 and 13√2 respectively.
Learn more about the trigonometric ratios here:
brainly.com/question/25122825.
#SPJ2
Suppose you are a designer making the traffic sign above. What is the sum of the interior angles of the equilateral triangle? What is the measure of ∠N? What is the measure of ∠M? Explain your reasoning. (2 points)
Answer:
Measure of <N = 60°
(angles in an equilateral triangle are all equall 60°)
the measure of ∠M= 60°
(angles in an equilateral triangle are all equall 60°)
Step-by-step explanation:
Sum of angles in a triangle is equall to 180....
And in equilateral triangle of all sides equall...all angles are equal to 60° because all sides are equal.
So <m= <n=<o=60°
An aquarium tank can hold 5400 liters of water. There are two pipes that can be used to fill the tank. The first pipe alone can fill the tank in 90 minutes. The second pipe can fill the tank in 60 minutes by itself. When both pipes are working together, how long does it take them to fill the tank?
Answer:
36 minutes when both pipes are working together
Step-by-step explanation:
capacity of tank = 5400 liters
Pipe A flow per mint. = 5400/90 = 60 liters per mint.
Pipe B flow per mint. = 5400/60 = 90 liters per mint.
Flow of A + B per mint. 60 + 90 = 150 liter per mint.
Therefore, 5400 / 150 = 36 minutes to fill the tank
Answer for me please
I don’t know about the first one the second one if it starts from the origin the point represents that it an proportional 3 is when they start together by seeing if it is x and y I don’t know if it is right
g(r) = r^2 – 6r – 55
1) What are the zeros of the function?
The zeros of the function [tex]G(r) = r^2 - 6r - 5[/tex]5 are r = 11 and r = -5.
To find the zeros of the function [tex]G(r) = r^2 - 6r - 55[/tex], we set G(r) equal to zero and solve for r:
Now, we can use the quadratic formula to solve for r:
r = [-b ± √[tex](b^2 - 4ac)[/tex]] / 2a
where a, b, and c are the coefficients of the quadratic equation [tex](r^2 - 6r - 55 = 0)[/tex].
In this case, a = 1, b = -6, and c = -55. Let's substitute these values into the formula:
r = [-( -6) ± √[tex]((-6)^2 - 4 * 1 * (-55))[/tex]] / 2 * 1
r = [6 ± √(36 + 220)] / 2
r = [6 ± √256] / 2
Now, let's consider the two possible solutions:
1) r = [6 + √256] / 2
r = [6 + 16] / 2
r = 22 / 2
r = 11
2) r = [6 - √256] / 2
r = [6 - 16] / 2
r = -10 / 2
r = -5
So, the zeros of the function are r = 11 and r = -5.
To know more about zeros, refer here:
https://brainly.com/question/31654189
#SPJ2
Find the trapezoid.The trapoized has an area of
Answer: what trapezoid?
An object is launched from a platform.
Its height (in meters), xxx seconds after the launch, is modeled by:
h(x)=-5(x-4)^2+180h(x)=−5(x−4)
2
+180h, left parenthesis, x, right parenthesis, equals, minus, 5, left parenthesis, x, minus, 4, right parenthesis, squared, plus, 180
How many seconds after being launched will the object hit the ground?
Answer:
10
Step-by-step explanation:
Ground level is where h = 0, so solve the equation ...
h(x) = 0
-5(x -4)^2 +180 = 0 . . . . substitute for h(x)
(x -4)^2 = 36 . . . . . . . . . . divide by -5, add 36
x -4 = 6 . . . . . . . . . . . . . . positive square root*
x = 10 . . . . . . add 4
The object will hit the ground 10 seconds after launch.
_____
* The negative square root also gives an answer that satisfies the equation, but is not in the practical domain. That answer would be x = -2. The equation is only useful for time at and after the launch time: x ≥ 0.
The object modeled by the quadratic equation h(x)=-5(x-4)²+180 will hit the ground 10 seconds after being launched.
The equation given is a quadratic equation which models the height of an object after being launched from a platform. To find out when the object will hit the ground, we need to determine when the height h(x) is equal to zero. The equation can be written as h(x) = -5(x - 4)² + 180.
To find the time when the object hits the ground, we set the height equal to zero and solve for x:
0 = -5(x - 4)² + 180
Solving the quadratic equation, we divide both sides by -5:
(x - 4)² = 36
Taking the square root of both sides gives two solutions: x - 4 = [tex]\pm6[/tex]. The positive root gives us the time after launch when the object hits the ground:
x - 4 = 6
x = 10
Therefore, the object will hit the ground 10 seconds after being launched.
If f(x)=3x+5/x find f(2)
Steps to solve:
f(x) = 3x+5/x; x = 2
~Substitute
f(2) = 3(2)+5/2
~Simplify
f(2) = 6+5/2
~Add
f(2) = 11/2
~Simplify
f(2) = 5.5
Best of Luck!
what is the solution of the system equations y =-3x +8 y = -5x -2
Answer:
Since both equations are equal to y, we can set them equal to each other.
y =-3x +8
y = -5x -2
-3x +8 = -5x -2
Solve for x.To do this, we need to get x by itself. First, move all the numbers to one side of the equation, and all the variables to the other.
-3x +8 = -5x -2
Add 5x to both sides
-3x+5x +8=-5x+5x -2
2x+8=-2
Subtract 8 from both sides
2x+8-8 = -2-8
2x=-10
Now, all the numbers are on one side, with the variables on the other. x is not by itself, it is being multiplied by 2. To undo this, divide both sides by 2
2x/2= -10/2
x= -5
Now, to find y, substitute -5 in for x in one of the equations.
y = -5x -2
y= -5(-5) -2
y=25-2
y=23
Put the solution into (x,y)
The solution is (-5, 23)
How to find radius diameter circumference and area
Answer:
To find the radius diameter circumference and area, The area of a circle = π x radius^2, Circumference of a circle = π x diameter, Remember that the diameter = 2 x radius.
Step-by-step explanation:
Find the volume of a right circular cone that has a height of 2.5 ft and a base with a diameter of 8 ft. Round your answer to the nearest tenth of a cubic foot.
Answer:
41.9 cubic feet
Step-by-step explanation:
The formula for the volume of a cone is
V = 1/3πr^2h, where r=radius and h=height.
Diameter = 2*radius, so our radius is 4 ft. Plug these values in:
V = 1/3πr^2h
= 1/3π4^2 * 2.5
= 40π/3 cubic feet = about 41.9 cubic feet
The volume of a right circular cone with a height of 2.5 ft and a base diameter of 8 ft is approximately 41.9 cubic feet when rounded to the nearest tenth.
To find the volume of a right circular cone, we'll use the formula for the volume of a cone: V = (1/3) π r^2 h. First, we need to find the radius of the cone's base. Since the diameter is given as 8 ft, the radius (r) is half that value, so r = 4 ft.
The volume (V) is then calculated as follows:
V = (1/3) πr^2 hV = (1/3) × π× (4 ft)^2 × 2.5 ftV = (1/3) × π× 16 ft^2 × 2.5 ftV = (1/3) × π× 40 ft^3V ≈ (1/3) × 3.1416 × 40 ft^3V ≈ 41.887 ft^3Rounding to the nearest tenth, the volume is approximately 41.9 cubic feet.
SAT scores have a mean of 1026 and a standard deviation of 209. ACT scores have a mean of 20.8 and a standard deviation of 4.8. A student takes both tests while a junior and scores 860 on the SAT and 16 on the ACT. Compare the scores.
Answer:
The z-score for SAT exam of junior is much small than his ACT score. This means he performed well in his ACT exam and performed poor in his SAT exam.
Step-by-step explanation:
Mean SAT scores = 1026
Standard Deviation = 209
Mean ACT score = 20.8
Standard Deviation = 4.8
We are given SAT and ACT scores of a student and we have to compare them. We cannot compare them directly so we have to Normalize them i.e. convert them into such a form that we can compare the numbers in a meaningful manner. The best way out is to convert both the values into their equivalent z-scores and then do the comparison. Comparison of equivalent z-scores will tell us which score is higher and which is lower.
The formula to calculate the z-score is:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Here, μ is the mean and σ is the standard deviation. x is the value we want to convert to z score.
z-score for junior scoring 860 in SAT exam will be:
[tex]z=\frac{860-1026}{209}=-7.59[/tex]
z-score for junior scoring 16 in ACT exam will be:
[tex]z=\frac{16-20.8}{4.8}=-1[/tex]
The z-score for SAT exam of junior is much small than his ACT score. This means he performed well in his ACT exam and performed poor in his SAT exam.
An arch for a bridge over a highway is in the form of a semi ellipse. The top of the arch is 35 feet above ground (the major axis). What should the span of the bridge be (the length of its minor axis) if the height 27 feet from the center is to be 15 feet above ground? Round to two decimal places
To find the span of the bridge, or the length of its minor axis, we use the equation for an ellipse with the given dimensions and solve for 'b'. Then, we multiply 'b' by 2 to find the total span.
To determine the span of the bridge, or the length of its minor axis, we know that the top of the arch (which coincides with the semi-major axis) is 35 feet above the ground and the height is 15 feet above the ground at a distance of 27 feet from the center. The equation for an ellipse with a vertical major axis is:
(x^2/b^2) + (y^2/a^2) = 1where 'a' is the semi-major axis and 'b' is the semi-minor axis. Since the total height is 35 feet, the semi-major axis, 'a', is 35/2 = 17.5 feet. The distance of 27 feet from the center to the point where the height is 15 feet can be plugged into the equation with 'y' being the remaining height from that point to the top of the arch:
(27^2/b^2) + ((35-15)^2/(17.5)^2) = 1Upon calculating and rearranging the terms, we have:
b^2 = 27^2 / (1 - 400/306.25)Rounding 'b', the semi-minor axis, to two decimal places will give us the span of the bridge which is twice 'b' because it's a complete minor axis.
To find the span of the bridge (the length of its minor axis), we first need to determine the equation of the ellipse.
The standard equation of an ellipse with the center at the origin and the major axis along the x-axis is:
[tex]\[ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \][/tex]
Where \( a \) is the semi-major axis (half of the major axis) and [tex]\( b \)[/tex] is the semi-minor axis (half of the minor axis).
Given that the top of the arch is 35 feet above the ground (the major axis) and the height 27 feet from the center is to be 15 feet above the ground, we can set up the following system of equations:
1. When [tex]\( y = 0 \)[/tex] (ground level), [tex]\( x = a \)[/tex]
2. When [tex]\( y = 27 \)[/tex] (height above the center), [tex]\( x = 15 \)[/tex]
Using these conditions, we can solve for [tex]\( a \) and \( b \):[/tex]
[tex]1. \( \frac{a^2}{a^2} + \frac{0}{b^2} = 1 \)2. \( \frac{15^2}{a^2} + \frac{27^2}{b^2} = 1 \)[/tex]
Solving equation 1 for[tex]\( a \):[/tex]
[tex]\[ \frac{a^2}{a^2} = 1 \]\[ a = a \][/tex]
Solving equation 2 for [tex]\( b \):[/tex]
[tex]\[ \frac{15^2}{a^2} + \frac{27^2}{b^2} = 1 \]\[ \frac{225}{a^2} + \frac{729}{b^2} = 1 \]\[ \frac{729}{b^2} = 1 - \frac{225}{a^2} \]\[ b^2 = \frac{729a^2}{a^2 - 225} \]\[ b = \sqrt{\frac{729a^2}{a^2 - 225}} \][/tex]
We already know that [tex]\( a = 35 \)[/tex](since it's the distance from the center to the top of the arch).
[tex]\[ b = \sqrt{\frac{729 \times 35^2}{35^2 - 225}} \][/tex]
Now we can calculate [tex]\( b \):[/tex]
[tex]\[ b = \sqrt{\frac{729 \times 1225}{1225 - 225}} \]\[ b = \sqrt{\frac{893025}{1000}} \]\[ b ≈ \sqrt{893.025} \]\[ b ≈ 29.88 \][/tex]
So, the span of the bridge (the length of its minor axis) should be approximately 29.88 feet, rounded to two decimal places.
Maria drives at a rate of 60 miles per hour. It takes her 3 hours to get to her aunt's house. How long will it take if she drives at a rate of 50 miles per hour?
Answer:
3.4 miles
Step-by-step explanation:
60 × 3 = 180
she has to drive 180 miles
180 ÷ 50 = 3.4
3.4 miles
In this problem, we need to understand the relationship between rate, time and distance. Here, we establish that Maria's aunt's house is 180 miles away. When Maria drives at a rate of 50 miles per hour, it takes her 3.6 hours to reach her aunt's house.
Explanation:This is a problem of rate, time, and distance, specifically about understanding how changes in rate (or speed) affect time. Here, Maria drives to her aunt's house at a rate of 60 miles per hour, which takes 3 hours. The distance to her aunt's house, then, is 60 miles/hour times 3 hours, or 180 miles. We know that distance = rate times time (D = rt).
Now, when Maria drives at a rate of 50 miles per hour, the time will change. To find the new time, we rearrange the formula to t = D/r. Plugging the values in, t = 180 miles / 50 miles/hour, we get 3.6 hours. So, it would take Maria 3.6 hours to reach her aunt's house if she drives at a rate of 50 miles per hour.
Learn more about Rate, Time, and Distance here:https://brainly.com/question/35683374
#SPJ2