A zoo is designing a giant bird cage consisting of a cylinder of radius rr feet and height hh feet with a hemisphere on top (no bottom). The material for the hemisphere costs 2020 per square foot and the material for the cylindrical sides costs 1010 per square foot; the zoo has a budget of 45004500. Find the values of rr and hh giving the birds the greatest space inside assuming the zoo stays within its budget. Note: surface of a cylinder's side 2πrh2πrh, surface of a sphere 4πr24πr2, volume of a cylinder's side πr2hπr2h, volume of a sphere 43πr343πr3
Answer:
r = 42,32 ft
h = 84.8 ft
Step-by-step explanation:
We are going to apply Lagrange multipliers method
The greatest space means maximum volume
V(cage) = Vol. of the cylinder + volume of the hemisphere
V(cylinder ) = π*r²*h
V(sphere) = (4/3)*π*r² ⇒ V(hemisphere) = (2/3)*π*r³
V(cage) = π*r²*h + (2/3)*π*r³
Associated costs:
Costs = cost of cylinder + cost of hemisphere
Area of the cylinder = Lateral area ( no bottom no top)
Area of the cylinder = 2*π*r*h
Area of hemisphere = 2*π*r²
A(r,h) = 2*π*r*h + 2*π*r²
C(r , h ) = 10* 2*π*r*h + 20* 2*π*r² C(r , h ) = 20*π*r*h + 40*π*r²
4500 = 20*π*r*h + 40*π*r²
20*π*r*h + 40*π*r² - 4500 = 0 20*π*r*h + 40*π*r² - 4500 = g(r,h)
V(cage) = π*r²*h + (2/3)*π*r³
δV/δr = 2*r*π*h + 2*π*r² δg(r,h)/δr = 20*π*h + 80*π*r
δV/δh = π*r² δg(r,h)/δh = 20*π*r
δV/δr = λ* δg(r,h)/δr
2*r*π*h + 2*π*r² = λ* 20*π*h + 80*π*r
2*r*π* ( h + r ) = 20*π* λ* ( h + 4*r)
r* ( h + r ) = 10*λ* ( h + 4*r) (1)
δV/δh = λ* δg(r,h)/δh
π*r² = 20*λ*π*r r = 20*λ (2)
20*π*r*h + 40*π*r² - 4500 = 0 (3)
We need to sole the system of equation 1 ; 2 ; 3
r = 20*λ plugging that value in equation 1
20*λ ( h + 20*λ ) = 10*λ* ( h + 4*r)
2( h + 20*λ ) = ( h + 4*20*λ)
2*h + 40*λ = h + 80*λ
h = 40*λ
20*π*r*h + 40*π*r² - 4500 = 0
20*π*20*λ*40*λ + 40*π+400λ² - 4500 = 0
16000*π*λ² + 16000*π*λ² = 4500
32000*π*λ² = 4500
320*π*λ² = 4500
λ² = 4500/1004,8 λ² = 4.48 λ = 2.12
Then
r = 20* λ r = 42,32 ft
h = 40* λ h = 84.8 ft
khalil has a circular cake that he plans to share equally betweeb himself and 5 friends. if tge cake is 8 inched in a diameter, what will be the length of the arc of each slice of cake.
Answer:
4.2
Step-by-step explanation:
The length of the arc of each slice of cake will be 4.18 inches if Khali shares the cake between him and 5 friends equally.
What is the circumference of a circle?
The circumference is the length of the outer boundary of the circle. It can be calculated as under:
Circumference=2πr
How to find length of arc?
We have been given that the diameter of the cake is 8 inches So, the radius becomes 4 inches. We have to calculate the circumference of the cake. so the circumference becomes:
Circumference=2π(4)=8π
=8*22/7
=25.1
Then we have to divide it into 6 people so it will be 25.1/6=4.18 inches.
Hence the length of the arc will be 4.8 inches.
Learn more about circumference at https://brainly.com/question/20489969
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Find the percent of decrease from 46 songs to 41 songs. Round to the nearest tenth of a percent if necessary.
percent of decrease
%
Answer:
10.9 %
Step-by-step explanation:
46 - 41 = 5
5/46 * 100% = 10.8695652174%
Rounded
10.9 %
You decide to increase your Utah county coronavirus sample to 10 counties and estimate the same sample standard deviation you did with your sample of 5 counties. This will ______________ the margin of error associated with your 90% confidence interval.
Answer:
This will decrease the margin of error associated with your 90% confidence interval.
Step-by-step explanation:
Margin of error:
The margin of error of a confidence interval is given by a formula that follows the following format:
[tex]M = z\frac{s}{\sqrt{n}}[/tex]
In which z is related to the confidence level, s is related to the standard deviation and n is related to the size of sample.
From the formula:
M and n are inversely proportional, which means that if the sample size is increased, the margin of error decreases.
In this question:
Sample size increases from 5 to 10, so the margin of error decreases.
\left(a+b\right)^2 hihihihihiihihihihihih
Consider, we need to find the expanded form of the given expression.
Given:
The expression is:
[tex]\left(a+b\right)^2[/tex]
To find:
The expanded form of the given expression.
Solution:
We have,
[tex]\left(a+b\right)^2[/tex]
It can be written as:
[tex]\left(a+b\right)^2=(a+b)(a+b)[/tex]
Using distributive property of multiplication over addition, we get
[tex]\left(a+b\right)^2=a(a+b)+b(a+b)[/tex]
[tex]\left(a+b\right)^2=a(a)+a(b)+b(a)+b(b)[/tex]
[tex]\left(a+b\right)^2=a^2+ab+ab+b^2[/tex]
[tex]\left(a+b\right)^2=a^2+2ab+b^2[/tex]
Therefore, the expanded form of the given expression is [tex]a^2+2ab+b^2[/tex].
Find the output, y, when the input, x, is -1
Answer:
No solution is possible from the information provided
Step-by-step explanation:
How many times bigger is a group of 20 coins than a group of 5 coins
Answer:
It is there difference:
20-5
15
There are 9 students in a class: 7 boys and 2 girls.
If the teacher picks a group of 3 at random, what is the probability that everyone in the group is a boy?
Answer: 9/7
Step-by-step explanation:
find the slope from the graph. Leave the answer as a reduced fraction. *
I attached a picture below: I will give brainliest
Answer:
Slope = -2
Step-by-step explanation:
Point 1 (-1, 2)
Point 2 (1, -2)
Formula to find slope = y2 - y1 / x2 - x1
Slope = 2-(-2) / -1-1
Slope = 4 / -2
Slope = -2
Noah is ordering a taxi from an online taxi service. The taxi charges $2.50 just for the pickup and then an additional $2 per mile driven. How much would a taxi ride cost if Noah is riding for 4 miles? How much would a taxi ride cost that is mm miles long?
Answer:
$10.50
Step-by-step explanation:
We can make an equation
2.50+2x=?
x=4 because we are riding 4 miles.
so it's 2.5+2*4=?
let's solve
2.5+8=$10.50
The Cost of the taxi ride for 4 miles is $10.50 and Charge for m miles is 2.50 + 2m
Given:
Pick up charge = $2.50
Charge per mile = $2
Number of miles = 4
Cost of the taxi ride for 4 miles = Pick up charge + (Charge per mile + Number of miles)
= 2.50 + (2 × 4)
= 2.50 + 8
= $10.50
Charge for m miles = Pick up charge + (Charge per mile + Number of miles)
= 2.50 + (2 × m)
= 2.50 + 2m
Therefore, Cost of the taxi ride for 4 miles is $10.50 and Charge for m miles is 2.50 + 2m
Read more:
https://brainly.com/question/8957185
Joe drives for 3 hours and covers 201 miles. In miles per hour, how fast was he driving?
Answer:
50
Step-by-step explanation:
A, B, and C are collinear points:
B is between A and C.
If AB = 3x + 4, BC = 4x - 1, and AC = 6x + 5,
find AC.
9514 1404 393
Answer:
AC = 17
Step-by-step explanation:
The segment sum theorem tells you ...
AB +BC = AC
Substituting the given expressions, we have ...
(3x +4) +(4x -1) = (6x +5)
x = 2 . . . . . . . . . . . . . . . . . . subtract 3+6x from both sides
AC = 6x +5 = 6(2) +5
AC = 17
_____
AB = 10, BC = 7
guys i need this an answers full please
Answer:
See below.
Step-by-step explanation:
14.
12.5/2.5 = 5
15.
(i) [(-75)/15]/5 = -5/5 = -1
(ii) 13 / [(-2) + 1] = 13 / (-1) = -13
16.
(i) 39 + (-24) - 15 = 0
36 + (-52) - (-36) = 20
Answer: <
(ii) (-10) - 4 = -14
(-10) - (-4) = -10 + 4 = -6
Answer: <
17.
He reads 1/4 book in 1 hour.
He reads 1 book in 4 hours.
In 2 1/6 hours he reads:
(2 1/6)/4 part of the book = (13/6) / 4 = 13/24 part of the book
(i) 2/5 / 1 1/2 = 2/5 / 3/2 = 2/5 * 2/3 = 4/15
(ii) 7/3 / 2 = 7/3 * 1/2 = 7/6
Answer:
14. 5
15. (i) -1 (ii) -13
16. (i) < (ii) <
17. 24/13
Step-by-step explanation:
4n-6 in as a undistributed expression
Answer:
2( 2n-3)
Step-by-step explanation:
4n-6
2*2 n - 2*3
Factor out the greatest common factor
2( 2n-3)
6. A company builds a model of its earning, and finds that its profit fits the linear model()=5―2500 Where p is the profit in dollars and q is the quantity of its product sold. a) Explain what the slope and y-intercept mean in the context of the problem. Be specific and answer in complete sentence. (2 points)
Answer:
The slope of 5 means that for each product sold, the profit increases by 5, and the intercept of -2500 means that if no products are sold, the company loses 2500.
Step-by-step explanation:
Linear function:
A linear function has the following format:
[tex]y = mx + b[/tex]
In which m is the slope, that is, by how much y changes for each unit of x, and b is the y-intercept, which is the values of y when x = 0.
In this question:
[tex]p(q) = 5q - 2500[/tex]
p is the profit in dollars and q is the quantity of its product sold.
a) Explain what the slope and y-intercept mean in the context of the problem.
The slope of 5 means that for each product sold, the profit increases by 5, and the intercept of -2500 means that if no products are sold, the company loses 2500.
Graph the image of Kite BCDE after a translation 5 units down.
Answer:
Move each point, one by one, 5 units down
so, D(-7,10) becomes [tex]D^{1}[/tex](-7,5). Y value was decreased by 5
Find the sine of ZF.
H
2/2
3/3
F
Write your answer in simplified, rationalized form. Do not round.
sin (F) =
Answer:
1/9 √57
Step-by-step explanation:
the length of HG = √(3√3² - 2√2²)
= √(27-8) = √19
sin L F = HG/GF = √19/ 3√3
= 1/9 √57
the sum of 1+2-3-4+5+6-7-8+9+10-...+1378
Answer:
1389
Step-by-step explanation:
hope this helps?
find the value of x if 3x over 2 equals to 3
Answer:
x = 2
Step-by-step explanation:
3x/2 = 3/1
cross-multiply to get:
3x = 6
divide each side by 2 to get:
x = 2
the solution set for -2x[tex]-2x^{2}+12x=0[/tex]
PLEASE HELP
A salesperson works 40 hours per week at a job where has two options for being paid. Option A is an hourly wage of $25. Option B is a commission rate of 5% on weekly sales. How much does need to sell this week to earn the same amount with the two options?
he needs to sell$___this week
Answer:
He must sell 20,000 to make the same amount
Step-by-step explanation:
Option A
25 h where hourly rate time number of hours ( 40 hours)
25 * 40 = 1000
Option B =
.05 * s where s is the amount of sales and 5% commission
We want them to be equal
1000 = .05s
Divide each side by .05
1000/.05 = .05s/.05
20000 = s
He must sell 20,000 to make the same amount
A road has a scale of 1:50 000 The length of a road on the map is 8.5cm.Work out the length of the real road in kilometres
Answer:
ok so
8.5*150000
1275000 cm into kilometers is
12.75 kilometers
Hope This Helps!!!
Choose the equation of the line that is parallel to the x-axis.
x = 4
x + y = 0
x = y
y = 4
reflectiion across y=x
9514 1404 393
Answer:
see attached
Step-by-step explanation:
The reflection across y=-x swaps the coordinates and negates both of them. The first-quadrant figure becomes a third-quadrant figure.
(x, y) ⇒ (-y, -x)
1. Determine the length and perimeter of Laura's property.
(5)
9514 1404 393
Answer:
length: 40 mperimeter: 136 marea: 653 m²volume: 6.52 m³Step-by-step explanation:
1.The outer dimensions of the property are 20 squares (length) by 14 squares. Each square is 2 m on a side, so the overall length of the property is ...
(20 squares)×(2 m/square) = 40 m . . . . length
The overall width of the property is ...
(14 squares)×(2 m/square) = 28 m . . . . width
Then the perimeter is ...
P = 2(length + width) = 2(40 +28) m = 136 m . . . . perimeter
__
Additional comment
We have computed the perimeter as though the plot were a rectangle. If you carefully consider the total length of horizontal edges and the total length of vertical edges, you see that those totals are the same as they would be for a 20×14 square (40×28 m) rectangle.
_____
2.The area of open ground is perhaps most easily computed by finding the area that must be subtracted from the overall 20×14 square rectangle. Those exclusions will be (in dimensions of squares) ...
lower right corner: 8 wide by 3 high = 24 squaresfish pond: 2 wide by 3 high = 6 squaresveranda: 4 wide by 4 high = 16 squareshouse: 9 wide by 7 high = 63 squarespavement: 4 wide by 2 high = 8 squaresThe total area of exclusions is 24+6+16+63+8 = 117 squares. The bounding rectangle is 20 by 14 = 280 squares, so the open ground is ...
280 squares - 117 squares = 163 squares
At (2 m)(2 m) = 4 m² per grid square, that's an area of ...
(163 squares)(4 m²/square) = 652 m²
The surface area of the open ground is 652 m².
_____
3.The volume is given by the formula ...
V = Bh
where B is the base area and h is the height.
1 cm = 1/100 m = 0.01 m thickness. That means the total volume is ...
V = (652 m²)(0.01 m) = 6.52 m³
6.52 cubic meters of topsoil are needed to cover the open ground to a depth of 1 cm.
6. a semicircle has as its diameter the hypotenuse of a right triangle shown below. determine the area of the semicircle to the nearest tenth of a square centimeter. show how you arrived at your answer.
Answer:
[tex]A = 137.3cm^2[/tex]
Step-by-step explanation:
Given
See attachment
Required
The area of the semicircle
First, we calculate the hypotenuse (h) of the triangle
Considering only the triangle, we have:
[tex]\cos(68) = \frac{7}{h}[/tex] --- cosine formula
Make h the subject
[tex]h = \frac{7}{\cos(68)}[/tex]
[tex]h = \frac{7}{0.3746}[/tex]
[tex]h = 18.7[/tex]
The area of the semicircle is then calculated as:
[tex]A = \frac{\pi h^2}{8}[/tex]
This gives:
[tex]A = \frac{3.14 * 18.7^2}{8}[/tex]
[tex]A = \frac{1098.03}{8}[/tex]
[tex]A = 137.3cm^2[/tex]
graph the
function f(x)=10(2)x
Answer:
G.o.o.g.l.e
Step-by-step explanation:
If you search up 'f(x)=10(2)x' on g.o.o.g.l.e it will draw the graph for you.
If this helps you, please give brainliest!
A picture frame (see figure) has a total perimeter of 3 feet. The width of the frame is 0.64 times its length. Find the dimensions of the frame. (Round your answers to two decimal places.)
Answer:
[tex]\approx 0.59\text{ ft by }0.91\text{ ft}[/tex]
Step-by-step explanation:
Let [tex]\ell[/tex] represent the length of the rectangle. The width can be represented as [tex]0.64\ell[/tex].
The perimeter of a rectangle with lengths [tex]l[/tex] and [tex]w[/tex] is given by [tex]p=2l+2w[/tex].
Thus, we have:
[tex]2\ell+2(0.64\ell)=3,\\2\ell +1.28\ell=3,\\3.28\ell=3,\\\ell=0.91463414634\approx 0.91[/tex]
The width is then [tex]0.64(0.91463414634)=0.58536585365\approx 0.59[/tex].
Cho mặt bậc hai
z=\sqrt(x^(2)+y^(2))
. Đây là mặt gì?
Answer:
ñkxkdbdidvdv
Step-by-step explanation:
hsu3jdjfiebdic ic8 e
Police response time to an emergency call is the difference between the time the call is first received by the dispatcher and the time a patrol car radios that it has arrived at the scene. Over a long period of time, it has been determined that the police response time has a normal distribution with a mean of 9.6 minutes and a standard deviation of 2.3 minutes. For a randomly received emergency call, find the following probabilities. (For each answer, enter a number. Round your answers to four decimal places.)
a. between 5 and 10 min
b. less than 5 min
c. more than 10 min
Answer:
a) 0.5447
b) 0.0228
c) 0.4325
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Normal distribution with a mean of 9.6 minutes and a standard deviation of 2.3 minutes.
This means that [tex]\mu = 9.6, \sigma = 2.3[/tex]
a. between 5 and 10 min
This is the p-value of Z when X = 10 subtracted by the p-value of Z when X = 5. So
X = 10
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{10 - 9.6}{2.3}[/tex]
[tex]Z = 0.17[/tex]
[tex]Z = 0.17[/tex] has a p-value of 0.5675
X = 5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{5 - 9.6}{2.3}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a p-value of 0.0228
0.5675 - 0.0228 = 0.5447 probability that a randomly received emergency call is between 5 and 10 minutes.
b. less than 5 min
p-value of Z when X = 5, which from item a), is 0.0228, so 0.0228 probability that a randomly received emergency call is of less than 5 minutes.
c. more than 10 min
1 subtracted by the p-value of Z when X = 10, which, from item a), is of 0.5675.
1 - 0.5675 = 0.4325
0.4325 probability that a randomly received emergency call is of more than 10 minutes.