The graph of the function with the given values f(-2)=-5 and f(4)=4

cylinder shaped can needs to be constructed to hold 200 cubic centimeters of soup. The material for the sides of the can costs 0

Dafna11 [192]

Answer:

Radius=2.09 cm

Height,h=14.57 cm

Step-by-step explanation:

We are given that

Volume of cylinderical shaped can=200 cubic cm.

Cost of sides of can=0.02 cents per square cm

Cost of top and bottom of the can =0.07 cents per square cm

Curved surface area of cylinder= $2\pi rh$

Area of circular base=Area of circular top= $\pi r^2$

Total cost,C(r)= $0.02\times 2\pi rh+2\pi r^2\times 0.07$

Volume of cylinder, $V=\pi r^2 h$

$200=\pi r^2 h$

$h=\frac{200}{\pi r^2}$

Substitute the value of h

$C(r)=0.02\times 2\pi r\times \frac{200}{\pi r^2}+2\pi r^2\times 0.07$

$C(r)=\frac{8}{r}+0.14\pi r^2$

Differentiate w.r.t r

$C'(r)=-\frac{8}{r^2}+0.28\pi r$

$C'(r)=0$

$-\frac{8}{r^2}+0.28\pi r=0$

$0.28\pi r=\frac{8}{r^2}$

$r^3=\frac{8}{0.28\pi}=9.095$

$r=(9.095)^{\frac{1}{3}}=2.09$

Again, differentiate w.r.t r

$C''(r)=\frac{16}{r^3}+0.28\pi$

Substitute the value of r

$C''(2.09)=\frac{16}{(2.09)^3}+0.28\pi=2.63>0$

Therefore,the product cost is minimum at r=2.09

h= $\frac{200}{\pi (2.09)^2}=14.57$

Radius of can,r=2.09 cm

Height of cone,h=14.57 cm

4 0

3 years ago

Calculate the length of the line segment. round your answer to the nearest tenth.

Sunny_sXe [5.5K]

Answer:

c) 8.6

Step-by-step explanation:

Take the coordinates of the two points.

(0,8) and (7,3)

Formula:

√(x₁ - x₂)² + (y₁ - y₂)²

Substitute:

√(0 - 7)² + (8 - 3)²

√(-7)² + (5)²

√(49) + (25)

√(74) ≈ 8.6

8 0

3 years ago

Find the sum using the formulas for the sums of powers of integers ( problem attached )

Natasha2012 [34]

Correct Answer: - 550

We can use the distributive property to distribute the summation to the variables and then get the constant out to apply the summation formulas as shown below in the attached image.

The equation editor does not have a summation symbol, so I have attached the solution using the image.

The correct answer to this question is -550. First option is the correct one.

7 0

3 years ago

5 + 4x + 6 - 2x<br> explain how you would do it

Alona [7]

Answer:

11+2x

Step-by-step explanation:

5+6=11

4x-2x=2x

8 0

2 years ago

Read 2 more answers

What is the equation of the line that passes through the point (3,4) and has an undefined slope?

rosijanka [135]

Answer:

The equation of the line that passes through the point (3,4) and has an undefined slope is x = 3

Step-by-step explanation:

The slope of the horizontal line is zero

The equation of the horizontal line passes through the point (a, b) is y = b

All the points on the horizontal line have the same y-coordinates

The slope of the vertical line is undefined

The equation of the vertical line passes through the point (a, b) is x = a

All the points on the vertical line have the same x-coordinates

Let us solve the question

∵ The line has an undefined slope

∴ The line is a vertical line

∵ The equation of the vertical line is x = a, where a is the x-coordinate

of any point on the line

∵ The line passes through the point (3, 4)

∴ a = 3

∴ The equation of the line is x = 3

The equation of the line that passes through the point (3,4) and has an undefined slope is x = 3

5 0

3 years ago