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alekssr [168]
3 years ago
14

Help geometry question

Mathematics
1 answer:
loris [4]3 years ago
6 0

Answer: x=16 t=5

Step-by-step explanation:

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Find the percent of discount. Round to the nearest tenth
maxonik [38]

Answer: 69%

Step-by-step explanation:

16820x100= 1682000

1682000÷24365=69.033

8 0
3 years ago
A metal cylinder can with an open top and closed bottom is to have volume 4 cubic feet. Approximate the dimensions that require
Aleksandr-060686 [28]

Answer:

r\approx 1.084\ feet

h\approx 1.084\ feet

\displaystyle A=11.07\ ft^2

Step-by-step explanation:

<u>Optimizing With Derivatives </u>

The procedure to optimize a function (find its maximum or minimum) consists in :

  •  Produce a function which depends on only one variable
  •  Compute the first derivative and set it equal to 0
  •  Find the values for the variable, called critical points
  •  Compute the second derivative
  •  Evaluate the second derivative in the critical points. If it results positive, the critical point is a minimum, if it's negative, the critical point is a maximum

We know a cylinder has a volume of 4 ft^3. The volume of a cylinder is given by

\displaystyle V=\pi r^2h

Equating it to 4

\displaystyle \pi r^2h=4

Let's solve for h

\displaystyle h=\frac{4}{\pi r^2}

A cylinder with an open-top has only one circle as the shape of the lid and has a lateral area computed as a rectangle of height h and base equal to the length of a circle. Thus, the total area of the material to make the cylinder is

\displaystyle A=\pi r^2+2\pi rh

Replacing the formula of h

\displaystyle A=\pi r^2+2\pi r \left (\frac{4}{\pi r^2}\right )

Simplifying

\displaystyle A=\pi r^2+\frac{8}{r}

We have the function of the area in terms of one variable. Now we compute the first derivative and equal it to zero

\displaystyle A'=2\pi r-\frac{8}{r^2}=0

Rearranging

\displaystyle 2\pi r=\frac{8}{r^2}

Solving for r

\displaystyle r^3=\frac{4}{\pi }

\displaystyle r=\sqrt[3]{\frac{4}{\pi }}\approx 1.084\ feet

Computing h

\displaystyle h=\frac{4}{\pi \ r^2}\approx 1.084\ feet

We can see the height and the radius are of the same size. We check if the critical point is a maximum or a minimum by computing the second derivative

\displaystyle A''=2\pi+\frac{16}{r^3}

We can see it will be always positive regardless of the value of r (assumed positive too), so the critical point is a minimum.

The minimum area is

\displaystyle A=\pi(1.084)^2+\frac{8}{1.084}

\boxed{ A=11.07\ ft^2}

8 0
3 years ago
Please help I really need it
yan [13]

Answer:

A) Yes, because there is a steady correlation between the 2 variables

B) After 2 hours, they have traveled 100 miles

C) After 5 hours, they traveled 250 miles

D) After 1 Hour, they traveled 50 miles

In conclusion, for every hour of time, they travel a comstant speed of 50 miles.

5 0
3 years ago
I am stuck on |x+3|&lt;5. Can someone help?
NeTakaya
the answer would be -8<x<2
5 0
3 years ago
The cost of going to the big playland park for a family is given by c = 15x + 50, where c represents the cost and x represents t
marusya05 [52]
C = 15x + 50

let c be $125 since c represents the cost
15x + 50 = 125
15x = 125 - 50
15x = $75
x = 75 ÷ 15
x = 5
3 0
3 years ago
Read 2 more answers
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