What is the solution to the equation below round your answer to two decimal places 7^x=77

a cylinder shaped can needs to be constructed to hold 400 cubic centimeters of soup. the material for the sides of the can costs

fredd [130]

The dimensions of the can are radius of can = 4cm and

height of can = 78.6cm

What is the volume of cylinder?

A cylinder can be seen as a collection of multiple congruent disks, stacked one above the other. In order to calculate the space occupied by a cylinder, we calculate the space occupied by each disk and then add them up.

Thus, the volume of the cylinder can be given by the product of the area of base and height.

Volume of cylinder = πr²h

According to the given question:

We have V cylinder = V = 400cc

We will first find the areas involved

Let x = radius of base then area of the base = π*x² and this is the area of the top too

For lateral area we need to get h the height of the cylinder as function of x

V = πx²h ⇒ h= v/πx² ⇒ h = 400/πx²

Now the total area of the cylinder is:

A(x) = Area of the base + area of the top + lateral area

A(x) = 2*π*x² + 2πx h ⇒ A(x) = 2*π*x² + 2πx (V/πx² )

A(x) = 2*π*x² + 800/x

Taking derivatives:

A´(x) = 4πx - 800/x²

A´(x) = 0 4πx - 800/x² =0 ⇒ πx - 200/x² = 0

( πx³ - 200 )/ x² = 0

πx³ - 200 = 0

x = 4 cm

and h = 400/πx² ⇒ h = 78.6 cm

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3 0

9 months ago

How to do I solve this

padilas [110]

4. 2b-6+3b=
5b-6=143
5b=143+6
5b=149

b=149
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5

5 0

3 years ago

Enos took out a 25-year loan for $135,000 at an APR of 6.0%, compounded monthly, and he is making monthly payments of $869.81. W

Alborosie

Present value = 135000
Monthly interest, i = 0.06/12 = 0.005
Monthly payment, A= 869.81

Future value of loan after 16 years
$F=P(1+i)^n$ [compound interest formula]
$=135000(1+.005)^{16*12}$
$=351736.652$

Future value of payments after 16 years
$\frac{A((1+i)^n-1)}{i}$
$=\frac{869.81((1+0.005)^{16*12}-1)}{0.005}$
$=279287.456$

Balance = future value of loan - future value of payments
=351736.652-279288.456
= $ 72448.20

Note: the exact monthly payment for a 25-year mortgage is
$A=\frac{P(i*(1+i)^n)}{(1+i)^n-1}$
$=\frac{135000(0.005*(1+0.005)^{25*12}}{(1+0.005)^{25*12}-1}$
$=869.806892$

Repeating the previous calculation with this "exact" monthly payment gives
Balance = 72448.197, very close to one of the choices.

So we conclude that the exact value obtained above differs from the answer choices is due to the precision (or lack of it) of the provided data.

The closest choice is therefore <span>$72,449.19</span>

6 0

2 years ago

Read 2 more answers

Solve for x <br> 23=7/9(6z-36)+9

zzz [600]

Answer: $z=9$