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3 years ago

If the volume of a sphere inscribed in a cubic box is 36pi, find the surface area of the box

Mathematics

1 answer:

Kruka [31]3 years ago

3 0

Answer:

Surface area of the cube = 216 square units

Step-by-step explanation:

Let the length of a side of a cube = x unit

Diameter of the sphere inscribed in this cube = length of a side of the cube

Volume of the sphere = $\frac{4}{3}\pi r^{3}$

Where r = radius of the sphere = $\frac{x}{2}$ units

36π = $\frac{4}{3}\pi (\frac{x}{2})^{3}$

36π = $\frac{4x^{3}\pi }{24}$

36×24 = 4x³

x = $\sqrt[3]{\frac{36\times 24}{4} }$

x = 6 units

Length of a side of the cube = 6 units

Surface area of the cube = 6×(Side)²

= 6×(6)²

= 216

= 216 square units

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A certain college graduate borrows 7864 dollars to buy a car. The lender charges interest at an annual rate of 13%. Assuming tha

White raven [17]

Answer:

Therefore rate of payment = $ 3145.72

Therefore the rate of interest = =$1573.17

Step-by-step explanation:

Consider A represent the balance at time t.

A(0)=$ 7864.

r=13 % =0.13

Rate payment = $k

The balance rate increases by interest (product of interest rate and current balance) and payment rate.

$\frac{dB}{dt} = rB-k$

$\Rightarrow \frac{dB}{dt} - rB=-k$ .......(1)

To solve the equation ,we have to find out the integrating factor.

Here p(t)= the coefficient of B =-r

The integrating factor $=e^{\int p(t) dt$

$=e^{\int (-r)dt$

$=e^{-rt}$

Multiplying the integrating factor the both sides of equation (1)

$e^{-rt}\frac{dB}{dt} -e^{-rt}rB=-ke^{-rt}$

$\Rightarrow e^{-rt}dB - e^{-rt}rBdt=-ke^{-rt}dt$

Integrating both sides

$\Rightarrow \int e^{-rt}dB -\int e^{-rt}rBdt=\int-ke^{-rt}dt$

$\Rightarrow e^{-rt}B=\frac{-ke^{-rt}}{-r} +C$ [ where C arbitrary constant]

$\Rightarrow B(t)=\frac{k}{r} +Ce^{rt}$

Initial condition B=7864 when t =0

$\therefore 7864= \frac{k}{r} - Ce^0$

$\Rightarrow C= \frac{k}{r} -7864$

Then the general solution is

$B(t)=\frac{k}{r}-( \frac{k}{r}-7864)e^{rt}$

To determine the payment rate, we have to put the value of B(3), r and t in the general solution.

Here B(3)=0, r=0.13 and t=3

$B(3)=0=\frac{k}{0.13}-( \frac{k}{0.13}-7864)e^{0.13\times 3}$

$\Rightarrow- 0.48\frac{k}{0.13} +11614.98=0$

⇒k≈3145.72

Therefore rate of payment = $ 3145.72

Therefore the rate of interest = ${(3145.72×3)-7864}

=$1573.17

4 0

3 years ago

Write an equation of the line in slope-intercept form for the graph<br><br> Please helppp

Anvisha [2.4K]

Answer:

y=-4/3+2

Step-by-step explanation:

Sin the slope is going up to the left we can already infer that it is going to be a negative. Still we do the equation y2-y1/x2-x1. In this case 0 is x1 and 2 is y1, 3 is x2, and -2 is y2. Once inserted into the equation you get -2-2/3-0 which equals -4/3 and the y intercept is 2 since thats the point shown were it intercepts the y-axis

8 0

3 years ago

Which expression is equivalent to (4x+11)+7x?

Anna007 [38]

HEY THERE FAM.

THE CORRECT ANSWER IS....<span> D.(4x-7x)+11</span>

4 0

3 years ago

Help me answer 99 plz

Vitek1552 [10]

One tick behind one is 3/4, 1/8 is basically half of 1/4, so find 1/4 and find 1/8, 0 is sort of obvious but then not obvious. three ticks behind 3/4. 2 2/3, count UP from 1 1/4 to find 2 2/3. I really hope I helped! :)

5 0

4 years ago

How much it will take for a bag to travel 5 meters across the floor of it is traveling at 1 m/s

tester [92]

Time = $\frac{distance}{speed}$

The distance the bag will travel is 5 meters, and the speed it is traveling at is 1 m/s. Plug these into the formula for time.

$\frac{5 m}{1 m/s}$ = 5 s
5/1 = 5 and the m (meters) cancel out, so you are left with s, seconds.

It will take the bag 5 seconds to travel across the floor.

5 0

3 years ago