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ANTONII [103]
3 years ago
5

The height of the pyramid in the diagram is three times the radius of the cone. The base area of the pyramid is the same as the

base area of the cone. What is the expression for the volume of the pyramid in terms of the radius r of the cone?
Mathematics
2 answers:
jeyben [28]3 years ago
8 0
It is said that the area of the base of the pyramid and that of the cone are equal. In this case, the are a of the square base is s^2 while the area of circle is pi r^2. Hence, s = sqrt pi * r. The volume of the pyramid has a formula of 1/3 bh. h is equal to 3r. Hence, V =  1/3 bh = 1/3 pi r^2 * 3r =  pi r^3. 
nataly862011 [7]3 years ago
7 0

Answer:

1/3 pi r^2 * 3r =  pi r^3.

Step-by-step explanation:

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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
Rewrite the equation 2x + 3y = 6 in slope-intercept form.
valkas [14]
2x+3y=6
3y=6-2x
y=2-2/3x
y=-2/3x+2
the 3rd one is correct
3 0
3 years ago
The expression 1.08 + 1.02b predicts the end- of the year value if a financial portfolio where S is the value of the stocks and
iragen [17]

Answer:

We have

Stock = $200

Bonds = $100

Substitute these values into 1.08s+1.02b, where 's' is stock and 'b' is bond

.() + .() =

Predicted end of year value is $318

4 0
3 years ago
PLEASE HELP!!! I WILL GIVE BRAINY!!!
11111nata11111 [884]
The first one is 4/3

We can solve by,

{x}^{2} \times 180 = 320

x = \frac{4}{3}

{ \frac{4}{3} }^{2} \times 180 = 320 = true

~~

The second one is 35.

Idk how to explain...

~~

The third one is a 6 - gon therefore cannot be C or D.

I'd say the third one is A., it looks like it's caving in.
4 0
2 years ago
Read 2 more answers
The radius,r , of a sphere is 4 . 3m Calculate the sphere's volume,v . Use the value 3.14 for sqaure, and round your answer to t
kotykmax [81]

Answer:

V(s) = 332,9 m³

Step-by-step explanation:

The volume of a sphere is:

V(s) = (4/3)*π*r³

if we know  r  = 4,3 m then

V(s)  = (4/3)*3,14*(4,3)³

V(s)  = 332,8693 m³

Rounding the answer to the nearest tenth

V(s) = 332,9 m³

4 0
3 years ago
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