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strojnjashka [21]
3 years ago
5

the diameter of a spherical basketball is 10 inches what is the volume of the basketball give the exact solution or round your a

nswer to the nearest cubic inch. plzzzzzz!!!! urgent!!!!!!!
Mathematics
2 answers:
DiKsa [7]3 years ago
7 0
Volume of a sphere is 4/3(pi r ^3)

You were given d = 10 so r = 5

Then just plug and chug
Mkey [24]3 years ago
6 0

Answer:

Exact volume:  

\displaystyle\frac{500}{3}\pi \text{ in}^3

Rounded volume: 524 cubic inches.

Step-by-step solution:

The formula for the volume of a sphere is:

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

Where r is the radius of the sphere.

The radius is half the diameter, therefore it is r=10/2=5

We plug it into the formula and we get:

\displaystyle V=\frac{4}{3}\pi (5)^3

Then we get:

\displaystyle V=\frac{4}{3}\pi (125)=\frac{500}{3}\pi

If we do it in our calculator we get 523.599 that rounded to the nearest whole is 524 cubic inches .

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I got x = 1

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Find the equation of the tangent line to the curve y equals left parenthesis x minus 3 right parenthesis superscript 7 baseline
Rashid [163]

We have been given the expression to be y=(x-3)^7(x+1)^2

Since we need to find the tangent at a point, we will have to find the derivative of y as the slope of the tangent at a given point on the curve is always equal to value of the derivative at that point.

Thus, we have to find \frac{dy}{dx}=\frac{d}{dx} (x-3)^7(x+1)^2

We will use the product rule of derivatives to find \frac{dy}{dx}

Thus, y'=7(x-3)^6(x+1)^2+(x-3)^7\times2(x+1) (using the product rule which states that (fg)'=f'g+fg')

Taking the common factors out we get:

y'=(x-3)^6(x+1)(7(x+1)+2(x-3))

y'=(x-3)^6(x+1)(7x+7+2x-6)=(x-3)^6(x+1)(9x+1)

Thus, y' at x=4 is given by:

y'_{x=4}=Slope of the tangent of y at x=4=m

Thus, m=(4-3)^6(4+1)(9\times4+1)=185

Now, the equation of the tangent line which passes through (x_{1}, y_{1}) and has slope m is given by:

y-y_{1}=m(x-x_{1})

Thus, the equation of the tangent line which passes through (4,25) and has the slope 185 isy-25=185(x-4)

Which can be simplified to y=185x-740+25=185x-715

Thus, y=185x-715

This is the required equation of the tangent.

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3 years ago
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