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Virty [35]
3 years ago
15

Find the surface are of a sphere that has a diameter of square root of 29

Mathematics
1 answer:
brilliants [131]3 years ago
5 0

Hello!


The surface area of a sphere can be found using this equation: SA = 4πr².


The radius is half the diameter. So, half of √29 is √29 / 2, in simple terms.


SA = 4π(√29/2)²

SA = 4π(7.25)

SA = 4(7.25)π

SA = 29π

SA = 91.10618...


Therefore, the surface area of this sphere is 91.11 units².

Without multiplying π, the surface area is 29π units².

If the question asked substitute π for 3.14, the answer is 91.06 units².

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Step-by-step explanation:

a) P(X > 6) = (9.5-6)/(9.5-5.5) = 3.5/4 = 0.875

b) P(X < 7) = (7-5.5)/(9.5-5.5) = 1.5/4 = 0.375

c) E(X) = (9.5+5.5)/2 = 7.5

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5 0
3 years ago
find the slope of the curve y=x^2-2x-5 at the point P(2,5) by finding the limit of secant slopes through point P
Fynjy0 [20]

The point (2, 5) is not on the curve; probably you meant to say (2, -5)?

Consider an arbitrary point Q on the curve to the right of P, (t,y(t))=(t,t^2-2t-5), where t>2. The slope of the secant line through P and Q is given by the difference quotient,

\dfrac{(t^2-2t-5)-(-5)}{t-2}=\dfrac{t^2-2t}{t-2}=\dfrac{t(t-2)}{t-2}=t

where we are allowed to simplify because t\neq2.

Then the equation of the secant line is

y-(-5)=t(x-2)\implies y=t(x-2)-5

Taking the limit as t\to2, we have

\displaystyle\lim_{t\to2}t(x-2)-5=2(x-2)-5=2x-9

so the slope of the line tangent to the curve at P as slope 2.

- - -

We can verify this with differentiation. Taking the derivative, we get

\dfrac{\mathrm dy}{\mathrm dx}=2x-2

and at x=2, we get a slope of 2(2)-2=2, as expected.

4 0
3 years ago
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