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Dovator [93]
3 years ago
10

The radius of a sphere is measured to be 3.0 inches. If the measurement is correct within 0.01 inches, use differentials to esti

mate the error in the volume of sphere.
Mathematics
1 answer:
Zarrin [17]3 years ago
5 0

Answer:

ΔV = 0.36π   in³

Step-by-step explanation:

Given that:

The radius of a sphere = 3.0

If the measurement is correct within 0.01 inches

i.e the change in the radius Δr = 0.01

The objective is to use differentials to estimate the error in the volume of sphere.

We all know that the volume of a sphere

V =  \dfrac{4}{3} \pi r^3

The differential of V with respect to r is:

\dfrac{dV}{dr }= 4 \pi r^2

dV = 4 πr² dr

which can be re-written as:

ΔV = 4 πr² Δr

ΔV = 4 × π × (3)² × 0.01

ΔV = 0.36π   in³

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scoray [572]

Answer:

The angle of elevation of the sun is 39⁰

Step-by-step explanation:

Given;

height of the tree, h = 96 ft

length of the shadow, L = 120 ft

                                                   |

                                                   | 96ft

                                                   |

                                                   |

       θ------------------------------------

                    120ft

Completing this triangle to cut across the top of the tree gives you a right angled triangle with θ as the angle of elevation of the sun.

Apply trig-ratio to determine the angle of elevation of the sun;

tanθ = opposite side / adjacent side

tanθ = 96 / 120

tanθ = 0.8

θ = tan⁻¹(0.8)

θ = 38.7⁰

θ = 39⁰

Therefore, the angle of elevation of the sun is 39⁰

4 0
2 years ago
8. A carpenter cut the top section of a window frame with a 37 degree angle on each end. The side pieces each have 50 degree ang
marshall27 [118]

Answer:

I will assume that the end of the top section if it were cut at 0 degrees would be cut at right angles to the length of the section.  

Joining a top section with a 37 degree end angle to a side piece with a 50 degree end angle will result in the length of the side piece being at an angle of  

37 + 50 = 87 degrees to each other.  

The same will be true for the other side.  

If the sides were parallel, then going up one side, across the top and then down the other side will result in a change of direction of 180 degrees. However, in this frame the direction turns 87 degrees at the first top corner and another 87 degrees at the second top corner. This is a total of  

87 + 87 = 174 degrees instead of 180 degrees.  

The two sides diverge at an angle of  

180 - 174 = 6 degrees from each other as they extend downwards from the top of the frame

Step-by-step explanation:

4 0
3 years ago
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Svetllana [295]
Change you’ll receive is = 0.09
you can only buy 11 because if you divide 20/11 it will give you 1.81 and if you multiply 11x 1.81 it will give you 19.91 which is close to $20 & that’s the most you can buy .
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3 years ago
PLEASE HELP! IT’S 40 POINTS! What is the area of this octagon?
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Answer:

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Step-by-step explanation:

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In the figure below, APQR is a reflection of ATSA.
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Answer:

both student one and student two

Step-by-step explanation:

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