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Lady bird [3.3K]

3 years ago

15

Find the value of x. Round to the nearest tenth.please help.

1 answer:

Serga [27]3 years ago

5 0

Answer:

39.9

Step-by-step explanation:

A good trick to remember is SOH CAH TOA.

Sine = Opposite / Hypotenuse

Cosine = Adjacent / Hypotenuse

Tangent = Opposite / Adjacent

Here, we're given an angle and the opposite side, and we want to find the adjacent side. So we need to use tangent.

tan 31° = 24 / x

x = 24 / tan 31°

x ≈ 39.9

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A lampshade has a height of 12cm and upper and lower diameters of 10cm and 20cm A)what area of material is required to cover tha

netineya [11]

Answer:

$(a)\ Area = 195\pi$

$(b)\ Volume = 700\pi$

Step-by-step explanation:

Given

$h = 12$

$d_1 = 10$ --- lower diameter

$d_2 = 20$ --- upper diameter

Solving (a): The curved surface area

This is calculated as:

$Area = \pi l(r_1 + r_2)$

Where

$r_1 = 0.5 * d_1 = 0.5 * 10 = 5$ --- lower radius

$r_2 = 0.5 * d_2 = 0.5 * 20 = 10$ --- upper radius

And

$l = \sqrt{h^2 + (r_1 - r_2)^2$ ---- l represents the slant height of the frustrum

$l = \sqrt{12^2 + (5 - 10)^2$

$l = \sqrt{12^2 + (-5)^2$

$l = \sqrt{144 + 25$

$l = \sqrt{169$

$l = 13$

So, we have:

$Area = \pi l(r_1 + r_2)$

$Area = \pi * 13(5 + 10)$

$Area = \pi * 13(15)$

$Area = 195\pi$

Solving (b): The volume

This is calculated as:

$Volume = \frac{1}{3}\pi * h * (r_1^2 + r_2^2 + (r_1 * r_2))$

This gives:

$Volume = \frac{1}{3}\pi * 12 * (5^2 + 10^2 + (5 * 10))$

$Volume = \frac{1}{3}\pi * 12 * (25 + 100 + (50))$

$Volume = \frac{1}{3}\pi * 12 * (175)$

$Volume = \pi *4 * 175$

$Volume = 700\pi$

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