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3 years ago

Use the definition of logarithm to simplify each expression.

1 answer:

7 0

$1)\ \ \ log 10 ^{10}=x\ \ \ \Leftrightarrow\ \ \ 10^x=10^{10}\ \ \ \Leftrightarrow\ \ \ \ \ \ x=10\\\\2) \ \ \ log 10 ^{100}=x\ \ \ \Leftrightarrow\ \ \ 10^x=10^{100}\ \ \ \Leftrightarrow\ \ \ x=100\\ \\ 3)\ \ \ log 10 ^ {10-4}=x\ \ \ \Leftrightarrow\ \ \ 10^x=10^{10-4}\ \ \ \Leftrightarrow\ \ \ x=6$

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3 years ago

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3 years ago

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3 years ago

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Svetlanka [38]

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2 years ago

An oblique cone has a radius of 4 units, a height of 8.5 units, and a slant length of 11.7 inches. What is the volume of the obl

trasher [3.6K]

Oblique Cone

The volume of the oblique cone is 144.49 cubic inches , if an oblique cone has a radius of 4 units, a height of 8.5 units, and a slant length of 11.7 inches.

Step-by-step explanation:

An oblique cone has a radius of 4 units

A height of 8.5 units

A slant length of 11.7 inches

We have to use the slant height to calculate actual base

So in a right angle triangle when two sides are given the third side is calculated by

Root (sqr(11,7) - sqr(8.5)) = 8.03 units

$\sqrt{11.7^{2} - 8.5^{2} }$

⇒ 8.03 units

Formula to calculate the volume of oblique cone,......................(1)

V = $\frac{1}{3} bh$

If r is the distance of the base of the height from the center of the circle [ this is because the base of the height is outside the oblique cone]

V = $\frac{1}{3} \pi r^{2} h$

Where r is the distance if the base of the height from the center of the circle [ this is because the base of the height is outside the oblique cone]

Here r = 8.03 - 4 = 4.03 units

Volume = $\frac{1}{3}$ × 3.14 × 4.03 × 4.03 × 8.5

Volume = 144.49 cubic inches

Hence, the volume of the oblique cone is 144.49 cubic inches , if an oblique cone has a radius of 4 units, a height of 8.5 units, and a slant length of 11.7 inches.

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2 years ago

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