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Gennadij [26K]
3 years ago
14

Use the definition of logarithm to simplify each expression.

Mathematics
1 answer:
konstantin123 [22]3 years ago
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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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

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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

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