Answer: 63 ft^2
Step-by-step explanation:
the formula for the area of a circle is A = π r ^2. the radius (r) is 1/2 of the diameter.
first, we'll plug in the radius of table #1 into the equation (A = π 4 ^2) and get an answer of 50.27 ft^2. then plug in radius of table #2 (A = π 6 ^2) and get 113.1 ft^2. now find the difference of the areas by subtracting (113.1 - 50.27) to get an answer of 62.83 ft^2. which will round up to 63 ft^2.
Answer:
angle 5 = 102
Step-by-step explanation:
angle 2 = angle 6 { they are corresponding angles }
and then angle 6 and angle 5 = 180
78 + angle 5 = 180
angle 5 = 180-78
angle 5 = 102
5 square root of 2 is 25.
-9-6 is -15
Answer:
Step-by-step explanation:
Consider the given expression is
![\ln (x\sqrt[3]{x^2+1})](https://tex.z-dn.net/?f=%5Cln%20%28x%5Csqrt%5B3%5D%7Bx%5E2%2B1%7D%29)
We need to rewrite the expression as a sum,difference,or multiple of logarithms.
![[\because \sqrt[n]{x}=x^{\frac{1}{n}}]](https://tex.z-dn.net/?f=%5B%5Cbecause%20%5Csqrt%5Bn%5D%7Bx%7D%3Dx%5E%7B%5Cfrac%7B1%7D%7Bn%7D%7D%5D)
Using the properties of logarithm we get
![[\because \ln (ab)=\ln a+\ln b]](https://tex.z-dn.net/?f=%5B%5Cbecause%20%5Cln%20%28ab%29%3D%5Cln%20a%2B%5Cln%20b%5D)
![[\because \ln (a^b)=b\ln a]](https://tex.z-dn.net/?f=%5B%5Cbecause%20%5Cln%20%28a%5Eb%29%3Db%5Cln%20a%5D)
Therefore, the simplified form of the given expression is .
Answer:
142.1π in³
Step-by-step explanation:
Given that:
The radius (r) = 7 in
The slant height (y) = 25 in
Then the height (x) can be determined by using the Pythagoras rule:
y² = x² + r²
25² = x² + 7²
125 = x² + 49
125 - 49 = x²
x² = 76
x = √76
x = 8.7
The formula for the volume of a cone is;
= 1/3 πr²h
where;
height(h) is calculated as "x" from above = 8.7
Then;
= 1/3 × π × (7 in)² × 8.7 in
= 142.1π in³
