Answer:
782.5inch³
Step-by-step explanation:
The question is on volume of a prism and that of a cylinder
Finding the volume of the prism
V=Bh where B is the base area and h is the height
Base area=14"×14"=196 inch²
height =8"
v=196×8= 1568 in³
Finding volume of the cylinder
v=r²h where r is the radius of cylinder and h is the height of cylinder
r=10/2=5 inches and h=10 inches
v=3.142×5×5×10=785.5inch³
The difference in volume
Difference in volume=1568-785.5=782.5in
Answer:
-6i
Step-by-step explanation:
Complex roots always come in pairs, and those pairs are made up of a positive and a negative version. If 6i is a root, then its negative value, -6i, is also a root.
If you want to know the reasoning, it's along these lines: to even get a complex/imaginary root, we take the square root of a negative value. When you take the square root of any value, your answer is always "plus or minus" whatever the value is. The same thing holds for complex roots. In this case, the polynomial function likely factored to f(x) = (x+8)(x-1)(x^2+36). To solve that equation, you set every factor equal to zero and solve for the x's.
x + 8 = 0
x = -8
x - 1 = 0
x = 1
x^2 + 36 = 0
x^2 = -36 ... take the square root of both sides to get x alone
x = √-36 ... square root of an imaginary number produces the usual square root and an "i"
x = ±6i
If during a given month your average daily credit card balance is $800 and your yearly interest rate is 17%, then the interest you owe on your credit card for that month would be: $11.33
Answer: Polygon Q's area is 1/4 of Polygon P's area
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Explanation:
Imagine we had a square with side length 8. The area of this square is 8*8 = 64.
Now let's reduce each side of the square by the scale factor 1/2. So each new side is 8*(1/2) = 4. The area of this smaller square is 4*4 = 16.
Comparing the new area (16) to the old one (64), we see that the new area is 16/64 = 1/4 of the old area.
In other words,
new smaller area = (1/4)*(old larger area)
So this is one example to see why (1/2)*(1/2) = 1/4 is the area scale factor based on the linear scale factor of 1/2. In short, (1/2)^2 = 1/4. Whatever the original scale factor is, square it and you'll get the area scale factor.
Answer:
30
Step-by-step explanation:
