Answer:
a. π(9^2)(9) - (1/3)(9^2)(9)
step-by-step explanation:
we assume that container a is the whole cylinder, and that container b is the cylinder with the cone carved out.
the formula for the volume of a cylinder is
vcyl = πr²h
the formula for the volume of a cone is
vcon = (1/3)πr²h
here, we have r=h=9 in both cases, and we want to find the difference of volumes. filling in the numbers gives
vcyl - vcon = π(9²)(9) - (1/3)(9²)(9) . . . matches choice a
comment on notation
exponents rarely get copied properly from other applications to brainly, so some editing may be required. if you don't use the equation editor or special mathematical symbols, the plain-text form for an exponent is
(base)^(exponent) . . . the exponent is signified by a caret (^)
note that grouping symbols may be required. if the exponent has an arithmetic operation in it, then it needs parentheses:
√(x) = x^(1/2)
(x^a)(x^b) = x^(a+b)
the use of the word "over" to signify a fraction is unnecessary and ambiguous. the forward slash (/) is usually used for that purpose. as with the caret, any numerator or denominator consisting of more than a single number or letter needs parentheses: (1/a) + (1/b) = (a+b)/(ab). even if you know that the denominator is a single number, as in 1/3, it understanding to put the fraction in parentheses so the appropriate interpretation is clear. (see above for examples. many people write 1/x+1 when they mean 1/(x+1), so if you mean (1/x)+1, it is to write it that way--even though that is how it should be interpreted.)
Answer:
The slope of f(x) is -1 which means that it rises -1 for every time it goes over 1. The slope of g(x) is 0, because it has a rise of 0 over an infinite run. The slope of g(x) is greater because 0>-1.
Step-by-step explanation:
You get the slope of the f(x) by doing 7-5/-4-(-2)= 2/-2=-1
Answer:
20%×X=30
x=150
Step-by-step explanation:
30÷20%=150
20%×150=30
Answer:
16666666666/100000000000.
Step-by-step explanation:
The volume of the box is the amount of space in it.
The dimension of the postcard is:
Let x represents the length of the cut.
So, the dimension of the box is:
<u>(a) The function that represents the volume of the box</u>
This is calculated as:
So, we have:
Expand
Hence, the volume function is:
<u>(b) The dimension that maximizes the volume</u>
We have:
Differentiate
Set to 0
Using a calculator, we have:
The value x = 7.3 is greater than the dimension of the box.
So, we have:
Recall that:
So, we have:
Hence, the dimension that maximizes the volume is 5.8 by 13.8 by 2.1
<u>(c) The maximum volume</u>
This is calculated as the product of the dimension of the box
So, we have:
Hence, the maximum volume of the box is 168.1 cubic inches
Read more about volumes at:
brainly.com/question/17056191
