Answer: radius r = 2 inches
height h = 6 inches
Step-by-step explanation:
Given;
Volume V = 24πin3
Volume of a cylinder is given by
V = πr^2h
h = V/πr^2. ....1
Where, h = height and r = radius of cylinder
For the surface area of the cylinder with open top. we have,
S = 2πrh + πr^2
For the cost of materials used, let k represent the cost of materials used for the body of the cylinder.
Then, for the bottom will be 3k
Total cost will be represented by C, which gives
C = 2πrhk + 3πr^2k. .....2
Substituting eqn 1 to 2, we have;
C = 2πrVk/πr^2 + 3πr^2k
C = 2Vk/r + 3πr^2k
The material cost is minimum at dC/dr = 0
dC/dr = -2Vk/r^2 + 6πrk =0
6πrk = 2Vk/r^2
r^3 = 2V/6π
r = (2×24π/6π)^-3
r = (8)^-3
r = 2
Substituting r = 2 into eqn1
h = 24π/π(2^2)
h = 24/4 = 6
h = 6
Answer:
<h2>All three functions have a y-intercept.</h2>
Step-by-step explanation:
The table is attached, there you can observe functions f(x), g(x) and h(x).
Remember, when x = 0, it represents a y-intercept. So, we can deduct that all three functions have y-intercept, (0,1) for f(x), (0, -1/2) for g(x) and (0,-5) for h(x).
Also, x-values represent domain values, however, in this case, we can't say that all three function have the same domain values, because we don't know the domain defintion for each of them to determine such thing.
Additionally, in the table you can observe that f(x) has the greatest maxium, so the second choice is also false. And neither function has x-intercept.
Therefore, the only right answer is the third choice.
Answer:
Gerri spends 1/7 (A).
Step-by-step explanation:
If Gerri spends 1/21 of her money on pencils and 2/21 of her money on paper, adding these two fractions together will give us the total fraction of her money that she spent. Since 1/21 and 2/21 have the same denominator, we can add the numerators to get 3/21. However, fractions must always be in simplest form, meaning if the numerator (top number) and denominator (bottom number) can both be divided evenly by the same factor, then the fraction can be simplied to lower numbers. In this case the number 3 and the number 21 can both be divided evenly by 3: (3÷3)/21÷3) = 1/7.
Answer:
6x² + 4x + 10
Step-by-step explanation:
(2x - 2)(3x + 5)
2x(3x + 5) - 2(3x + 5)
6x² + 10x - 6x + 10
6x² + 4x + 10 ans.
hope this helps you !
Answer:
Angle L = 90 degrees
Step-by-step explanation:
