Answer:
r = 16 cm
g = 34 cm
LA = 1708.16 cm^2
Step-by-step explanation:
We have that for the cone, the formula is as follows:
v = pi / 3 * r ^ 2 * h
the first thing they ask is to calculate the radius, therefore we solve for r
r ^ 2 = 3 * v / (pi * h)
replacing the volume and height, it remains:
r ^ 2 = 3 * 2560 * pi / (pi * 30)
r ^ 2 = 3 * 2560/30 = 256
r = 16
Now, to calculate the slant height, that is to say g, we can calculate it knowing the height and the radius:
g ^ 2 = r ^ 2 + h ^ 2
g ^ 2 = 16 ^ 2 + 30 ^ 2
g ^ 2 = 1156
g = 34
The lateral area of the cone is given by the following equation:
LA = pi * r * g
replacing
LA = 3.14 * 16 * 34
LA = 1708.16 cm ^ 2
the lateral area is 1708.16 cm ^ 2
Find the volume of the large box:
15x25x29
375x29
10,875cm³
and the smaller box:
10x10x10
100x10
1,000
then subtract
10,875-1,000=9,875cm³ remaining
Answer:
1.5, -8, 0, 2f, 2/3
Step-by-step explanation:
j(x) = 2x means the function name is j, and it is a function of the variable x. To evaluate the function, you put the given value everywhere you see x, and do the arithmetic.
j(0.75) = 2(0.75) = 1.5
j(-4) = 2(-4) = -8
j(0) = 2(0) = 0
j(f) = 2f
j(1/3) = 2(1/3) = 2/3
<h2>Answer:</h2>
Option: D is the correct answer.
D. x < 397.9 and x > 402.1
<h2>Step-by-step explanation:</h2>
It is given that:
Each bag is advertised as weighing 400 grams.
Also, a bag must weigh within 2.1 grams in order to be accepted.
Hence, for the bag being accepted the weight must be no less than 2.1 gram from 400 gram and should be no more than 2.1 gram from 400 grams.
i.e. the weight of the bag must be such that:
400-2.1≤ x ≤ 400+2.1
i.e.
397.9 ≤ x ≤ 402.1
Hence, if the weight of the bag is less than 397.9 grams or is more than 402.1 grams then the bag will be rejected.
i.e. The range for the bag being rejected is: x<397.9 grams and x>402.1 grams.
Answer:
{12,15}
Step-by-step explanation:
Given the function f(x) = x+5, if the range of the function is {7,9}, the domain of the function is derived by simply finding the value of the function at each end point.
At endpoint x = 7,
f(7) = 7+5
f(7) = 12
At endpoint x = 9
f(9) = 9+5
f(9) = 14.
The function domain is therefore at {12,14}
