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sweet [91]
3 years ago
7

What is the best estimate for 83.74 2.93?

Mathematics
1 answer:
GalinKa [24]3 years ago
3 0
84 and 3 would be the best estimates for those numbers
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A circular cylindrical container, open at the top, and having a capacity of 24pi cubic inches, is to be manufactured. If the cos
otez555 [7]

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

5 0
3 years ago
Which of the following best describes the graph of this system of equations ? y=-2x+3 and 5y=-10x +15
ELEN [110]

Remark

When talking about straight lines, D is never true. Never.

C is possible, but in this case not true. Read on.

B. Might be true but in this case it is not. The lines (to be parallel) have to have the same number in front of the x. These two lines do when you divide through by 5. But the y intercept has to be different. That is not so in this case. So B is incorrect.

A is your answer. If you divide through by 5 on the second one, you get the first one. They are identical.

6 0
3 years ago
The common ratio of a geometric series is 1/4 and the sum of the first 4 terms is 170.
Illusion [34]

Answer: the first term of the series is 128

Step-by-step explanation:

In a geometric sequence, the consecutive terms differ by a common ratio. The formula for determining the sum of n terms, Sn of a geometric sequence is expressed as

Sn = a(1 - r^n)/(1 - r)

Where

n represents the number of term in the sequence.

a represents the first term in the sequence.

r represents the common ratio.

From the information given,

r = 1/4 = 0.25

n = 4

S4 = 170

Therefore, the expression for the sum of the 4 terms, S4 is

170 = a(1 - 0.25^4)/(1 - 0.25)

170 = a(1 - 0.00390625)/(1 - 0.25)

170 = a(0.99609375)/(0.75)

170 = 1.328125a

a = 170/1.328125

a = 128

5 0
3 years ago
If y varies directly as x and y=4 when x=-2 find y when x=30
katovenus [111]

Answer:

Step-by-step explanation:

y=kx

4=k(-2)

k=-2

y=-2x

when x=30

y=-2*30=-60

5 0
3 years ago
One angle of a triangle has a measure of 36°. The measure of the third angle is 28° less than 3 times the measure of the second
Alex_Xolod [135]

Answer:

  1. Define your variable and write your equation:  36 + b + (3b-28) = 180°.
  2. measure of the second angle: 43°.
  3. measure of the third angle: 101°

Step-by-step explanation:

a = 36

c = 3b - 28

a + b + c = 180°

a = measure of the first angle

b = measure of the second angle

c = measure of the third angle

then:

1)  36 + b + (3b-28) = 180   ⇒ )Define your variable. Write your equation and solve)

b + 3b + 36 - 28 = 180

4b + 8 = 180

4b = 180 - 8

4b = 172

b = 172/4

2)   b = 43°        ⇒   measure of the second angle

c = 3b - 28

c = 3*43 - 28

c = 129 - 28

3) c = 101°      ⇒   measure of the third angle

Check:

36° + 43° + 101° = 180°

8 0
3 years ago
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