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Arisa [49]
3 years ago
13

Simplify. 8u+9v+3u−5v

Mathematics
1 answer:
musickatia [10]3 years ago
8 0
Combine like terms
8u+3u= 11u
and
9v-5v= 4v
So the answer is 11u+4v
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The distance that a spring will stretch varies directly as the force applied to the spring. A force of 8080 pounds is needed to
Nimfa-mama [501]

Answer:

176 199 pounds

Step-by-step explanation:

To answer this it is first useful to find the proportionality constant.

F= kx

8080 pounds = k.88 in

k = 91.81 pound/inch

So what force is required to stretch the spring to 1919 inches?

F = kx

  = 91.81 pound/inch * 1919 inches

  = 176 199 pounds

It is worth noting that this force seems rather large and the spring might have long reached its elastic limit

7 0
3 years ago
Math question
strojnjashka [21]

Answer:

The candle has a radius of 8 centimeters and 16 centimeters and uses an amount of approximately 1206.372 square centimeters.

Step-by-step explanation:

The volume (V), in cubic centimeters, and surface area (A_{s}), in square centimeters, formulas for the candle are described below:

V = \pi\cdot r^{2}\cdot h (1)

A_{s} = 2\pi\cdot r^{2} + 2\pi\cdot r \cdot h (2)

Where:

r - Radius, in centimeters.

h - Height, in centimeters.

By (1) we have an expression of the height in terms of the volume and the radius of the candle:

h = \frac{V}{\pi\cdot r^{2}}

By substitution in (2) we get the following formula:

A_{s} = 2\pi \cdot r^{2} + 2\pi\cdot r\cdot \left(\frac{V}{\pi\cdot r^{2}} \right)

A_{s} = 2\pi \cdot r^{2} +\frac{2\cdot V}{r}

Then, we derive the formulas for the First and Second Derivative Tests:

First Derivative Test

4\pi\cdot r -\frac{2\cdot V}{r^{2}} = 0

4\pi\cdot r^{3} - 2\cdot V = 0

2\pi\cdot r^{3} = V

r = \sqrt[3]{\frac{V}{2\pi} }

There is just one result, since volume is a positive variable.

Second Derivative Test

A_{s}'' = 4\pi + \frac{4\cdot V}{r^{3}}

If \left(r = \sqrt[3]{\frac{V}{2\pi}}\right):

A_{s} = 4\pi + \frac{4\cdot V}{\frac{V}{2\pi} }

A_{s} = 12\pi (which means that the critical value leads to a minimum)

If we know that V = 3217\,cm^{3}, then the dimensions for the minimum amount of plastic are:

r = \sqrt[3]{\frac{V}{2\pi} }

r = \sqrt[3]{\frac{3217\,cm^{3}}{2\pi}}

r = 8\,cm

h = \frac{V}{\pi\cdot r^{2}}

h = \frac{3217\,cm^{3}}{\pi\cdot (8\,cm)^{2}}

h = 16\,cm

And the amount of plastic needed to cover the outside of the candle for packaging is:

A_{s} = 2\pi\cdot r^{2} + 2\pi\cdot r \cdot h

A_{s} = 2\pi\cdot (8\,cm)^{2} + 2\pi\cdot (8\,cm)\cdot (16\,cm)

A_{s} \approx 1206.372\,cm^{2}

The candle has a radius of 8 centimeters and 16 centimeters and uses an amount of approximately 1206.372 square centimeters.

3 0
3 years ago
Need the answer for x and y
d1i1m1o1n [39]

Answer:

x = 7°

y = 10°

Step-by-step explanation:

7x = 49

x = 7°

180 = 13y + 1 + 49

combine like terms:

13y = 130

y = 10°

8 0
2 years ago
Read 2 more answers
Which expression is equivalent to −4(2x − 8)−2x ?
Vesnalui [34]
C. -10x+32

Explanation: Solve the problem
( -4(2x-8)-2x )
5 0
1 year ago
A flea is jumping around on the number line. He starts at 3 and jumps 5 units to the left. Where is he now on the number line
weeeeeb [17]

Answer:

Answer. -2

Step-by-step explanation:

hope this helps!!

5 0
3 years ago
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