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3 years ago

In the arithmetic sequence {13,6,−1,−8,…}, what is the common difference? Enter your answer as a number, like this: 42

Mathematics

1 answer:

V125BC [204]3 years ago

6 0

Answer:

-7

Step-by-step explanation:

To find the common difference, you subtract a term from the term after it. For example, in the problem, you can subtract 13 from 6:

6 - 13 = -7

To check you can do the same thing with other consecutive numbers in the sequence like:

-1 - 6 = -7

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A force of 12 lb is required to hold a spring stretched 8 in. beyond its natural length. How much work W is done in stretching i

sattari [20]

Answer:

Work done in stretching the spring = 7.56 lb-ft.

Step-by-step explanation:

Normal length of the spring = 8 in or $\frac{8}{12}$ ft

= $\frac{2}{3}$ ft

If the spring has been stretched to 11 inch then the stretched length of the spring is = 11 in

= $\frac{11}{12}$ ft

Force applied to stretch the spring = 12 lb

By Hook's law,

F = kx [where k is the spring constant and x = length by which the spring is stretched]

12 = k( $\frac{2}{3}$ )

k = 18

Work done (W) to stretch the spring by $\frac{11}{12}$ ft will be

W = $\int\limits^\frac{11}{12} _0 {kx} \, dx$

= $\int\limits^\frac{11}{12} _0 {(18x)} \, dx$

= $18[\frac{x^{2}}{2}]^{\frac{11}{12}}_0$

= 9( $\frac{11}{12}$ )²

= 7.56 lb-ft

6 0

3 years ago

HELP PLEASE!! TON OF POINTS. RIGHT ANSWERS ONLY REWARDED. MATH GENIUSES?

Nonamiya [84]

Answer:

The graph is shifted 1 unit right

The graph is shifted 2 units down

Step-by-step explanation:

We are given

Parent function as

$f(x)=2^{x+3}-3$

New function as

$g(x)=2^{x+2}-1$

we can also write as

$g(x)=2^{x+3-1}-3+2$

We can see that

1 is subtracted to x-value

and 2 is added to y-value

So, f(x) is shifted right by 1 unit

and

f(x) is shifted up by 2 unit

3 0

3 years ago

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Nutka1998 [239]

Answer: -1536

Step-by-step explanation:

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Ksju [112]

Answer:

Step-by-step explanation:

First, multiply the length by two then, subtract the total by the sum, last divide by two.

(25 * 2)

(74 - 50)

(24/2)

Answer = 12

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1 year ago