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2 years ago

Find the remainder when f(x) = x3 − 14x2 + 7x − 10 is divided by x − 3.

Mathematics

1 answer:

serious [3.7K]2 years ago

4 0

Answer: -88

Step-by-step explanation:

To find the remainder, you can use long division, synthetic division, or input the x-value. I am going to input because it is the fastest method.

f(x) = x³ - 14x² + 7x - 10 divided by x - 3 = 0 ---> x = 3

f(3) = 3³ - 14(3)² + 7(3) - 10

= 27 - 126 + 21 - 10

= -88

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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

Anna and Carla are 9 miles apart on a path when they start moving toward each other. Anna runs at a constant speed of 4 miles pe

Sergio [31]

Answer:

The answer is 3 miles.

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2 years ago

Which is a rational number a) 1.4142135623 b) 3.6256256 c) 2 (pie) d) squared 5

vfiekz [6]

Answer:

Rational numbers can be expressed as a fraction

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25 can be expressed as a fraction- 25/1, so d is correct.

Let me know if this helps!

8 0

2 years ago

Read 2 more answers

sal is making bracalets for a fundraser he uses 6 inches of yarn per bracalet how many bracalets can sal make with 5 ft of yarn

Iteru [2.4K]

Answer:

10 bracelets

Step-by-step explanation:

we need to convert 5 ft to inches

1 ft = 12 inches

multiply by 5

5 ft = 60 inches

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60/6 = 10

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3 years ago

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olga_2 [115]

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3 years ago