Approximate the following numbers to the nearest whole number

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

The radius r of a cone is increasing at a rate of 4in/min. The height h of the cone is always 4 times the radius. Find the rate

AlekseyPX

$\bf \textit{volume of a cone}\\\\
V=\cfrac{\pi r^2 h}{3}\qquad h=4r\implies V=\cfrac{\pi r^2 \cdot 4r}{3}\implies V=\cfrac{4\pi r^3}{3}\\\\
-----------------------------\\\\
\cfrac{dv}{dt}=\cfrac{4\pi }{3}\cdot 3r^2\cdot \cfrac{dr}{dt}\implies \cfrac{dv}{dt}=4\pi r^2\cdot \cfrac{dr}{dt}\qquad 
\begin{cases}
\frac{dr}{dt}=4\\\\
r=7
\end{cases}
\\\\\\
\cfrac{dv}{dt}=4\pi (7)^2\cdot 4$

7 0

3 years ago

HELP MATH QUESTIONS!! WILL MARK CORRECT ANSWERS BRAINLIEST!! 40 POINTS!! DUE TODAY ASAP!!

yuradex [85]

Answer:

f(x) = 34.59 +3.74x
0.96
very strong
8.93

Step-by-step explanation:

1. The selection of answers offers a choice of positive or negative slope, a slope of about 4 or about 35, and y-intercepts from the same set of values.

If you consider a couple of points (at the ends of the domain is usually a good choice), you see the slope is about 4 and the y-intercept is around 30.

For example, the points (5, 50) and (15, 91) have a slope of (91-50)/(15-5) = 4.1 so will give rise to the equation ...

y -50 = 4.1(x -5)

Filling in x=0 gives y = 50 -20.5 = 29.5

So, the nearest of the offered choices is ...

f(x) = 34.59 +3.74x

Please note that no calculator is involved. We simply estimated the parameters of the regression line based on a couple of the data points. This estimate is sufficient to allow us to find the correct answer choice.

__

2. If we look at a few other data points, we see that they have a generally upward trend that matches the above equation pretty well. That suggests a very high value of correlation, so the appropriate choices would be 0.93 or 0.96. Of course, the correlation is positive, matching the sign of the slope of the regression line. (Since the data points do not fall exactly on a line, the correlation is not 1.00. My assessment is they fall close enough to the line to rate a correlation of .96 instead of .93.)

At this point, the output of your calculator can confirm that the correlation coefficient is closer to 0.96. Mine says r = 0.9624.

r = 0.96

__

3. We have already determined by examining the data points that the correlation is "very strong." The correlation coefficient of 0.96 confirms this.

__

4. Using the equation of part 1, we can find the number of study hours:

68 = 34.59 +3.74x

(68 -34.59)/3.74 = x ≈ 8.933

We expect a score of 68 is associated with about 8.93 study hours.

_____

Please note that we have used very little calculation to determine the answers to this question. The only requirement is a general understanding of what linear regression and correlation coefficients mean.

3 0

3 years ago

The ____ were very similar on the Galapagos and Ecuador

vredina [299]

Answer: I think it’s the plants.

sorry if it’s not right

8 0

3 years ago

you are considering 2 jobs. one job pays $250 per week, plus 4.5% commission on all sales. The second job pays $1,800 per month

Hoochie [10]

The correct answer is A. Not only does $250 a week equal $1000 a month but the commission is also higher.

first job: $250wk = $1000 Month + .045 commission
= $12000 year + .045 commission
second job = $1800 Month + .03 commission
= $21600 year + .03 commission
commission based on sales of $1,000,000

1,000,000 times .045 = $45000
1,000,000 times .030 = $30000

FIRST JOB: $12,000 + $45,000 = $57,000
SECOND JOB: $21,600 + $30,000 = $51,600

The answer is definitely A.

5 0

3 years ago