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3 years ago

Find the two x-intercepts of the function f and show that f '(x) = 0 at some point between the two x-intercepts.

Mathematics

1 answer:

suter [353]3 years ago

7 0

Step-by-step explanation:

f(x) = x√(x+8)

When f(x) = 0,

0 = x√(x+8)

x = 0, x + 8 = 0

x = -8

f'(x) = (1)√(x+8) + x • ½(x+8)^(-½) = 0

0 = √(x+8) + 1/[2√(x+8)] (x)

-2(x+8) = x

-2x - 16 = x

x = -16/3

(-8 < -16/3 < 0)

Therefore, x-intercept of f'(x) = 0 is somewhere between the two x-intercepts, ranging from -8 to 0.

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The following sector has a radius of 10 inches and a central angle of 30 . Which of the following is its arc length, in inches?

Marianna [84]

Answer:

option 1

Step-by-step explanation:

step 1

Find the arc length of the complete circle

The circumference of the circle ios given by

$C=2\pi r$

we have

$r=10\ in$

substitute

$C=2\pi (10)$

$C=20\pi\ in$

step 2

Find the arc length for a sector with a cenytral angle of 30 degrees

we know that

The complete circle subtends a central angle of 360 degrees

using proportion

$\frac{20\pi}{360^0}=\frac{x}{30^o}\\\\x=20\pi(30)/360\\\\x=\frac{5}{3} \pi\ in$

5 0

4 years ago

In a random sample of fivefive microwave ovens, the mean repair cost was $75.0075.00 and the standard deviation was $13.0013.

Radda [10]

<h2>Answer with explanation:</h2>

As per given , we have

Sample size : n= 5

Degree pf freedom = : df= 5-1=4

$\mu=\$75.00$

$\sigma=\$13.00$

Significance level for 90% confidence = $\alpha=1-0.90=0.1$

Using t-value table , t-critical value for 90% confidence:

$t_{\alpha/2, df}=t_{0.05, 4}=2.132.$

Margin of error of $\mu$ : $E=t_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}\\\\(2.132)\dfrac{13}{\sqrt{5}}=12.3949720129\approx12.39$

Interpretation : The repair cost will be within $12.39 of the real population mean value $\mu$ 90% of the time.

7 0

4 years ago

Problem 1: The Jefferson Band is selling baked goods to raise money for their trip. Their goal is to

Evgen [1.6K]

Answer:

334

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

find the area of the following shape. A(-5,-8) B(1,-8) C(3,-5) D(1,0) E(-5,-3) F(-3,-6). just show work

Juliette [100K]

Check the picture below

so hmmm, all you really have is 4 triangles and 1 rectangle, notice the bases and altitude of each triangle

so, get the area of each, sum them up, and that's the area of the shape

6 0

3 years ago

Given the points (5,7)and(2,4)<br>find the equation passing through<br>these points

Elena-2011 [213]

Answer:

y=x+2

Step-by-step explanation:

Im going to start by presuming its a linear equation so the formula is:

y=mx+n so now we just make a simulanious equation:

7=5m+n

4=2m+n

which we subtract to get

3=3m

m=1

then we plug it into the first equation

7=5+n

n=2

so the equation is:

y=x+2

5 0

3 years ago