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3 years ago

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The table shows values of a function f(x). What is the average rate of change of f(x) over the interval from x = 5 to x = 9? Sho

w your work.

1 answer:

Snezhnost [94]3 years ago

7 0

F(x) is increasing when x increase. <span />

You might be interested in

Which subtraction expression

Bond [772]

If you would like to know which subtraction expression has the difference 1 + 4i, you can calculate this using the following steps:

a. (–2 + 6i) – (1 – 2i) = –2 + 6i – 1 + 2i = –3 + 8i

b. (–2 + 6i) – (–1 – 2i) = <span>–2 + 6i + 1 + 2i = </span>–1 + 8i

c. (3 + 5i) – (2 – i) = 3 + 5i – 2 + i = 1 + 6i

d. (3 + 5i) – (2 + i) = 3 + 5i – 2 – i = 1 + 4i

The correct result would be <span>d. (3 + 5i) – (2 + i).</span>

5 0

3 years ago

Read 2 more answers

Please Help!!<br><br>Use Euler’s formula to write in exponential form.

LekaFEV [45]

Answer:

C, $4e^{i(7\pi/4)}$

Step-by-step explanation:

To remind you, Euler's formula gives a link between trigonometric and exponential functions in a very profound way:

$e^{ix}=\cos{x}+i\sin{x}$

Given the complex number $2\sqrt{2}-2i\sqrt{2}$ , we want to try to get it in the same form as the right side of Euler's formula. As things are, though, we're unable to, and the reason for that has to do with the fact that both the sine and cosine functions are bound between the values 1 and -1, and 2√2 and -2√2 both lie outside that range.

One thing we could try would be to factor out a 2 to reduce both of those terms, giving us the expression $2(\sqrt{2}-i\sqrt{2})$

Still no good. √2 and -√2 are still greater than 1 and less than -1 respectively, so we'll have to reduce them a little more. With some clever thinking, you could factor out another 2, giving us the expression $4\left(\frac{\sqrt{2}}{2} -i\frac{\sqrt{2}}{2}\right)$ , and <em>now </em>we have something to work with.

Looking back at Euler's formula $e^{ix}=\cos{x}+i\sin{x}$ , we can map our expression inside the parentheses to the one on the right side of the formula, giving us $\cos{x}=\frac{\sqrt2}{2}$ and $\sin{x}=-\frac{\sqrt2}{2}$ , or equivalently:

$\cos^{-1}{\frac{\sqrt2}{2} }=\sin^{-1}-\frac{\sqrt2}{2} =x$

At this point, we can look at the unit circle (attached) to see the angle satisfying these two values for sine and cosine is 7π/4, so $x=\frac{7\pi}{4}$ , and we can finally replace our expression in parentheses with its exponential equivalent:

$4\left(\frac{\sqrt2}{2}-i\frac{\sqrt2}{2}\right)=4e^{i(7\pi/4)}$

Which is c on the multiple choice section.

4 0

3 years ago

Prime factor of 2080

MariettaO [177]

Answer:

2 x 2 x 2 x 2 x 2 x 5 x 13

Step-by-step explanation:

The Prime Factorization is:

2 x 2 x 2 x 2 x 2 x 5 x 13

In Exponential Form:

25 x 51 x 131

CSV Format:

2, 2, 2, 2, 2, 5, 13

7 0

3 years ago

What is the distance between the points (-2,4) and (6,-4), rounded to the nearest tenth

jarptica [38.1K]

9514 1404 393

Answer:

11.3 units

Step-by-step explanation:

The distance can be found using the distance formula:

d = √((x2 -x1)² +(y2 -y1)²)

d = √((6 -(-2))² +(-4-4)²) = √(8² +(-8)²) = √(64·2)

d = 8√2 ≈ 11.3

The distance is approximately 11.3 units.

5 0

3 years ago

Someone please help with parts a b c and d. I will mark brainlest!!!

maria [59]

Answer:

A. 49 feet

B. 66 feet (round to the nearest foot)

C. 4 seg

Step-by-step explanation:

A. What is the height of the ball after 3 seconds?

For $t=3 seg$

$h(3)=-16(3)^{2} +63(3)+4$

$h(3)=-144+189+4\\h(3)=-144+193\\h(3)=49 feet$

B. What is the maximum height of the ball? round to the nearest foot

$h(t)=-16(t)^{2} +63(t)+4\\h'(t)=-32(t) +63\\$

then

$-32(t)+63=0\\t=\frac{-63}{-32}\\t=1.969seg$

For $t=1.969seg$

$h(1.969)=-16(1.969)^{2}+63(1.969)+4\\h(1.969)= 66.016\\h(1.969)=66 feet$

C. When will the ball hit the ground?

The ball will hit the ground when $h(t)=0$

so, $-16t^{2} +63(t)+4=0$

Using the quadratic equation

$t=4seg$

6 0

3 years ago