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3 years ago

Solve f(-4) if f(x) = -4x - 2.

Mathematics

1 answer:

nirvana33 [79]3 years ago

3 0

F(-4)= -4(-4) -2
F(-4)= 14

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Suppose a ball is dropped from a height of 16 feet. Each time it drops h feet, it rebounds 0.81h feet. Find the total distance t

Roman55 [17]

When the ball is first dropped, it falls $h$ feet. On the first bounce, it rebounds $0.81h$ feet, which means on the second "drop" it must travel $0.81h$ feet again. On the second bounce, the ball rebounds $0.81(0.81h)=0.81^2h$ feet, and on the third drop falls the same distance. And so on.

So there are two directions to track:

$\text{downward: }\displaystyle h+0.81h+0.81^2h+\cdots=\sum_{n=0}^\infty 0.81^nh$
$\text{upward: }\displaystyle 0.81h+0.81^2h+\cdots=\sum_{n=1}^\infty 0.81^nh$

The total distance is the sum of these two:

$\displaystyle\sum_{n=0}^\infty 0.81^nh+\sum_{n=1}^\infty 0.81^nh=h+2h\sum_{n=1}^\infty 0.81^n$

Recall that for an infinite geometric sum, you have

$\displaystyle\sum_{n=0}^\infty r^n=1+\sum_{n=1}^\infty r^n=\frac1{1-r}$

provided that $|r|$ . So the total distance traveled by the ball is

$h+2h\left(\dfrac1{1-0.81}-1\right)\approx9.53h$

Starting with a height of $h=16$ means the total distance is about 152.42 ft.

4 0

3 years ago

Find the perimeter of triangle CDE. Round to the nearest tenth.

nevsk [136]

Here's how you do it: you find all the distances between the three points and add them together to calculate the perimeter of the triangle. To calculate for the distance between two points, the formula is

d = √[(x2 - x1)² + (y2 - y1)²]

So, just take two points, assign x1 and x2 with corresponding y1 and y2, then you get the answer.

Points: D(1,4), E(3,-2), C(-3,1)

After substituting the answers would be:
DE = 6.3 units
CE = 6.7 units
CD = 5 units

Perimeter = 6.3 + 6.7 + 5
Perimeter = 18 units

7 0

4 years ago

Read 2 more answers

Help pls also show work if needed!

mr Goodwill [35]

Answer:

yes, no, yes, no

Step-by-step explanation:

For it to be a line, that means that when x goes up by 1 y goes up by the same thing every time.

7a. from (1, 12) to (2, 8), the x coordinate goes up by 1 and the y coordinate goes down by 4. From (2, 8) to (3, 4) the y coordinate again goes down by 4 when the x coordinate goes up by 1. This pattern continues for the other points, so yes.

Do the same thing for the rest and you should get:

7b. No

7c. Yes

7d. No

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3 years ago

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Simplify. (-2)^-3<br><br> PLEASE HELP

nika2105 [10]

You have a negative exponent so you have to bring the -2 down : 1/-2^3. Then you multiply the -2*-2*-2 which is -8 so you get 1/-8 or -1/8. It means the same thing.

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3 years ago

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Last 2 questions could i have a hand with them?

motikmotik

The first one is c.
3x+5<23
-5. -5
3x=18
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3 years ago