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1 year ago

A parachutist descends 44 feet in 4 seconds. Express the rate of the parachutist's change in height as a unit rate.

Mathematics

1 answer:

Montano1993 [528]1 year ago

5 0

The unit rate of the parachutist change in height is 11 feet per second.

• In Mathematics, Unitary method is a technique for solving a question by first finding the value of a single unit and then finding the required value by multiplying the number by value of single unit .

• We use unitary method to find the ratio of one thing with respect to other thing.

• There are two types of unitary method one is Direct Variation and the other is Inverse variation.

We have the rate of descend as 44 feet in 4 sec.

So, in 1 second it will be = 44 / 4 = 11 feet.

Which is the unit rate.

Therefore, the unit rate of descend for the parachutist is 11 feet per second.

Learn more about unit rate here:

brainly.com/question/19493296

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Match each set of numbers with their least common multiple.

mylen [45]

Answer:

27, 12, and 36 = 108

22 and 4 = 44

14 and 12 = 84

25 and 8 =200

9, 8, and 7 = 504

32, 24, and 18 = 288

Step-by-step explanation: You are welcome.

5 0

2 years ago

Just need the answer. no explanation needed. ASAP answers!

LUCKY_DIMON [66]

You should definitely improve the quality of the image, because I can't see anything clearly.

Also, the 4th answer is hidden.

6 0

3 years ago

Read 2 more answers

1. (5pts) Find the derivatives of the function using the definition of derivative.

andreyandreev [35.5K]

2.8.1

$f(x) = \dfrac4{\sqrt{3-x}}$

By definition of the derivative,

$f'(x) = \displaystyle \lim_{h\to0} \frac{f(x+h)-f(x)}{h}$

We have

$f(x+h) = \dfrac4{\sqrt{3-(x+h)}}$

and

$f(x+h)-f(x) = \dfrac4{\sqrt{3-(x+h)}} - \dfrac4{\sqrt{3-x}}$

Combine these fractions into one with a common denominator:

$f(x+h)-f(x) = \dfrac{4\sqrt{3-x} - 4\sqrt{3-(x+h)}}{\sqrt{3-x}\sqrt{3-(x+h)}}$

Rationalize the numerator by multiplying uniformly by the conjugate of the numerator, and simplify the result:

$f(x+h) - f(x) = \dfrac{\left(4\sqrt{3-x} - 4\sqrt{3-(x+h)}\right)\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)}{\sqrt{3-x}\sqrt{3-(x+h)}\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)} \\\\ f(x+h) - f(x) = \dfrac{\left(4\sqrt{3-x}\right)^2 - \left(4\sqrt{3-(x+h)}\right)^2}{\sqrt{3-x}\sqrt{3-(x+h)}\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)} \\\\ f(x+h) - f(x) = \dfrac{16(3-x) - 16(3-(x+h))}{\sqrt{3-x}\sqrt{3-(x+h)}\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)} \\\\ f(x+h) - f(x) = \dfrac{16h}{\sqrt{3-x}\sqrt{3-(x+h)}\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)}$

Now divide this by <em>h</em> and take the limit as <em>h</em> approaches 0 :

$\dfrac{f(x+h)-f(x)}h = \dfrac{16}{\sqrt{3-x}\sqrt{3-(x+h)}\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)} \\\\ \displaystyle \lim_{h\to0}\frac{f(x+h)-f(x)}h = \dfrac{16}{\sqrt{3-x}\sqrt{3-x}\left(4\sqrt{3-x} + 4\sqrt{3-x}\right)} \\\\ \implies f'(x) = \dfrac{16}{4\left(\sqrt{3-x}\right)^3} = \boxed{\dfrac4{(3-x)^{3/2}}}$

3.1.1.

$f(x) = 4x^5 - \dfrac1{4x^2} + \sqrt[3]{x} - \pi^2 + 10e^3$

Differentiate one term at a time:

• power rule

$\left(4x^5\right)' = 4\left(x^5\right)' = 4\cdot5x^4 = 20x^4$

$\left(\dfrac1{4x^2}\right)' = \dfrac14\left(x^{-2}\right)' = \dfrac14\cdot-2x^{-3} = -\dfrac1{2x^3}$

$\left(\sqrt[3]{x}\right)' = \left(x^{1/3}\right)' = \dfrac13 x^{-2/3} = \dfrac1{3x^{2/3}}$

The last two terms are constant, so their derivatives are both zero.

So you end up with

$f'(x) = \boxed{20x^4 + \dfrac1{2x^3} + \dfrac1{3x^{2/3}}}$

8 0

2 years ago

37-(-3)squared+30\(-3)x2

vampirchik [111]

Simplify:
37 - (-3)^2 + 30/(-3)x^2
= 37 + - 9 + - 10x^2

Combine like terms:
= 37 + - 9 + - 10x^2
= ( - 10x^2) + (37 + - 90
= - 10X^2 + 28
Answer: - 10x^2 + 28

To Factor:
37 - (- 3)^2 + 30/- 3x^2

- 10x^2 + 28
- 2(5x^2 - 14)

Answer: - 2(5x^2 - 14)

I simplify, and factor, because, you didn't really specify what you wanted help on with this equation. - Thanks -

Hope that helps!!!!

6 0

3 years ago

Billy says that he can add 23 and 40 without regrouping is Bill correct how do you know

bija089 [108]

Yes he is correct because if you do the algorithm, 0+3=3 and 20+40=60 and 60+3=63. There is no regrouping needed.

6 0

3 years ago