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3 years ago

Find dy/dx if f(x) = (x + 2)^7x.

Mathematics

1 answer:

lana [24]3 years ago

4 0

$\dfrac{\mathrm d}{\mathrm dx}(x+2)^{7x}=\dfrac{\mathrm d}{\mathrm dx}e^{7x\ln(x+2)}$

By the chain rule, the derivative reduces to

$e^{7x\ln(x+2)}\dfrac{\mathrm d}{\mathrm dx}(7x\ln(x+2))=(x+2)^{7x}\dfrac{\mathrm d}{\mathrm dx}(7x\ln(x+2))$

Then using the product rule, we get

$(x+2)^{7x}\left(7\ln(x+2)+\dfrac{7x}{x+2}\right)$

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Some answers include: 8/6, 12/9, 20/15.

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6. Regroup the numbers in the following problems, putting the numbers that add up to 10 or a multiple of 10 in parentheses.

svetoff [14.1K]

Answer:

a) (2+8)+9

b) (3+7)+5+4

c) (4+16)+2

d) (31+9)+4

Step-by-step explanation:

a) 2+9+8

2 and 8 add up to 10, so we regroup them in parentheses

(2+8)+9

b) 3 + 5 + 4 + 7

3 and 7 add up to 10, so we regroup them in parentheses

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c) 4 + 2 + 16

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4 0

3 years ago

In a lottery, the top cash prize was $642 million, going to three lucky winners. Players pick five different numbers from 1 t

kramer

Answer:

$\frac{10}{53 \times 46 \times 26}$

Step-by-step explanation:

The probability of matching the number drawn on the gold ball is

$\frac{1}{46}$

The number of possible pairs of numbers from 1 to 53 is

$\binom{53}{2} = \frac{53 \times 52}{2} = 53 \times 26$

Choosing 5 numbers, you are choosing 10 different pairs:

$\binom{5}{2} = \frac{5 \times 4}{2} = 10$

Therefore the probability of correctly matching the drawn pair is

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Thus, the probability of winning (matching the pair AND the gold ball) is

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3 years ago

Here are two paint mixtures: • 3 cups of white and 4 cups of blue. • 6 cups of white and 8 cups of blue. Both mixtures make the

lesantik [10]

Answer:

The mixture that is an equivalent ratio is:

1.5 white 2 blue

Step-by-step explanation:

a) Data and Calculations:

Mixtures of the same color because they are in equivalent ratios:

3 cups of white and 4 cups of blue: equivalent ratio = 0.75: 1 (75%) since 3/4 = 75%

6 cups of white and 8 cups of blue. equivalent ratio = 0.75: 1 (75%) since 6/8 = 75%

Other mixtures:

5 cups white 6 blue: equivalent ratio = 0.83: 1 (83%) since 5/6 = 83%

1 white 1 1/2 blue: equivalent ratio = 0.67: 1 (67%) since 1/1.5 = 67%

4 white 3 blue: equivalent ratio = 1: 75 (1.33%) since 4/3 = 1.33%

1.5 white 2 blue: equivalent ratio = 0.75: 1 (75%) since 1.5/2 = 75%

Therefore, the mixture with equivalent ratio as the initial mixtures is 1.5 while 2 blue.

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3 years ago