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4 years ago

Function f has constant first differences. Which of the following must be true?

Mathematics

1 answer:

notka56 [123]4 years ago

4 0

Answer:

A,D

Step-by-step explanation:

i hope it right plz mark if it right if

you got to chose one its D for everyone

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In order to evaluate 7 sec(θ) dθ, multiply the integrand by sec(θ) + tan(θ) sec(θ) + tan(θ) . 7 sec(θ) dθ = 7 sec(θ) sec(θ) + ta

Maurinko [17]

Answer:

$\int {7 \sec(\theta) } \, d\theta = 7\ln(\sec(\theta) + \tan(\theta)) + c$

Step-by-step explanation:

The question is not properly formatted. However, the integral of $\int {7 \sec(\theta) } \, d\theta$ is as follows:

$\int {7 \sec(\theta) } \, d\theta$

Remove constant 7 out of the integrand

$\int {7 \sec(\theta) } \, d\theta = 7\int {\sec(\theta) } \, d\theta$

Multiply by 1

$\int {7 \sec(\theta) } \, d\theta = 7\int {\sec(\theta) * 1} \, d\theta$

Express 1 as: $\frac{\sec(\theta) + \tan(\theta) }{\sec(\theta) + \tan(\theta)}$

$\int {7 \sec(\theta) } \, d\theta = 7\int {\sec(\theta) * \frac{\sec(\theta) + \tan(\theta) }{\sec(\theta) + \tan(\theta)}} \, d\theta$

Expand

$\int {7 \sec(\theta) } \, d\theta = 7\int {\frac{\sec^2(\theta) + \sec(\theta)\tan(\theta) }{\sec(\theta) + \tan(\theta)}} \, d\theta$

Let

$u = \sec(\theta) + \tan(\theta)$

Differentiate

$\frac{du}{d\theta} = \sec(\theta)\tan(\theta) + sec^2(\theta)$

Make $d\theta$ the subject

$d\theta = \frac{du}{\sec(\theta)\tan(\theta) + sec^2(\theta)}$

So, we have:

$\int {7 \sec(\theta) } \, d\theta = 7\int {\frac{\sec^2(\theta) + \sec(\theta)\tan(\theta) }{u}} \,* \frac{du}{\sec(\theta)\tan(\theta) + sec^2(\theta)}$

Cancel out $\sec(\theta)\tan(\theta) + sec^2(\theta)$

$\int {7 \sec(\theta) } \, d\theta = 7\int {\frac{1}{u}} \,du}}$

Integrate

$\int {7 \sec(\theta) } \, d\theta = 7\ln(u) + c$

Recall that: $u = \sec(\theta) + \tan(\theta)$

$\int {7 \sec(\theta) } \, d\theta = 7\ln(\sec(\theta) + \tan(\theta)) + c$

8 0

3 years ago

Yakvenalex [24]

Answer:

4. 35 times larger

Step-by-step explanation:

Doing Question #4 Only

Before we see this problem's solution. Lets get a background.

Suppose something has an area of "A" sq. meters.

and

Suppose another land has an area of "B" sq. meters.

and suppose A > B

If we want to know how many times A is larger than B, we simply have to divide the larger one (A) by the smaller one (B).

Now, onto our question:

We want to know how many times larger the national is than state park. So we divide the area of national by the area of state. That would be:

$\frac{7*10^8}{2*10^7}$

Since the numbers are in scientific notation, we look at the rule below on how to divide scientific notation numbers:

$\frac{a*10^b}{c*10^d}=(\frac{a}{c})*10^{b-d}$

Now, we apply the rule:

$\frac{7*10^8}{2*10^7}\\=\frac{7}{2}*10^{8-7}\\=3.5*10^1\\=3.5*10\\=35$

So, the national park is 35 times larger than the state park.

3 0

3 years ago

What is the solution to the equation 6Y -2(Y + 1) = 3(Y - 2) +6?

Andrej [43]

Answer:

Y =2

Step-by-step explanation:

6Y -2(Y + 1) = 3(Y - 2) +6

Distribute

6Y -2Y -2 = 3Y -6 +6

4Y -2 = 3Y

Subtract 4Y from each side

4Y - 4Y -2 = 3Y-4Y

-2 = -Y

Multiply each side by -1

2 = Y

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WINSTONCH [101]

The greater is -10 because -10 is closer to the positive 1 so its -10

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How old would you be today if you were born in 1977?

Montano1993 [528]

Current year is 2016
born year is 1977

old
2016 - 1977
39 years

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