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nata0808 [166]
2 years ago
5

Consider the line y=-4/7x+4.

Mathematics
1 answer:
Wittaler [7]2 years ago
7 0

Answer:

1). y = -4/7x         2). y = 7/4x - 65/4

Step-by-step explanation:

1). When a line is parallel, the slope remains the same.

y = -4/7x + b

-4 = -4/7(7) + b

-4 = -4 + b

0 = b

The equation is simply y = -4/7x.

2). When a line is perpendicular, the slope becomes the exact opposite.

y = 7/4x + b

-4 = 7/4(7) + b

-4 = 49/4 + b

-65/4 = b

The equation is y = 7/4x - 65/4.

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Answer:

C

Step-by-step explanation:

An approximation of an integral is given by:

\displaystyle \int_a^bf(x)\, dx\approx \sum_{k=1}^nf(x_k)\Delta x\text{ where } \Delta x=\frac{b-a}{n}

First, find Δx. Our a = 2 and b = 8:

\displaystyle \Delta x=\frac{8-2}{n}=\frac{6}{n}

The left endpoint is modeled with:

x_k=a+\Delta x(k-1)

And the right endpoint is modeled with:

x_k=a+\Delta xk

Since we are using a Left Riemann Sum, we will use the first equation.

Our function is:

f(x)=\cos(x^2)

Therefore:

f(x_k)=\cos((a+\Delta x(k-1))^2)

By substitution:

\displaystyle f(x_k)=\cos((2+\frac{6}{n}(k-1))^2)

Putting it all together:

\displaystyle \int_2^8\cos(x^2)\, dx\approx \sum_{k=1}^{n}\Big(\cos((2+\frac{6}{n}(k-1))^2)\Big)\frac{6}{n}

Thus, our answer is C.

*Note: Not sure why they placed the exponent outside the cosine. Perhaps it was a typo. But C will most likely be the correct answer regardless.

5 0
3 years ago
100 POINTS PLEASE HELP ASAP!!!!
Alika [10]

Answer: To clear an equation of decimals, multiply each term on both sides by the power of ten that will make all the decimals whole numbers. In our example above, if we multiply .25 by 100, we will get 25, a whole number. Since each decimal only goes to the hundredths place, 100 will work for all three terms.

So let's multiply each term by 100 to clear the decimals:

(100)0.25x + (100)0.35 = (100)(-0.29)

25x + 35 = -29

Now we can solve the equation as normal:

25x + 35 - 35 = -29 - 35

25x = -64

x = -2.56 Since the original was in decimal form, the answer should most likely also be in decimal form.

Let's look at one more:

1.75x + 4 = 6.2

We have to think a little more carefully about what multiple of ten to use here. 6.2 only needs to be multiplied by 10, but 1.25 needs 100, so we will multiply every term by 100. Don't forget to multiply the 4 by 100 as well.

(100)(1.75x) + (100)(4) = (100)(6.2)

175x + 400 = 620

We had to be extra careful as we multiplied by 100. Now we can solve the equation as normal:

175x + 400 - 400 = 620 - 400

175x = 220

x = 1.26

Step-by-step explanation:

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