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3 years ago

Can someone plz help me with this math equation!

Mathematics

1 answer:

kakasveta [241]3 years ago

5 0

Answer:

x² + 2x + 9 - $\frac{7}{x+3}$

Step-by-step explanation:

Using Synthetic division

- 3 | 1 5 15 20

↓ - 3 - 6 - 27

----------------------------

1 2 9 - 7 ← remainder r(x)

Quotient Q(x) = x² + 2x + 9

Thus

x³ + 5x² + 5x + 20 = x² + 2x +9 - $\frac{7}{x+3}$

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Iteru [2.4K]

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2 years ago

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Marina86 [1]

Answer: A.) y=-2/3x-3

7 0

3 years ago

Evaluate the following integral using trigonometric substitution

serg [7]

Answer:

The result of the integral is:

$\arcsin{(\frac{x}{3})} + C$

Step-by-step explanation:

We are given the following integral:

$\int \frac{dx}{\sqrt{9-x^2}}$

Trigonometric substitution:

We have the term in the following format: $a^2 - x^2$ , in which a = 3.

In this case, the substitution is given by:

$x = a\sin{\theta}$

$dx = a\cos{\theta}d\theta$

In this question:

$a = 3$

$x = 3\sin{\theta}$

$dx = 3\cos{\theta}d\theta$

$\int \frac{3\cos{\theta}d\theta}{\sqrt{9-(3\sin{\theta})^2}} = \int \frac{3\cos{\theta}d\theta}{\sqrt{9 - 9\sin^{2}{\theta}}} = \int \frac{3\cos{\theta}d\theta}{\sqrt{9(1 - \sin^{\theta})}}$

We have the following trigonometric identity:

$\sin^{2}{\theta} + \cos^{2}{\theta} = 1$

$1 - \sin^{2}{\theta} = \cos^{2}{\theta}$

Replacing into the integral:

$\int \frac{3\cos{\theta}d\theta}{\sqrt{9(1 - \sin^{2}{\theta})}} = \int{\frac{3\cos{\theta}d\theta}{\sqrt{9\cos^{2}{\theta}}} = \int \frac{3\cos{\theta}d\theta}{3\cos{\theta}} = \int d\theta = \theta + C$

Coming back to x:

We have that:

$x = 3\sin{\theta}$

$\sin{\theta} = \frac{x}{3}$

Applying the arcsine(inverse sine) function to both sides, we get that:

$\theta = \arcsin{(\frac{x}{3})}$

The result of the integral is:

$\arcsin{(\frac{x}{3})} + C$

8 0

3 years ago

What is this number in standard form? 5.75 x 10^9

sergey [27]

Step-by-step explanation:

57,500,000,000 is in standard form

5 0

2 years ago

Read 2 more answers

You have$560 in an account which pays 4.8% compounded annually. If you invest your money for 8 years, then how many dollars of i

SCORPION-xisa [38]

Answer:

$ 254.85

Step-by-step explanation:

Total amount invested = $ 560

Interest rate = r = 4.8% = 0.048

Time in years = t = 8 years

The formula for compound interest is:

$A =P(1+\frac{r}{n})^{nt}$

Here,

A is the total amount accumulated after t years. P is the amount invested initially and n is the compounding periods per year. Since in this case compounding is done annually, n will be 1. Using the values in the above formula, we get:

$A=560(1+\frac{0.048}{1})^{8} = \$ 814.85$

Thus, the total amount accumulated after 8 years will be $ 814.85

The amount of interest earned will be:

Interest = Amount Accumulated - Principal Amount

Interest = $ 814.85 - $ 560 = $ 254.85

By the end of 8 years, $ 254.85 would be earned in interest.

7 0

3 years ago