(1 point) Find the antiderivative F of f(x)=4−3(1+x2)−1 that satisfies F(1)=−3.

Perform the indicated operations. Write the answer in standard form, a+bi. 5-3i / -2-9i

Vsevolod [243]

$\huge \boxed{\mathfrak{Answer} \downarrow}$

$\large \bf\frac { 5 - 3 i } { - 2 - 9 i } \\$

Multiply both numerator and denominator of $\sf \frac{5-3i}{-2-9i} \\$ by the complex conjugate of the denominator, -2+9i.

$\large \bf \: Re(\frac{\left(5-3i\right)\left(-2+9i\right)}{\left(-2-9i\right)\left(-2+9i\right)}) \\$

Multiplication can be transformed into difference of squares using the rule: $\sf\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$ .

$\large \bf \: Re(\frac{\left(5-3i\right)\left(-2+9i\right)}{\left(-2\right)^{2}-9^{2}i^{2}}) \\$

By definition, i² is -1. Calculate the denominator.

$\large \bf \: Re(\frac{\left(5-3i\right)\left(-2+9i\right)}{85}) \\$

Multiply complex numbers 5-3i and -2+9i in the same way as you multiply binomials.

$\large \bf \: Re(\frac{5\left(-2\right)+5\times \left(9i\right)-3i\left(-2\right)-3\times 9i^{2}}{85}) \\$

Do the multiplications in $\sf5\left(-2\right)+5\times \left(9i\right)-3i\left(-2\right)-3\times 9\left(-1\right)$ .

$\large \bf \: Re(\frac{-10+45i+6i+27}{85}) \\$

Combine the real and imaginary parts in -10+45i+6i+27.

$\large \bf \: Re(\frac{-10+27+\left(45+6\right)i}{85}) \\$

Do the additions in $\sf-10+27+\left(45+6\right)i$ .

$\large \bf Re(\frac{17+51i}{85}) \\$

Divide 17+51i by 85 to get $\sf\frac{1}{5}+\frac{3}{5}i \\$ .

$\large \bf \: Re(\frac{1}{5}+\frac{3}{5}i) \\$

The real part of $\sf \frac{1}{5}+\frac{3}{5}i \\$ is $\sf \frac{1}{5} \\$ .

$\large \boxed{\bf\frac{1}{5} = 0.2} \\$

3 0

3 years ago

Evaluate the expression for a = 14, b = 29, c = 1, d = 1: a + b - C-d

grandymaker [24]

Answer:

Solution,

a=14

b=29

c=1

D=1

Now,

 $a + b - c - d \\ = 14 + 29 - 1 - 1 \\ = 43 - 1 - 1 \\ =42 - 1 \\ = 41$ 

hope this helps...

Good luck on your assignment...

7 0

3 years ago

Read 2 more answers

The speed of light is 299,792.458 .

andrezito [222]

Answer:

a

when you round the number up it becomes 300,000.00

3 0

2 years ago

Employee x earned $5250 in 3 weeks. at this rate how much will employee x earn in 8 weeks

iVinArrow [24]

Answer:

$14000

Step-by-step explanation:

Given parameters:

Amount earned by employee x = $5250

Time duration = 3weeks

Unknown:

Amount earned in 8 weeks = ?

Solution:

Let us first find the rate of employee x earning;

Rate = $\frac{Amount earned}{Time duration}$

Insert parameters;

Rate = $\frac{5250}{3}$ = $1750/week

So,

In 8 weeks;

Amount earned = rate x time duration

Amount earned = $1750/week x 8weeks

Amount earned = $14000

8 0

3 years ago

I Need Help With Statistics

Ilya [14]

Answer: Choice A) mean, there are no outliers

Have a look at the image attached below. I made two dotplots for the data points. The blue points represent bakery A. The red points represent bakery B. For any bakery, the points are fairly close together. There is no point that is off on its own. So there are no outliers, making the mean a good choice for the center. If there were outliers, then the median is a better choice. The mean is greatly affected by outliers, while the median is not.

5 0

3 years ago