All categories

4 years ago

Divide and express the result in standard form. 8/7-i

2 answers:

5 0

$i=\sqrt{-1}\to i^2=-1\ (i-the\ imaginary\ unit)\\----------------------\\\\\frac{8}{7-i}\\\\use\ (a-b)(a+b)=a^2-b^2\\\\\frac{8}{7-i}\cdot\frac{7+i}{7+i}=\frac{56+8i}{7^2-i^2}=\frac{56+8i}{49-(-1)}=\frac{56+8i}{49+1}=\frac{56+8i}{50}=\frac{56}{50}+\frac{8}{50}i\\\\=\boxed{\frac{28}{25}+\frac{4}{25}i}$

Pani-rosa [81]4 years ago

5 0

Assuming the problem is 8/(7-i) you would multiply the fraction by (7+i)/(7+i)
This would then simplify to 8(7+i)/50 which can be simplified down to 4(7+i)/25

You might be interested in

If the number of bacteria in a colony triples every 60 minutes and the population is currently 2,000 bacteria, what will the pop

lora16 [44]

It's exponential. And you will triple the size every 60 minutes in 240 minutes, so triples 4 times. 2000 times 3 is 6000. 6000 times 3 is 18000. 18000 times 3 is 54000. 54000 times 3 is 162000 so D is the answer.

8 0

3 years ago

the distance from the earth to the sun is( 1.496 x 10^11 ) m and the distance between earth and moon is 3.84 x 10^8 m. during so

melamori03 [73]

Answer:

1.49216 x 10^11 m.

Step-by-step explanation:

That would be the following difference:

1.496 x 10^11 - 3.84 x 10^8

= 1.49216 x 10^11 m.

5 0

3 years ago

The area of a rectangle is 4w - 10 square units.

podryga [215]

Area of rectangle = 2(2w - 5) is the factored form of given expression

Multiplying the length and width of a rectangle, we get the area of the rectangle

Solution:

Given that, area of rectangle is 4w - 10 square units

We have to factor the expression

From given,

Area of rectangle = 4w - 10

Take 2 as common factor

Area of rectangle = 2(2w - 5)

Thus the given expression is factored

The area of rectangle is given as:

$Area\ of\ rectangle = length \times width$

$Area\ of\ rectangle = 2 \times (2w - 5)$

Thus, multiplying the length and width of a rectangle, we get the area of the rectangle

When we multiply 2 with 2w - 5 we get the area of rectangle

From above we can say,

Length = 2 or 2w - 5

Width = 2w - 5 or 2

So when dimensions of rectangle are multiplied we get area of rectangle

3 0

3 years ago

What are the vertical and horizontal asymptotes for the function f (x) =<img src="https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E%7B2%7D%

yaroslaw [1]

Answer:

B. vertical asymptote: x = 1

horizontal asymptote: y = 0

Step-by-step explanation:

1) Vertical asymptotes of a function are determined by what input of x makes the denominator equal 0. So, let's set the denominator, $x^3-1$ , equal to 0 and solve for x:

$x^3-1= 0\\x^3 = 1\\\sqrt[3]{x^3} = \sqrt[3]{1} \\x = 1$

Thus, the vertical asymptote is x = 1.

2) If the degree of the polynomial in the denominator is greater than the one on the top, the horizontal asymptote is automatically y = 0. Thus, the horizontal asymptote is y = 0.

8 0

3 years ago

Read 2 more answers

seven different names are written into sticks and placed into a cup. A stick is chosen 100 times,out of which the name Grace is

NeX [460]

Answer:

The experimental and theoretical probabilities are considerably different. This has to do with the small number of trials. For a higher number of trials, the experimental probability should be very close to the theoretical probability of 0.1429.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Theoretical probability:

The theoretical probability is calculated without considering previous trials.

Experimental probability:

Calculated considering previous trials.

For a small number of trials, these probabilities can differ, but the experimental probability approximates the theoretical as the number of trials increase.

Seven different names are written into sticks and placed into a cup.

So the theoretical probability of choosing Grace is:

$p_T = \frac{1}{7} = 0.1429$

A stick is chosen 100 times,out of which the name Grace is chosen 23 times.

So the experimental probability is:

$p_E = \frac{23}{100} = 0.23$

How do the theoretical probability and experimental probability compare?

6 0

3 years ago