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3 years ago

Write the product in standard form. ( 9 + 5i)( 9 + 8i)

Mathematics

1 answer:

disa [49]3 years ago

8 0

( 9 + 5i)( 9 + 8i)
= 9(9+8i)+5i(9+8i)
= 81+72i+45i+40i^2
= 81+117i+40(-1)
= 81-40+117i
= 41+117i. Answer

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Assume varies inversely with . Find the constant of proportionality and the function.

Eddi Din [679]

Answer:

$k = 40$ and $y = \frac{40}{x}$

$k = 33$ and $y = \frac{33}{x}$

$k = 5000$ and $y = \frac{5000}{x}$

Step-by-step explanation:

Given

y varies inversely with x.

This is represented as:

$y =\frac{k}{x}$

Where k is the constant of proportionality.

(a): $y = 8\ when\ x= 5$

This gives:

$8 =\frac{k}{5}$

$k = 8 * 5$

$k = 40$ -- the constant of proportionality.

To calculate the function, substitute 40 for k in $y =\frac{k}{x}$

$y = \frac{40}{x}$

$(b): y= 3\ when\ x = 11$

This gives:

$3 =\frac{k}{11}$

$k = 3 * 11$

$k = 33$ -- the constant of proportionality.

To calculate the function, substitute 33 for k in $y =\frac{k}{x}$

$y = \frac{33}{x}$

$(c): y= 50\ when\ x = 100$

This gives:

$50 =\frac{k}{100}$

$k = 50 * 100$

$k = 5000$ -- the constant of proportionality.

To calculate the function, substitute 5000 for k in $y =\frac{k}{x}$

$y = \frac{5000}{x}$

4 0

2 years ago

Need help with 2,3,4

Harman [31]

Answers:

In these exercices are ilustrated the representations of the fractions

2) Firstly, we have 3 equal segments, each one representing $\frac{1}{4}$ , hence:

$\frac{3}{4}$ is 3 copies of $\frac{1}{4}$

Let's prove it, taking into account we are adding fractions with the same denominator:

$\frac{1}{4}+\frac{1}{4}+\frac{1}{4}=\frac{3}{4}$

There are 4 equal parts that make a whole

Four copies of $\frac{1}{4}$ make $\frac{4}{4}$ or 1 whole

$\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}=\frac{4}{4}=1$

3) Here we have a line divided into four segments, each one of $\frac{1}{5}$ . Hence:

This is $\frac{4}{5}$ of a line. $\frac{4}{5}$ is 4 lengths of $\frac{1}{5}$

$\frac{1}{5}+\frac{1}{5}+\frac{1}{5}+\frac{1}{5}=\frac{4}{5}$

If we draw one more $\frac{1}{5}$ we will have $\frac{5}{5}$ or 1 whole.

Then:

5 lengths of $\frac{1}{5}$ make $\frac{5}{5}$ or 1 whole.

4) In this part the answer is in the attached image. If we have two equal segments, each one of $\frac{1}{3}$ we will have as a result $\frac{2}{3}$ .

If we add another $\frac{1}{3}$ segment, we will have three segments of $\frac{1}{3}$ , having as a result $\frac{3}{3}=1$

3 0

2 years ago

Gnesinka [82]

Answer:

a is 25 b is 15 percent

Step-by-step explanation:

8 0

2 years ago

What is the value of X?

Ugo [173]

∆ABC similar to ∆CBD

DB/AC = CB/AB

$\frac{x}{7.5} = \frac{7.5}{x + 3} \\ x(x + 3) = {7.5}^{2} = { (\frac{15}{2}) }^{2} \\ {x}^{2} + 3x = \frac{225}{4} \\ 4 {x}^{2} + 12x = 225 \\ 4 {x}^{2} + 12x + 9 = 216 \\ {(2x + 3)}^{2} = 216 \\ 2x + 3 = 6 \sqrt{6} \\ x = - 1.5 + 3 \sqrt{6}$

approximately 6.1485

4 0

2 years ago

A cone-shaped tent has a diameter of 12 ft and a height of 6 ft. What is the approximate volume of the tent? Question 2 options:

inessss [21]

Answer:

Step-by-step explanation:

The formula of volume of cone is

V=\frac{1}{3}\pi r^{2} h

where, r is the radius

we have given diameter = 12 =2r

r=6 ft

h is the height h=6 ft

\pi =3.14

Substitute the value in the formula,

V=\frac{1}{3}\pi r^{2} h

V=\frac{1}{3}\times (3.14)\times 6^{2}\times 6

V=\frac{1}{3}\times 3.14\times 36\times 6

V=226.08 ft^3

Therefore, The volume of cone is 226.08 cubic ft.

Read more on Brainly.com - brainly.com/question/9177514#readmore

3 0

2 years ago