Mathematics High School

Find a · b, given a = 12(cos pi/3 + i sin(pi/3)), b = 3 (cos(pi/4)+ i sin(pi/4))
Show 3 decimal places.
Please and thank you!!!

Answers

Answer 1

a = 12 (cos(π/3) + i sin(π/3))

b = 3 (cos(π/4) + i sin(π/4))

a • b = 36 (cos(π/3) cos(π/4) + i cos(π/3) sin(π/4) + i cos(π/4) sin(π/3) + i ² sin(π/3) sin(π/4))

… = 36 (cos(π/3 + π/4) + i sin(π/3 + π/4))

… = 36 (cos(7π/12) + i sin(7π/12))

… ≈ -9.32 + i 34.8

Related Questions

In the triangle below AC =____________ cm.

Answers

Answer:

25

Step-by-step explanation:

a^2+b^2=c^2

9+16=25cm

at least i think so

Answer:

AC = 5 cm

Step-by-step explanation:

STEP 1: Find the last side of the triangle using the Pythagorean theorem.

[tex]a^2+b^2=c^2[/tex]

STEP 2: Solve the equation for  c.

[tex]c=\sqrt{b^2+a^2}[/tex]

STEP 3: Substitute the actual values into the equation.

[tex]c=\sqrt{3^2+4^2}[/tex]

STEP 4: Raise  3 to the power of  2.

[tex]c=\sqrt{9+4^2}[/tex]

STEP 5: Raise  4 to the power of  2.

[tex]c=\sqrt{9+16}[/tex]

STEP 6: Add  9 and  16.

[tex]c=\sqrt{25}[/tex]

STEP 7: Solve for [tex]\sqrt{25}[/tex].

[tex]c=5 cm[/tex]

help asap pls! slope intercept form of the equation!! brainliest givin!!

Answers

Answer:

you need to use rise over run to the left on the graph

Step-by-step explanation:

It B
Rise over run would give you up 5 over 2 and it would be a negative. I hope this helps you out!

THERE ARE 55 QUESTIONS ONLY ON 43

Answers

Answer:

D. 40x - 16

General Formulas and Concepts:

Pre-Algebra

Distributive Property

Step-by-step explanation:

Step 1: Define

4(10x - 4)

Step 2: Expand

Distribute 4:                    4(10x) - 4(4)Multiply:                           40x - 16

8.859, 8.8, 8.89, 8.99, 8.815, 8.997

LESSER GRATER ASAP PLS

Answers

Answer:

8.8, 8.815, 8.859, 8.89, 8.99, 8.997.

Step-by-step explanation:

P.S Can I have brainliest?

calculate S17 for the geometric series 256 - 128 + 64 - 32 +... using the finite geometric sum formula. Round your answer to three decimal places.

Answers

Answer:

the answers for the practice:

1. 170.668

2. -6.250

3. 16

4. $51,291.57

i just took it and these are all correct

S₁₇ is 168157.8 for the geometric series 256 - 128 + 64 - 32 +... using the finite geometric sum formula.

What is Sequence?

Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

A geometric series is the sum of an infinite number of terms that have a constant ratio between successive terms.

The given series is 256 - 128 + 64 - 32 +..

First term a=256

Common ratio r=-128/256=-0.5

finite geometric sum formula.

Sₙ=a(1-r)ⁿ/1-r

Put n=17

S₁₇=256(1-(-0.5))¹⁷/1+0.5

=256(1.5)¹⁷/1.5

=256(985.3)/1.5

=252236.8/1.5

=168157.8

Hence, S₁₇ is 168157.8 for the geometric series 256 - 128 + 64 - 32 +... using the finite geometric sum formula.

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Sarah has 600 and dimes in her piggy bank which totals to $123.75 how many quarters and dimes does she have

Answers

Answer:100

Step-by-step explanation:

Because

Answer: Sarah has 425 quarters and 75 dimes

Explanation:
Quarters+Dimes= 600
Quarters+175=600
600-175= 425 quarters

of 8
The perimeter of an equilateral triangle is
150mm.
State the length of one of its sides.
mm​

Answers

Answer:50mm

Step-by-step explanation:

An equilateral triangle has 3 equal sides. So the 150mm is divided by 3 to get the length of each side

The length of one of the sides of equilateral triangle is 50mm.

Equilateral TriangleWhat is equilateral triangle?

Any triangle with three equal sides is said to be equilateral.

Formula for perimeter of a triangle:

The fundamental formula used to determine an equilateral triangle's perimeter.

P = 3a,

where 'a' is one of the triangle's sides.

The equation becomes a + a + a = 3a because an equilateral triangle has three equal sides.

Calculation for the length of the side of equilateral triangle:

The perimeter of an equilateral triangle is 150mm.

Use perimeter formula

P = 3a

150 = 3a

a = 150/3

a = 50

Thus, one side of the equilateral triangle comes to be 50mm.

To know more about types of triangles, here

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A store normally sells certain dress for $160 during a special sale, the store reduces the price of the dress to $120 by what percent is the price of the dress reduced for the sale?

Answers

Answer:

25%

Step-by-step explanation:

Step one:

A store normally sells certain dress for $160 during a special sale

the store reduces the price of the dress to $120

Step two:

Percent reduction= change in price/initial price *100

Percent reduction= 160-120/160 *100

Percent reduction= 40/160*100

Percent reduction==0.25*100

Percent reduction=25%

WILL GIVE BRAINLIEST!!!
which statement describes the locations of the two numbers in the inequality-4/5 < -0.4 on the number line shown. Plz answer thankyou! ​
-4/5 is to the right of - 0.4 and to the left of 0
-4/5 is to the left of -0.4 and to the right of 0
-4/5 is to the right of -0.4 and to the right of 0
-4/5 is to the left of -0.4 and to the left of 0

Answers

Answer:

-4/5 is to the left of -0.4 and to the left of 0

Step-by-step explanation:

so, we have -4/5 and -0.4

we know that -4/5 as a decimal is -0.8

we know that -0.4 as a fraction is -2/5

so, -4/5 is less than -0.8.

this means tbat on a number line, -4/5 would be to the left of -0.4.

because both numbers are negative, both numbers would be left of 0.

so, -4/5 is to the left of -0.4 and to the left of 0

Answer:

-4/5 is to the left of  -0.4  and to the left is 0

Step-by-step explanation:

A book sold 35400 copies in its first month of release. Suppose this represent 9.7 % of the number of copies sold to date. How many copies have been sold to date?

Answers

Answer:

ADDDDDDDD

Step-by-step explanation:

1.
Which of these represents slope-intercept form of a linear equation?
a) y - y1 = m(X-X1)
b) AX + By = C
c) y = mx + b

Answers

Slope intercept form is y = Mx + b

The slope-intercept form of a linear equation that represents a line is: c) y = mx + b

What is the Slope-intercept of a Linear Equation?A linear equation that represents a line can be represented in the slope-intercept form.Where, m = the slope of the line; b represents the y-intercept of the line, therefore, the slope-intercept form is written as: y = mx + b.

Thus, the slope-intercept form of a linear equation that represents a line is: c) y = mx + b

Learn more about slope-intercept form on:

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The total cost for 4 friends to attend a concert is $94.56.

How much does 1 concert ticket cost?

Answers

Answer:

$23.64

Step-by-step explanation:

Answer:

$23.64

Step-by-step explanation:

Divide the total cost by the four tickets to get the price of one ticket

94.56/4=23.64

To train for a triathlon, Mr. Grey swims, bikes, and runs every day. He bikes 10 times the distance that he swims, and he runs 1.5 miles more than half the miles he bikes. If Mr. Grey covers 25.5 miles on each day of training, how many miles does he swim? Bike? Run?

Answers

He bikes 15 miles which is 10 times more than he swims. He runs 9 miles which is half of what he bikes 15/2=7.5. Plus the addition 1.5 miles which is 9. He swims .10 of what he bikes which is 15x.10 which is 1.5 . So he swims 1.5 miles.

Bikes = 15 miles
Run= 9 miles
Swim= 1.5 miles

Add all of them and you get 25.5 which the total amount of miles for his training that day.

A certain plant grows 134 inches every week. How long will it take the plant to grow 714 inches?

Answers

The information we know:

1 week = 134 inches

x = 714

What I did was, I divided 714 by 134 to find the amount of weeks:

[tex]714/134 = 5.3[/tex]

So, from the equation, basically, in 6 weeks (actually 5.3 weeks) the plant will grow 714 inches long

thank you! ps can u give me brainly :3

True or false, if y=7, then 5+27 < 20

Answers

false (take a look at the screenshot below)

What is the product? 3k/k+1 * k2-1/3k3​

Answers

The product of the equations is A = ( k - 1 ) / k²

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

Let the first variable be p = ( 3k / ( k + 1 ) )

Let the second variable be q = ( k² - 1 ) / 3k³

And , A = p x q

Substituting the values in the equation , we get

A = ( 3k / ( k + 1 ) ) x ( k² - 1 ) / 3k³

On simplifying the equation , we get

A = ( 3k / ( k + 1 ) ) [ ( k + 1 ) ( k - 1 ) ] / 3k³

A = ( 1 ) ( k - 1 ) / k²

On further simplification , we get

A = ( k - 1 ) / k²

Hence , the equation is A = ( k - 1 ) / k²

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What is the value of x?

Enter your answer in the box.

X =

Answers

Answer:

x=54

Step-by-step explanation:

2x + 2 = 3x - 52

subtract 2x from both sides, now u have:

2 = x - 52

add 52 from both sides, now u have

54 = x

Answer:

X=54

Step-by-step explanation:

I got it right on the test :)

Pls I need help !!!!

Answers

Answer: x=117

Step-by-step explanation:

180-63=117 because of supplementary angles.

What is a Unit Rate? Give an example to support your answer​

Answers

A unit rate is a rate where the second quantity is one unit , such as $34 per pound, 25 miles per hour, 15 Indian Rupees per Brazilian Real, etc. Example 1: A motorcycle travels 230 miles on 4 gallons of gasoline.

A hiker starts hiking in Death Valley at an elevation of 143 feet below sea level. He climbs up 435 feet and enjoys the view. Then he climbs up another 267 feet. What is his new elevation relative to sea level?

Answers

First you want to take 435 and subtract it by 143 which is 292 then you want to add 292 + 267 which is 559 so 559 is your new elevation related to sea level (if an explanation is needed just ask I can give you one)

Pls helppppp tyyyyyyyy

Answers

Answer:

ghhhushhshshhzhzhhsbshhs

What is the radius for the circle given by the equation
(x - 2)^2+y^2 = 14?
Round your answer to the nearest thousandth.

Answers

Answer: 3.742

Step-by-step explanation:

find the HCF of 50 and 70 by using euclid s division method​

Answers

Answer:

This is answer

Photo beja h Dekhna

determine if each relationship represtents a fuctikn chose yes or no for each relationship​

Answers

Answer:

Yes

no

no

yes

Step-by-step explanation:

I hope it's serving

:v

which linear equation models the relationship shown on the graph ​

Answers

Answer:

D y=2/3x+3

Step-by-step explanation:

I hope that helps

Find the missing values of the variables.The diagram is not to scale.

Answers

Answer:

option A x=115,y=63

Step-by-step explanation:

y+117=180 linear pair

y=180-117=63

again

x+y+120+62=360 sum of interior angle of quadrilateral is 360

x+63+120+62=360

x=360-245=115°

Sally and her best friend Susan like going to the beach to collect seashells. On
Tuesday, Sally found 18 seashells and Susan collected 37. How many seashells did
they find? *

Answers

Answer:

55?

Step-by-step explanation:

PLEASE ANSWER ALL OF THESE
THANK YOU

Answers

5. 10
6. 3
7. 1
8. 23

This is just adding and subtracting. You better get studying

A sign says the distance to the next exit is 5 mi. The actual distance is 5.2 mi. To the nearest percent, what is the percent error of the sign?

Answers

Answer:

About 4%

because 5 of 5.2 is about 96% so 100% - 96% = 4%

Answer:

4%

Step-by-step explanation:

vA = actual value

vE = expected value

percent error = ((vA - vE) / vE) x 100

((5.2 - 5) / 5) x 100 = 4

4%

please answer down below and please use all the boxes

Answers

Answer:

Step-by-step explanation:

7

364

318

6

all of the answers are in order of the boxes

hope this helps <3

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