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Arturiano [62]
3 years ago
8

Find the product of the complex numbers. Express your answer in trigonometric form.

Mathematics
1 answer:
alekssr [168]3 years ago
4 0
<span>10(cos(4pi/3) + i sin(4pi/3)) To multiply complex numbers in trigonometric form, you simply multiply the radii and add the thetas. We have: z1=5(cos(pi/2)+i sin(pi/2)) z2=2(cos(5pi/6)+i sin(5pi/6)) The radii for the above 2 numbers are 5 and 2. So the result will have a radius of 5*2 = 10. The thetas are pi/2 and 5pi/6, so the new theta will be pi/2 + 5pi/6 = 3pi/6 + 5pi/6 = 8pi/6 = 4pi/3. So the answer is: 10(cos(4pi/3) + i sin(4pi/3))</span>
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What is the height of a rectangular prism that has a volume of 280 cubic meters,a length of 8 meters, and a width of 7 meters? S
lyudmila [28]
When looking at a rectangular prism, we know that Volume = length * width * height

If we are given that the volume of the prism is 280 cubic meters (m^3), the length is 8 meters, and the width is 7 meters, we can fill in our equation.

280 = 8 * 7 * height
280 = 56 * height

Because we are solving for the height, we divide both sides by 56

280/56 = height

height = 5 meters

8 0
3 years ago
Dati gli insiemi A(1,2,3,4,5) B(3,4,5,6,7) C(2,4,6,8) calcola il risultato della seguente espressione: (A∩B)∩C
Oduvanchick [21]

Answer:

(4)

Step-by-step explanation:

L'intersezione si occupa di elementi comuni

segno per intersezione = ∩

A = (1,2,3,4,5)

B = (3,4,5,6,7)

C = (2,4,6,8)

(A∩B)∩C

(A∩B) = (3, 4, 5)

(A∩B)∩C = (4)

6 0
3 years ago
A local eat-in pizza restaurant wants to investigate the possibility of starting to deliver pizzas. The owner of the store has d
Alinara [238K]

Answer:

Read step by step explanation

Step-by-step explanation:

The owner already knows that the limit for the average time delivered pizzas is 38 minutes. So we conclude

1.-The resulting mean from sample data ( x ) ( 27 customers) need to be smaller than 38 minutes, any value of sample above 38 minutes means more time for the delivery action and will indicate a failure for the future project

2.-As sample size is smaller than 30 the test has to be  t-student one tail test to the left

Test hypothesis

Null hypothesis                       H₀                  x  = 38

Alternative hypothesis           Hₐ                  x  <  38

We should test at a significance level α  = 0,05       (α = 5%)

If the result of the test is to accept  H₀  delivery project won´t be implemented, if on the other hand, H₀ is rejected then in the condition of the alternative hypothesis we accept Hₐ the sample indicates that we have a smaller average time than 38 minutes.

4 0
3 years ago
Use the discriminate to determine the number and the nature of the solutions of the giving equation.
PolarNik [594]

Answer:

Since b^2 -4ac = 256 we have 2 real distinct root roots

Step-by-step explanation:

4x^2+12x=7

We need to subtract 7 to get it in the proper form

4x^2+12x-7=7-7

4x^2+12x-7=0

The discriminant is b^2 -4ac

when the equation is ax^2 +bx+c

so a =4   b=12 and c=-7

(12)^2 - 4(4)(-7)

144 +112

256

If b^2 -4ac > 0 we have 2 real distinct roots

If b^2 -4ac = 0 we have one real root

If b^2 -4ac < 0 we have two complex root

Since b^2 -4ac = 256 we have 2 real distinct root roots

7 0
3 years ago
What is the slope the line?
laila [671]

Answer:

the slope is 3/4x

Step-by-step explanation:

if you need it in slope intercept form too its y=3/4x-1

4 0
3 years ago
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