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3 years ago

Consider the set of points defined by z = 5 cos(theta) + 3i sin(theta).

Mathematics

1 answer:

vitfil [10]3 years ago

4 0

Answer:

This is an ellipse.

Step-by-step explanation:

$z=5cos(\theta)+3isin(\theta)$

Applying the angle values in intervals of right angles (90°), the resulting set of values for z are:

$\theta = 0,90,180,270,360$

$z=5,3i,-5,-3i,5$ (again)

If you look at the plot, you will observe how these values represent points in the xy plain. All of them belong to either the x or the y axis.

The resulting figure for the whole set of values of $\theta$ is in fact an ellipse.

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if a, b, and c are prime numbers, do (a b) and c have a common factor that is greater than 1? (1) a, b, and c are all different

klio [65]

If a,b, and c are prime numbers, do (a*b) and c have a common factor that is greater than 1

(1) a,b, and c are all different prime numbers

(2) c≠2

1. Let's assume values of 1,3 and 5 to a, b, and c respectively

a b = 1*3 = 3

3 and 5 do not have any common factor aside 1

Let's assume values of 1,3 and 2 to a,b and c respectively

a *b = 1*3 = 3

3 and 2 does not have a common factor aside 1

2. c $\neq$ 2

Let's assume values of 2,7 and 3 to a b and c response

a * b = 2 *7 = 14

14 and 3 does not have a common factor aside 1

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1 year ago

Can someone help me with these problems? The majority of them I have answers but I don't understand them. Thanks!

zaharov [31]

Question 1:

The area of the triangle is $9\frac{5}{8}$ cm², if you want it rounded to the nearest whole number it will be 10 cm²

Question 2:

The area of the parallelogram is 304.5 m²

Question 3:

The ratio of grilled chicken salads sold to the total number of lunches sold is 1 : 3 in the simplest form

Question 4:

The ratio of odd to even digits in the following number: 7,208,631

is 3 : 4

Question 5:

5 tons is equal to 10,000 pounds

Question 6:

A table measures 3 feet across is 36 inches across

Step-by-step explanation:

Question 1:

The formula of the area of a triangle is $A=\frac{1}{2}bh$ , where

b is the base of the triangle
h is the height of the triangle

∵ The base of the triangle = $5\frac{1}{2}$ cm

∵ The height of the triangle = $3\frac{1}{2}$ cm

- Change the mixed numbers to improper fractions

∵ $5\frac{1}{2}$ = $\frac{(5*2)+1}{2}=\frac{11}{2}$

∵ $3\frac{1}{2}$ = $\frac{(3*2)+1}{2}=\frac{7}{2}$

∴ $A=\frac{1}{2}(\frac{11}{2})(\frac{7}{2})=\frac{77}{8}$ cm²

- To change the improper fraction to mixed number divide 77 by 8

∵ 77 ÷ 8 = 9 and remainder 5 (8 × 9 = 72 , 77 - 72 = 5)

∴ 77 ÷ 8 = $9\frac{5}{8}$

∴ $A=9\frac{5}{8}$ cm²

The area of the triangle is $9\frac{5}{8}$ cm²

If you want to round it to the nearest whole number the area will

be 10 cm²

Question 2:

The formula of the area of a parallelogram is A = b h , where

b is the base of the parallelogram
h is the height of this base of the parallelogram

∵ The base of the parallelogram = 14.5 m

∵ Its height = 21 m

∵ A = b h

∴ A = 14.5 × 21 = 304.5 m²

The area of the parallelogram is 304.5 m²

Question 3:

∵ The cafeteria sold 200 grilled cheese sandwiches, 100 tacos, and

150 grilled chicken salads

∴ The cafeteria sold = 200 + 100 + 150 = 450 lunches

- To find the ratio between the grilled chicken salads sold to the total

number of lunches sold divide them and simplify the answer to the

lowest term

→ G.C.S : Lunches

→ 150 : 450 ⇒ divide both by 10

→ 15 : 45 ⇒ divide both by 5

→ 3 : 9 ⇒ divide both by 3

→ 1 : 3

The ratio of grilled chicken salads sold to the total number of lunches sold is 1 : 3 in the simplest form

Question 4:

The even numbers are the numbers whose one digit is 0 , 2 , 4 , 6 , 8

The odd numbers are the numbers whose one digit is 1 , 3 , 5 , 7 , 9

∵ The number is 7,208,631

∵ The odd digits are 7 , 3 , 1

∴ There are 3 odd digits

∵ The even numbers are 2 , 0 , 8 , 6

∴ there are 4 even digits

∴ The ratio of odd to even digits is 3 : 4

The ratio of odd to even digits in the following number: 7,208,631

is 3 : 4

Question 5:

∵ One ton is equal to 2000 pounds

∵ There are 5 tons

→ Ton : Pound

→ 1 : 2000

→ 5 : x

Use the cross multiplication

∵ 1 × x = 5 × 2000

∴ x = 10,000 pounds

5 tons is equal to 10,000 pounds

Question 6:

∵ A table measures 3 feet across

∵ 1 foot = 12 inches

∴ 3 × 12 = 36 inches

A table measures 3 feet across is 36 inches across

Learn more:

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