All categories

3 years ago

WILL MARK

Mathematics

1 answer:

Alex777 [14]3 years ago

5 0

Answer:

about 3.492

Step-by-step explanation:

The distance between points in polar coordinates can be found using the Law of Cosines. For vector magnitudes a and b, and angular difference C, the distance between them (c) can be found from ...

c^2 = a^2 +b^2 -2ab·cos(C)

= 7^2 +5^2 -2(7)(5)cos((217/180π -(-23/36)π)

= 74 -70cos(332°) ≈ 12.1937

c = √12.1937 ≈ 3.492

The distance between the given points is about 3.492 units.

You might be interested in

Tickets to a school musical cost $7.25. The amount received from ticket sales is $833.75. How many tickets were sold?

KonstantinChe [14]

Answer: 115

Divide 833.75 by 7.25

5 0

3 years ago

Read 2 more answers

A rectangular bedroom is 4 ft longer than it is wide. Its area is 252 ft2. What is the width of the room?

Ksenya-84 [330]

Answer:

14 ft

Step-by-step explanation:

Given:

Bedroom is 4 ft longer than it is wide.
Area is 252 ft².

Let x = width of the bedroom:

width = x ft
length = (x + 4) ft

Therefore:

$\begin{aligned}\textsf{Area of a rectangle} & = \sf width \times length\\\implies 252 & = x(x+4)\\252 & = x^2+4x\\x^2+4x & = 252\end{aligned}$

To find the value(s) of x, complete the square.

Add the square of half the coefficient of the term in x to both sides:

$\implies x^2+4x+\left(\dfrac{4}{2}\right)^2=252+\left(\dfrac{4}{2}\right)^2$

$\implies x^2+4x+4=256$

Factor the perfect trinomial on the left side:

$\implies (x+2)^2=256$

Square root both sides:

$\implies x+2= \pm \sqrt{256}$

$\implies x+2= \pm 16$

Therefore:

$\implies x=-2+16=14$

$\implies x=-2-16=-18$

As width cannot be negative, the width of the room is 14 ft.

3 0

2 years ago

The cost to produce the master disc of a DVD is $2000, while additional discs costs $4 each. Determine a profit function P that

Mkey [24]

Answer:

9000

Step-by-step explanation:

$13200 is the cost to produce all of the cds.

if they sell them all, for $15 each, we get $4200,

so, if we subtract the cost to produce them, versus what they made off them we get:

$9000.

the profit is $9000

6 0

3 years ago

Read 2 more answers

Select the correct answer from each drop-down menu.

Lilit [14]

Answer:

The probability of the spinner landing on an even number or a multiple of 3 is 0.6667 .

The probability of the spinner landing on an odd number or a number between 4 and 15 (both numbers excluded) is 0.7778 .

Step-by-step explanation:

Be the events

A = even number

B = Multiple of 3

C = Odd Number

D = Number between 4 and 15, both numbers excluded

The sets are as follows:

A = {2,4,6,8,10,12,14,16,18}

B = {3,6,9,12,15,18}

C = {1,3,5,7,9,11,13,15,17}

D = {5,6,7,8,9,10,11,12,13,14}

To calculate the probability that the roulette lands in an even number or in a multiple of 3, we make the union of A and B:

A U B = {2,3,4,6,8,9,10,12,14,15,16,18} = 12 numbers of 18

P (A U B) = 12/18 = 2/3 = 0.6667

To calculate the probability that roulette lands on an odd number or a number between 4 and 15 (both numbers excluded), we make the union of C and D:

C U D = {1,3,5,6,7,8,9,10,11,12,13,14,15,17} = 14 numbers of 18

P (C U D) = 14/18 = 7/9 = 0.7778

The first answer is 0.6667

The second answer is 0.7778

Hope this helps!

7 0

3 years ago

What is the exact area and arc length of these sectors? Please helppp

Karolina [17]

Answers with step-by-step explanation:

1. Area of sector 1 = $\frac{90}{360} \times \pi \times 12^2 = 36\pi$

2. Area of sector 2 = $\frac{45}{360} \times \pi \times 19^2 = \frac{2527}{8} \pi$

3. Area of sector 3 = $\frac{270}{360} \times \pi \times 15^2 = \frac{675}{4} \pi$

4. Area of sector 4 = $\frac{270}{360} \times \pi \times 6^2 = 27 \pi$

5. Arc length of sector 1 = $\frac{90}{360} \times 2 \times \pi \times 12 = 6\pi$

6. Arc length of sector 2 = $\frac{315}{360} \times 2 \times \pi \times 19 = \frac{133}{4} \pi$

7. Arc length of sector 3 = $\frac{270}{360} \times 2 \times \pi \times 15 = \frac{45}{2}\pi$

8. Arc length of sector 4 = $\frac{270}{360} \times 2 \times \pi \times 6 = 9\pi$

4 0

3 years ago