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3 years ago

What is the arc length if θ = 7 pi over 4 and the radius is 5?

Mathematics

2 answers:

PolarNik [594]3 years ago

4 0

The formula for arc length is:

s= r∅

Given that ∅= 7π/4

and r= 5

Therefore, arc length s= 7π/4 *5 = 35π/4

jarptica [38.1K]3 years ago

4 0

Answer: The required arc length will be 27.5 units.

Step-by-step explanation: We are given to find the arc length with the following information :

$\theta=\dfrac{7\pi}{4},~~~\textup{radius},~r=5.$

We know that the length of an arc with angle subtended at the center α and radius of the circle r units is given by

$\ell=r\alpha.$

Therefore, the required arc length will be

$\ell=r\theta=5\times\dfrac{7\pi}{4}=\dfrac{35}{4}\times \dfrac{22}{7}=\dfrac{5\times 11}{2}=\dfrac{55}{2}=27.5.$

Thus, the required arc length will be 27.5 units.

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Question 8 Calculate the difference (4x2 + x - 5) – (5x2 - 1).

Rufina [12.5K]

Answer:

x - 6

Step-by-step explanation:

(4x2 + x - 5) - (5x2 - 1)

According to the order of operations, parenthesis come first so we will solve what is in the parenthesis first.

Then we do the multiplication because it comes before addition and subtraction.

4x2 = 8

Now we have 8 + x - 5

Combine like terms and 8-5=3 so we have 3 + x

Now for the second one.

5x2=10

10-1=9

Subtracting this from the first expression we have:

3+x-9 =

x - 6

7 0

2 years ago

Daine received 300 votes in the election for student council president. which was 60% of the students who voted in the election.

Leokris [45]

Answer:

Step-by-step explanation:

i did 300 divided by 60%

6 0

2 years ago

Read 2 more answers

Find the angle of depression from point A to point C. Angle of depression= ?

san4es73 [151]

Check the picture below.

3 0

3 years ago

Suppose that Adam rolls a fair six-sided die and a fair four-sided die simultaneously. Let AAA be the event that the six-sided d

myrzilka [38]

The question is incomplete. Here is the complete question.

Suppose that Adam rolls a fair six-sided die and a fair four-sided die simultaneously. Let A be the event that the six-sided die is an even number and B be the event that the four-sided die is an odd number. Using the sample space of possible outcomes below, answer each of the following questions.

What is P(A), the probabillity that the six-sided die is an even number?

What is P(B), the probability of the four-sided die is an odd number?

What is P(A and B), the probability that the six-sided die is an even number and the four-sided die is an odd number?

Are events A and B independent?

a) Yes, events A and B are independent events.

b) No, events A and B are not independent events.

Answer: P(A) = 1/2

P(B) = 1/2

P(A and B) = 1/4

a) Yes, events A and B are independent events.

Step-by-step explanation: The event A is related to a six-sided die, so total possibilities is 6.

For a six-sided die to show a even number, there are 3 possibilities: (2,4,6)

so, P(A) = 3/6 = 1/2

The event B is for a 4-sided die, i.e. total possibilities is 4.

To show an odd number, there are 2 possibilities: (1,3).

Then, P(B) = 2/4 = 1/2

Now, the probability of occuring A and B is:

P(A and B) = P(A).P(B)

P(A and B) = 1/2*1/2

P(A and B) = 1/4

The events are independent events because the probability of A happening does not influence the occuring of event B.

3 0

3 years ago

Find the perimeter of triangle PQR. Round your answer to the nearest tenth.

BabaBlast [244]

We are given the coordinate of the 3 vertices. From these coordinates we can find the length of the sides using the distance formula and the sum of all the sides will be equal to the perimeter of the triangle.

Side PQ = $\sqrt{ (6-(-2))^{2}+ (1-1)^{2} }=8$

Side QR = $\sqrt{ (4-6)^{2}+ (-3-1)^{2} }=4.5$

Side RP = $\sqrt{ (2-(-4))^{2}+ (-3-1)^{2} }=7.2$

So, the perimeter of the triangle will be 8 + 4.5 + 7.2 = 19.7

You probably misplaced the digits in option A. The correct answer is 19.7 units.

3 0

3 years ago