Mathematics College

1. Nancy is walking around a circular track with a radius of 45 feet. If she walks the equivalent of 210 degrees, find the total distance she has walked around the track to the nearest foot.

2. A windshield wiper blade is 18 inches long. Calculate the area covered by the blade as it rotates through an angle of 122 degrees. Round your answer ti the nearest square inch.

3. A spray irrigation system waters a section of a farmer's field. If the water shoots a distance of 75 feet, what is the area that is watered as the sprinkler rotates through an angle of 80 degrees? Round your answer to the nearest square foot.

Answers

Answer 1

Answer:

see explanation

Step-by-step explanation:

(1)

The distance walked ( arc length ) is calculated as

arc = circumference of circle × fraction of circle

= 2πr × [tex]\frac{210}{360}[/tex]

= 2π × 45 × [tex]\frac{21}{36}[/tex]

= 90π × [tex]\frac{7}{12}[/tex]

≈ 165 ft ( to the nearest foot )

(2)

The area (A) covered is calculated as

A = area of circle × fraction of circle

= πr² × [tex]\frac{122}{360}[/tex]

= π × 18² × [tex]\frac{61}{180}[/tex]

= 324π × [tex]\frac{61}{180}[/tex]

≈ 345 in² ( to the nearest square inch )

(3)

The area (A) is calculated as

A = area of circle × fraction of circle

= πr² × [tex]\frac{80}{360}[/tex] ( r is the distance shot by sprinkler )

= π × 75² × [tex]\frac{8}{36}[/tex]

= 5625π × [tex]\frac{2}{9}[/tex]

≈ 3927 ft² ( to the nearest square foot )

Answer 2

Answer:

9514 1404 393

Answer:

top down: 1, 5, 6, 4, 8, 2, 3, 7

Step-by-step explanation:

It appears the expected order may be ...

Write the formula for the arc length of a circle with central angle, θ, in degrees.

\textit{Arc Length}=\dfrac{\theta}{360^{\circ}}\cdot 2\pi rArc Length=

360

∘

⋅2πr

Replace 360° with 2π radians.

\dfrac{\theta}{360^{\circ}}=\dfrac{\theta}{2\pi}

360

∘

2π

Replace the angle ratio in degrees with the angle ratio in radians.

\textit{Arc Length}=\dfrac{\theta}{2\pi}\cdot 2\pi rArc Length=

2π

⋅2πr

Simplify by cancelling

\textit{Arc Length}=\theta rArc Length=θr

Related Questions

Solve 4h = 92 for h.

h = ___

Answers

Answer:

H= 23

Step-by-step explanation:

92 divided by 4 will give you 23

Answer:

h = 23

Step-by-step explanation:

Divide each term by 4 and simplify.

A science fair poster is a rectangle 4 feet long and 3 feet wide. What is the area of the poster in square inches?
Be sure to include the correct unit in your answer.
in
in?
in?
G
Х
?

Answers

4x3=12 the poster is 12 feet^2 but now you have to convert it into inches. 12 inches=1 foot so you multiply 12x12 =144 so the poster is 144in^2

Proving the Sum of the Interior Angle Measures of a Triangle Is 180

Answers

What Do you need help?

The sum of the interior angles of a triangle is 180° is proved below.

We are given that;

To prove angle sum property of triangle

Now,

There are different ways to prove that the sum of the interior angles of a triangle is 180°. Here are three common proofs:

Proof : Using parallel lines and alternate interior angles

Since the line PQ is parallel to the side BC, and AB and AC are transversals, we can use the property that alternate interior angles are congruent.

Therefore, we have:

∠QAC = ∠ACB

∠PAB = ∠ABC

Adding these equations, we get:

∠QAC + ∠PAB = ∠ACB + ∠ABC

But ∠QAC + ∠PAB is a straight angle, which measures 180°. So, we have:

180° = ∠ACB + ∠ABC

Adding ∠CAB to both sides, we get:

180° + ∠CAB = ∠ACB + ∠ABC + ∠CAB

Simplifying, we get:

180° = ∠ACB + ∠ABC + ∠CAB

Hence, by the triangles the answer will be given above.

Learn more about the triangles;

https://brainly.com/question/2773823

#SPJ4

Help me please, thank you :)

Answers

Answer:

300 children

Step-by-step explanation:

half hour: 25 children

1 hour: 25×2= 50 children

6 hours: 50×6= 300 children

hope it helps ☺️!

300 kids in 6 hours

Jim’s backyard is rectangular with dimensions of 75 feet by 120 feet. He is planning to designate part of the yard to plant a vegetable garden. The garden will be a similar rectangle, using a scale factor of 2/5. How much fencing will he need if he wants to enclose the garden on all four sides?
He will need __________ feet of fence.

Answers

Answer:

15.6 feet of fence

Answer:

The answer is 45 ft. I hope i helped <3

Step-by-step explanation:

Find the value of x
Please help

Answers

Answer:

x=67

Step-by-step explanation:

Two ways to solve it:

1st way: Just looking at it, x is definitely not 180° because it’s to big of an angle, it is definitely not 113° because it’s still to big of an angle, and it’s also not 90° because it doesn’t form a right angle. So it must be 67°.

2nd way: Since two angles in a straight line add up to 180°, you can subtract 113° from 180° to find what x is. You can tell that 180° - 113° is equal to 67°

So either way, the answer is: x=67

Hope this helped! :)

67 according to the vertical angle postulate

Consider the inequity

Answers

Answer:

What inequality??

Step-by-step explanation:

Answer:

where?

120

Step-by-step explanation:

Answer:

120

Step-by-step explanation:

first figure out parenthesis

replace n for 1 then you get 13-5, and you get 8.

then you just have to multiply 15 x 8.

then you get 120

(Giving brainliest)

Solve five ninths plus four sixths.

A) sixty six fifty fourths
B) ten fifteenths
C) thirty ninths

Answers

Answer:

Step-by-step explanation:

Make it the same denominator so you can add them (18.)
Multiply 5/9 by 2 and multiply 4/6 by 3.
10/18 + 12/18 = 22/18.
Since there is not 22/18 listed, you can use this fraction as a proportion. The only proportion that can be evident is answer A, as when you multiply 22/18 by 3, you get 66/54.
Your answer is A.

Determine the equation for the line that passes through (2,-1) and (6,5)
Write in point slope form
Write in slope intercept form
Write in standard form

Answers

Answer with explanation:

The equation of a line passing through (a,b) and (c,d) is given by :-

[tex](y-b)=\dfrac{d-b}{c-a}(x-a)[/tex]

Equation of line passing through (2,-1) and (6,5) is given by :-

[tex](y-(-1))=\dfrac{5-(-1)}{6-2}(x-2)\\\\\Rightarrow\ (y+1)=\dfrac{6}{4}(x-2)[/tex]

[tex]\\\\\Rightarrow\ (y+1)=\dfrac{3}{2}(x-2)\ \ \ \ \ \text{[point slope form} : (y-y_1)=m(x-x_1)] \\\\\Rightarrow\ y+1=\dfrac{3}{2}x-3\\\\\Rightarrow\ y=\dfrac32x-4\ \ \ \ \ [\text{ slope intercept form} : y= mx+c]\\\\\Rightarrow\ 2y= 3x-2\times4\\\\\Rightarrow\ 2y=3x-8\\\\\Rightarrow\ 3x-2y=8 \ \ \ \ [\text{Standard form : Ax + By = C}][/tex]

What is the range of fx) = 3^x

Answers

Answer: For the cubic function f(x)=x3 f ( x ) = x 3 , the domain is all real numbers because the horizontal extent of the graph is the whole real number line. The same applies to the vertical extent of the graph, so the domain and range include all real numbers.

Step-by-step explanation:

What is the missing value for the probability distribution table ?
X 1 2 3 4 5
P(X) 0.05 0.35 0.15 0.2

Answers

The answer is 0.3 cause when you subtract all of it you can get it

Solve 8a – 15 – 6a + 3a = 85

Answers

Answer:

a = 20

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Equality Properties

Step-by-step explanation:

Step 1: Define

8a - 15 - 6a + 3a = 85

Step 2: Solve for a

Combine like terms: 5a - 15 = 85Isolate a term: 5a = 100Isolate a: a = 20

Don’t PUT A Random Answer PLEASE

Answers

Answer:

314

Step-by-step explanation:

Answer:

ok I won't

Step-by-step explanation:

6. Slope =
Y-Intercept
Equation in slope-intercept form:

Answers

Slope = 0.5x
Y intercept = 1
Equation: 0.5x +1

PLEASE HELP it would be appreciated!!!!

Answers

Answer:

B 15

Step-by-step explanation:

Since the triangle has two same side lengths you can calculate that the other two are 54°.

Answer:

D. 33

Step-by-step explanation:

(3x+9)=72=180

3x + 81 = 180

subtract 81 from both sides

3x =180

divide 3 from both sides to get the x alone

x=33

Mark me brainliest by clicking the button at the bottom of this answer next to comments

thnk youuu

11. A tank is being filled up with water. At t=0, we know that the tank holds 150 gallons of
water, and after one hour ( t=1) , it holds 180 gallons of water.
a) Assuming that the volume of water in the tank, V, is a linear function of time, t, in hours,
find a formula for V ( linear function)

b) BY what percent did the volume of water increase from t=0 to t= 1?

Answers

Answer:

V = 30t + 15020%

Step-by-step explanation:

Given

Initial volume = 150 galVolume after 1 hour = 180 gal

a) The volume formula will be:

V = 30t + 150

As 150 is y-intersect (volume at zero time) and the rate of change (the slope) is 30 gal per hour

b) Increase of volume by percent:

30 gal increase on top of 150 gal

30/150*100% = 20%

Answer:

20%

Step-by-step explanation:

The volume formula is V = 30t + 150 → where 150 is y-intersect and the slope is 30 gals per hour

So you can do:

30 gals of increase on top of the 150 gals to get:

30/150×100% which equals 20%

There were 30 cars and 20 trucks in the parking garage. What is the ratio of cars to total vehicles?
A. 3 to 2
B. 7 to 2
C. 3 to 5
D. 2 to 3

Answers

I believe C. 3 to 5!

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