A golfer hits a golf ball with an initial velocity of 100 miles per hour. The range R of the ball as a function of the angle θ to the horizontal is given by R(θ)=672sin(2θ), where R is measured in feet. Round to two decimal places. Write DNE if the solution does not exist.

​A) At what angle θ should the ball be hit if the golfer wants the ball to travel 450 feet (150 yards)?

degrees

B) At what angle θ should the ball be hit if the golfer wants the ball to travel 540 feet (180 yards)?
degrees

" role="presentation" style="position: relative;">C) At what angle θ should the ball be hit if the golfer wants the ball to travel at least 480 feet (160 yards)?

degrees

D) At what angle ​ θ should the ball be hit if the golfer wants the ball to travel 720 feet (240 yards)?

Answers

Answer 1

Answer:

  A) 21.02°

  B) 26.74°

  C) 22.79°

  D) DNE

Step-by-step explanation:

We can solve the equation for the angle:

  D = 672·sin(2θ)

  D/672 = sin(2θ)

  arcsin(D/672) = 2θ

  θ = arcsin(D/672)/2

A) For D = 450, θ = arcsin(450/672)/2 = 21.0198° ≈ 21.02°

B) For D = 540, θ = arcsin(540/672)/2 = 26.7363° ≈ 26.74°

C) For D = 480, θ = arcsin(480/672)/2 = 22.7923° ≈ 22.79°

D) For D = 720, θ = arcsin(720/672)/2 = DNE

A Golfer Hits A Golf Ball With An Initial Velocity Of 100 Miles Per Hour. The Range R Of The Ball As

Related Questions

A box is 12 in, high, 24 in. long, and 8 in. wide. What is the longest poster you could fit in
the box? Use pencil and paper. Explain why you can only fit one maximum-length poster in the box
but you can fit multiple 26-in, posters in the same box.

Answers

The maximum length of the poster that can be put in the box is [tex]28in[/tex].

Cuboid

In a cuboid, the longest dimension is the diagonal of the cuboid.

   Diagonal = [tex]\sqrt{(length)^{2}+(width)^{2}+(height)^{2} }[/tex]

How to calculate the diagonal of a cuboid?

Let,    [tex]l=[/tex] the length of the cuboid

         [tex]b=[/tex] the width of the cuboid

         [tex]h=[/tex] the height of the cuboid

And   [tex]d=[/tex] the diagonal of the cuboid

So, as per the formulae [tex]d=\sqrt{l^{2}+b^{2}+h^{2} }[/tex]

Assigning the given values,

[tex]l=24[/tex]

[tex]b=8[/tex]

[tex]h=12[/tex]

Now, calculate [tex]d[/tex] using the formulae,

[tex]d=\sqrt{24^{2}+8^{2}+12^{2}}=\sqrt{576+64+144}=\sqrt{784}=28[/tex]

Hence, the maximum length of the poster that can be put in the box is [tex]28in[/tex].

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The longest poster that fits in the box is 28 inches, matching the diagonal length. Multiple 26-inch posters fit due to the box's length of 24 inches.

To determine the longest poster that can fit inside the box, we need to find the length of the diagonal of the box, as this represents the maximum length a poster can have and still fit within the box.

Given dimensions of the box:

- Height (h) = 12 inches

- Length (l) = 24 inches

- Width (w) = 8 inches

We will use the formula for the diagonal ( d ) of a rectangular box:

[tex]\[ d = \sqrt{h^2 + l^2 + w^2} \][/tex]

Substitute the given values:

[tex]\[ d = \sqrt{12^2 + 24^2 + 8^2} \][/tex]

[tex]\[ d = \sqrt{144 + 576 + 64} \][/tex]

[tex]\[ d = \sqrt{784} \][/tex]

[tex]\[ d = 28 \text{ inches} \][/tex]

Therefore, the diagonal ( d ) of the box is 28 inches.

Now, the longest poster that can fit inside the box cannot exceed this diagonal length of 28 inches. Hence, the longest poster that can fit in the box is 28 inches in length.

Regarding why you can fit multiple 26-inch posters but only one 28-inch poster:

- The box is 24 inches long, so a 26-inch poster can fit along the length of the box without exceeding it.

- However, a 28-inch poster matches the diagonal length exactly, meaning it stretches from one corner of the box to the opposite corner, utilizing the maximum space available inside the box. Trying to fit more than one 28-inch poster would require overlapping or exceeding the box's dimensions, which is not possible.

In conclusion:

- The longest poster that can fit in the box is **28 inches** in length, corresponding to the length of the diagonal of the box.

- You can fit multiple 26-inch posters in the box because each poster fits within the length of the box without overlapping or exceeding the dimensions.

A right prism has a base in the shape of an octagon. The side length of the octagon is 4 inches. The length of the apothem is 4.83 inches. The height of the prism is 12 inches. What is the volume of the prism? Round your answer to the nearest whole number.

___cubic inches

Answers

Answer:

your fricked I don't even know this lolll

Answer:

927 Cubic inches

Step-by-step explanation:

Area of Octagon, using the formula for finding the area of regular polygons (A = 1/2 x apothem x perimeter): A= 1/2 x 4.83 x 4(8) -> A = 77.28

Then using the Area of the base , you then multiply it with the height, and you get your volume: 77.28 x 12 = 927 cubic inches

The solution of the equation 2X-1.7 = 9
IS X =
NEED ASAP !!!!!!!

Answers

Answer:

x=5.35

Step-by-step explanation:

2x - 1.7 = 9

2x - 1.7 + 1.7 = 9 + 1.7

2x = 10.7

2x/2 = 10.7/2

x=5.35

Hope this Helps :)

The solution of the equation 2X-1.7 = 9 is x=5.35

What is an equation?

An equation is a mathematical statement that shows that two mathematical expressions are equal.

For example, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

For example, 3x – 5 = 16 is an equation.

Given is an equation, 2x-1.7 = 9 we need to solve for x,

2x - 1.7 = 9

2x - 1.7 + 1.7 = 9 + 1.7 [addition property of equality]

2x = 10.7

2x/2 = 10.7/2 [division property of equality]

x=5.35

Hence, the solution of the equation 2X-1.7 = 9 is x=5.35

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Use the given circle. Find the length “s” to the nearest tenth.

*picture*

A. 15.7 in.
B. 37.7 in.
C. 31.4 in.
D. 18.8 in.

Answers

Where the picture???

The arc length of the sector will be 15.7 inches. Then the correct option is A.

What is the arc length of the sector?

Let r is the radius of the sector and θ be the angle subtends by the sector at the center. Then the arc length of the sector of the circle will be

Arc = (θ/2π) 2πr

The diagram is given below.

r = 3

θ = 5/3 π

Then the arc length will be

Arc = (5/3 π/2π) 2π x 3

Arc = 5/3 x π x 3

Arc = 15.7 inches

Then the correct option is A.

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Please help me I don’t understand

Answers

Answer:

I think it's a or d I think

Josh washes cars for his neighbors to earn extra money. He charges $12 for every car he wash. Which of the following does not represent a relationship

Answers

Y=x+12
I guess!! Hope you find a better answer

Answer:

y = x + 12

Step-by-step explanation:

y= x+ 12 is the only one that does no represent the relationship because it adds x to 12, instead of multiplying x by 12, which would accurately represent the relationship

Which question is statistical?
What number of feet is equivalent to three miles?
How many miles did your family drive last week?
How many miles are between the library and the post off
How many miles does each member of the biking club ri

Answers

Answer:

How many miles does each member of the biking club ri de>

Step-by-step explanation:

This question is statistical, because 1) it provides a thing for you to study (how many miles does each member ride, as well as 2) provides (hopefully) enough respondents (the members of the biking club) that it will not skew the statistics.

~

Find the slope of a line passing through the given points. 2,5) and (4,-7) help me

Answers

-7 -5 / 4 -2 / -12/2

-12/2 = -6

Slope: -6x

5 = 2(-6) + b

5 = -12 + b

-12 + 17 = 5

Slope intercept Form: y = -6x + 17

^ Casey was able to map line segment UV onto line segment ST using a translation and a rotation.

WORTH 15 POINTS PLEASE HELP!!!

Casey concluded:

"I was able to map line segment UV onto line segment ST using a sequence of rigid transformations without a dilation, so the figures are congruent but they are not similar."

What error did casey make in her conclusion?

A. The correct conclusion is that the segments are congruent and similar.
B. The correct conclusion is that the segments are neither congruent, nor similar.
C. There is no error. This is a correct conclusion

Which one is it please?​​

Answers

Answer:

A. The correct conclusion is that the segments are congruent and similar.

Step-by-step explanation:

Congruent figures are also similar because when all sides are equal, they are in the same ratio too (i.e 1 : 1)

Represent the espression “A number, x, decreased by the sum of 2x and 5” algebraically.

Answers

It would be X-2x+5, hope this helps

NEED HELP FAST!!!!!!!Consider the right triangle below. A right triangle with a hypotenuse with length 6.5 feet, and side lengths of 2.5 feet and 6 feet. What is the perimeter and area of the given triangle? 8 feet, 7.5 square feet 15 feet, 39 square feet 12.5 feet, 39 square feet 15 feet, 7.5 square feet

Answers

Answer:

D. 15 feet, 7.5 square feet

I got it right on edge

Is (3, 4) a solution of y < 4x – 2 ?

Answers

Answer:

Yes

Step-by-step explanation:

4<10

which is true therefore it is a solution

Yes, (3, 4) is a solution of y < 4x – 2.

What is inequality?

An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.

here, we have,

y < 4x – 2

for (3,4),

we get,

4<10

which is true therefore it is a solution.

hence, Yes, (3, 4) is a solution of y < 4x – 2.

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A trapezoid was broken into a rectangle and two
triangles
The base of each triangle bis
The area of the rectangle is
The area of each triangle is
The area of the trapezoid is
LIT

Answers

Answer:

The base of each triangle B is: 2 ✓

The area of the rectangle is: 4 ✓

The area of each triangle is: 4 ✓

The area of the trapezoid is: 12 ✓

Step-by-step explanation:

Hope I helped, btw I'm following everyone who follows me! :)

Jasmine went shopping for a shirt the shirt was 35 dollars but it was 30% off

Answers

Answer:

$24.50

Step-by-step explanation:

Answer:

your answer will be 24.50

Which equation and solution can be used to solve this problem? Twenty-two less than a number is twenty-four. q + 22 = 24: Subtract 22 from both sides. The answer is 2. 24 + q = 22: Subtract 22 from both sides. The answer is 2. q minus 24 = 22: Add 24 to both sides. The answer is 46. q minus 22 = 24: Add 22 to both sides. The answer is 46.

Answers

Answer:

q-22=24. Hope this helps.

Step-by-step explanation:

22 less than a number, meaning 22 is subtracted FROM an unknown variable. Going by this you would add 22 on both sides, giving you an answer of 46.

Answer

The answer is 46. q minus 22 = 24: Add 22 to both sides.

Step-by-step explanation:

''Twenty-two less than a number is twenty-four''

The equation q -22 = 24 because a number [q] less than [22] is [24]

Therefore, the answer is 46.

where do i plot the shape ? please help;

Answers

Answer:

Coordinates of original figure:

(-9, 2), (-9, 7), (-7, 6), (-5, 8), (-6, 5)

Coordinates of new figure:

(1, 2), (1, 7), (-1, 6), (-3, 8), (-2, 5)

Plot these points. Then connect them to form the reflected figure.

Noah and Andre are 15 miles apart on a bike path when they start biking towards each other. Noah rides at a constant speed of 4 miles per hour, and Andre rides at a constant speed of 2 miles per hour. How long does it take until Noah and Andre meet?
Choose one of these answers
2 hours
2 1/2 hours
1 3/4 hours
3 hours

Answers

Answer:

2 1/2 hours

Step-by-step explanation:

multiply their rate by the number of hours

4*2=8

2*2=4

We want them to both equal 15 when added together

8+4≠15

So it's not 2 hours

So now our next answer choice is 2 1/2 hours

Ok that's easy, we can still use what we did from the last answer choice (2 hours)

Since it says 1/2 that means we can multiply the rate by 0.5 or divide it by 2

4/2=2

2/2=1

2+1=3

Now we add that to 8+4

8+4=12

2+1=3

12+3 = 15

Now that we've gotten 15 we know the rest of the answers are incorrect.

The key to solving a two-step equation is
isolating the variable on one side of the
equation. In which of the following equations is
the variable isolated?
A.x = 9/2 + 4
B.2x=8
C.3x = 8 + 5
D.X = 5x - 4

Answers

A because x is by itself where as the other ones, x is not by itself

The equations is the variable isolated

What is Variable?

A variable is an alphabet or phrase that stands in for an unknowable quantity, value, or number. Particularly in the case of algebraic expressions or algebra, the variables are utilised.

Given:

We know when we find the value of variable we need to isolate the variable.

We have given some equations, the isolated variable means only the variable on one side of the equal.

So, among the Equation only x = 9/2 + 4 has isolated variable x.

The other parts have some number or other quantities along with variable.

Learn more about Variable here:

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I need help on this question anyone know this ?

Answers

Answer:

y = 4[tex](2)^{x}[/tex]

Step-by-step explanation:

An exponential function in standard form is

y = a [tex]b^{x}[/tex]

Use ordered pairs from the table to find a and b

Using (0, 4), then

4 = a [tex]b^{0}[/tex] ( note that [tex]b^{0}[/tex] = 1 ), so

a = 4, then

y = 4 [tex]b^{x}[/tex]

Using (1, 8)

8 = 4 [tex]b^{1}[/tex] = 4b ( divide both sides by 4 )

b = 2

y = 4 [tex](2)^{x}[/tex] ← represents the values in the table

If AD = 20 centimeters, DC = 15 centimeters,

BC = 7 centimeters, and AB = 24 centimeters,

what is the area of quadrilateral ABCD?

answer plz

Answers

Answer:

Incomplete question, check attachment for diagram of the question

Step-by-step explanation:

Given that,

AD = 20cm

DC = 15cm

BC = 7cm

AB = 24cm

Since the shape consist of two right angle triangle,

Then, we will find the area of each triangle and add them together to find the area of the quadrilateral ABCD

Area of a triangle can be calculated using

A = ½b×h

Then,

For triangle 1, its area is

A_1 = ½ × DC × AD

A_1 = ½ × 15 × 20

A_1 = 150 cm²

Fro triangle 2

A_2 = ½ × BC × AB

A_2 = ½ × 7 × 24

A_2 = 84 cm²

Then, the total area is

A = A_1 + A_2

A = 150 + 84

A = 234 cm²

Area of the quadrilateral ABCD is 234cm²

Answer:

Step-by-step explanation: it’s 234 no cap

A cheetah can run 56 miles per hour. At that rate, a cheetah can run 27 miles in 15 minutes.
True
False

Answers

Answer:

false, they can run 14 miles in 15 minutes

Step-by-step explanation:

56 divide by 4 = 14

60 divided by 15 = 4

20 POINTS!!!!

What is the area of the following trapezoid in square feet?
135 ft^2
165 ft^2
82.5 ft^2
64.9 ft^2

Answers

Answer:

135 ft^2

Step-by-step explanation:

7yd = 7*3 feet = 21 feet

[tex]area \: of \: trapezoid \\ = \frac{1}{2} (15 + 21) \times 7.5 \\ = \frac{1}{2} \times 36 \times 7.5 \\ = 18 \times 7.5 \\ = 135 {feet}^{2} [/tex]

The answer to this question would be 82.5 because the formula for finding the area of a trapezoid is,
A=a+b /2 h,
Put the numbers in place,
A=15+7/2 7.5,
A=82.5

Three solutions of the equation Ax + By = Cz - 14 are

(-3,- 3, 2), (4, 1, -13), and (6.-2, -9). Find A, B, and C.

Answers

c ccccccccc
for extra space

Find the width of a box, that has a volume of 160,000 cubic centimeters. The length of the box is 80 cm, and the height of the box is 40 cm.

Answers

Answer:

W=50cm

Step-by-step explanation:

160000=80*W*40

Divide both sides by 80

2000=W*40

Divide both sides by 40

50=W

W=50

solve the following system y=-2 -2x-7y=24

Answers

Answer:

x = -5

y = -2

Step-by-step explanation:

Since you have y, plug that into the equation:

-2x - 7y = 24

-2x - 7(-2) = 24

-2x + 14 = 24

Then, subtract 14 from both sides:

-2x + 14 = 24

      - 14   - 14

__________

-2x = 10

Finally, divide both sides by -2:

-2x = 10

x = -5

So now you have, x = -5 and y = -2.

This is really confusing I couldn't find anything so If you know to do this please help or i will die (not literally)

Answers

Answer:

sry, didn't know how to answer #10

Step-by-step explanation:

3: 115°

4: 62°

5: ∠FED

6: 98°

7: 139°

8: 65°

9: 65°

10: unsure

11: 37

12: 16.97

13: 15.8

14: 71.063352017759

15: 13

The volume of a cone is 763.02. the radius and height of the cone are equal. What is the radius of the cone?

Answers

Answer:

The radius of the cone is 9cm

Step-by-step explanation:

This problem bothers on the mensuration of solid shapes, a cone

The volume of a cone is expressed as

V=1/3(πr²h)

We were told that the radius r and the height h are equal

I.e r=h

Substituting h=r in the formula we have

V= 1/3(πr²*r)

V =1/3(πr³)

To find the radius r let us substitute our given 763.02cm³ (note we assume unit in cm)

763.02= 1/3(3.142r³)

763.02= (3.142r³)/3

763.02*3=3.142r³

2289.06=3.142r³

r³=2289.06/3.142

r³= 728.54

r= ³√728.54

r= 8.99cm

≈r= 9cm

a dart board has 10 equally sized slices numbered from 1-10. some are grey and some are white. the slices numbered 1,2,3,4,5,6,8,9 and 10 are grey. the slice number 7 is white. a dart is tossed and lands on a slice at random. let X be the event that the dart lands on a grey slice, and let P(X) be the probability of x. let not X be the event that the dart lands on a slice that is not grey,and let P( not X) be the probability of not X.

Answers

Answer:

We have 10 sections, we can assume that the probability of hitting each of one of them is the same.

we have 9 grey slices and 1 white slice, then the probability of landing in a grey slice is equal to the number of grey slices divided by the total number of slices:

P(X) = 9/10 = 0.90

The probability of not landing in a grey slice is equal to the probability of landing in the white slice, this is:

P(not X) = 1/10 = 0.10

Also, when you have only two events, you can calculate this as:

P(not X) = 1 - P(X) = 1 - 0.90 = 0.10

Can someone please help me, will mark as brainliest... Solve questions 6-10 correctly...

Answers

Answer:

6- 9in

7- B

8- D

9-C

10-C

Step-by-step explanation:

What is the common ratio of the geometric sequence below?

625, 125, 25, 5, 1, ...

Answers

The common ratio of the geometric sequence 625, 125, 25, 5, 1, ... is 0.2, determined by dividing any term by the preceding term.

The common ratio of a geometric sequence is found by dividing any term by the previous term. In the given sequence 625, 125, 25, 5, 1, ..., to find the common ratio, we can divide the second term (125) by the first term (625), which gives us

[tex]= \frac{125}{625} \\=\frac{1}{5}[/tex].

This ratio is consistent throughout the sequence as each subsequent term is  rac{1}{5} of the previous term. Hence, the common ratio for this geometric sequence is 1/5 or 0.2.

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