What If? If the teacher always launches the ball with the speed found in part (a), what is the minimum angle (in degrees above the horizontal) at which he can launch the ball and still clear the playground railing? (Hint: You may need to use the trigonometric identity sec2(θ) = 1 + tan2(θ).)

Answers

Answer 1

9514 1404 393

Answer:

  43.303°

Step-by-step explanation:

Problem geometry varies. For this question, we will assume ...

The ball is launched at a 53° angle, 24 m from a buildingThe ball takes 2.20 seconds to reach the buildingThe railing is 6.4 m high

The equation of motion in this case is ...

  h(x, α) = x(tan(α) -4.9x/(v·cos(α))²)

where h(x) = height at distance x, α is the launch angle, vₓ is the horizontal speed of the ball.

__

The ball was launched at an angle of 53° in part (a) at a speed that gives it a horizontal speed of (24 m)/(2.2 s). That is, the speed in the direction of launch is ...

  (24 m)/(2.2 s)/cos(53°) ≈ 18.126983 m/s . . . . speed in part (a)

__

For the question at hand, we need to find α such that ...

  h(24) = 6.4

Substituting into the above equation gives ...

  6.4 = 24(tan(α) -24(4.9/18.126983^2·sec(α)^2)

  6.4 = 24(tan(α) -0.35789551(tan(α)^2 +1)) . . . . replacing sec(α) using hint

If we let z represent tan(α), this can be written in standard form as ...

  8.5894922·z^2 -24z +14.989492 = 0

Then the minimum solution (by the quadratic formula) is ...

  z = (24 -√(24^2 -4(8.5894922)(14.989492)))/(2·8.5894922)

  z = 0.94244774

And the angle is ...

  α = arctan(z) = arctan(0.94244774) ≈ 43.303°

The teacher must launch the ball at an angle of at least 43.3° to clear the railing.

What If? If The Teacher Always Launches The Ball With The Speed Found In Part (a), What Is The Minimum

Related Questions

I only got two so far...

Answers

Answer:NML iscocilese triangle

Step-by-step explanation:

Answer:

right angle, obtuse angle and straight angle

Step-by-step explanation:

i hope this is what you mean sry if it didn't help

From the sum of 3x +4y -3xy and 5x +3y -2xy subtract the sum of 2x +y – 3xy and 10x -9y -8xy

Answers

Answer:

5x-1y-11y

Step-by-step explanation:

3x+4y-3xy+5x+3y-2xy-2x+y-3xy+10x-9y-8xy

2x+5x+4y+3y-3xy-2xy-2x+10x+y-9y-3xy-8xy

7x+7y-5xy-12x-8y-11xy

7x-12x+7y-8y-11xy

-5x-1y-11xy

Jacob buys 6 game tickets and 3 ride tickets at a carnival for $39. Emily buys 2 game tickets and 2 ride tickets for $18. Find the cost of a game ticket and the cost of a ride ticket at the carnival. Set up and solve a system of equations.
Your answer:

Answers

Answer:

Cost of ride ticket = $5

Cost of game ticket = $4

Step-by-step explanation:

Given that:

Let ;

game ticket = g

Ride ticket = r

Jacob :

6g + 3r = 39 - - - (1)

Emily :

2g + 2r = 18 - - - - (2)

Divide (2) b y 2

g + r = 9 - - - - (3)

From (3)

g = 9 - r

Substitute ; g = 9 - r into (1)

6(9 - r) + 3r = 39

54 - 6r + 3r = 39

54 - 3r = 39

-3r = 39 - 54

-3r = - 15

r = 5

Put r = 5 in (g = 9 - r)

g = 9 - 5

g = 4

Hence,

Cost of ride ticket = $5

Cost of game ticket = $4

Two angles are complementary. One angle is twice the size of the other. The bigger angle measures

Answers

Sum of two angles that are complementary = 90°

Let the smaller angle be x .

Then the larger angle = 2x

Let us make an equation to find the measure of both the angles :-

[tex]2x + x = 90[/tex]

[tex]3x = 90[/tex]

[tex]x = \frac{90}{3} [/tex]

[tex]x = 30[/tex]

Which means :-

Measure of the small angle = 30°

Measure of the larger angle = 2 × 30 = 60°

Therefore , the measure of the bigger angle is 60° .

Consider the complex number i 6.
What is the real part?

Answers

Answer:

For example, 2 + 3i is a complex number. ... The real number a is called the real part of the complex number a + bi; the real number b is called its imaginary part. To emphasize, the imaginary part does not include a factor i; that is, the imaginary part is b, not bi.

I honestly don’t know

A marathon is 26.2 miles long. There is a water station every 114 miles along the race route. How many water stations are needed for this marathon? here is the "answer" aka the options you have. 12,16,21,26. Please help me!!!!!!!!

Answers

Answer:

I think 21

Step-by-step explanation:

Please help!! I need a correct answer because it’s a test and I need a good grade. Thank you!

Answers

Answer:

Minimum = 55 F

Maximum = 71 F

Step-by-step explanation:

The temperature is changing by 8 degrees either up or down.

Because you don't know which way it is changing, you add and subtract to find the maximum and minimum, respectively.

63 + 8 = 71. Add for maximum.

63 - 8 = 55. Subtract for minimum.

63 min. 8 max. ?

answer

Jason solved the following equation to find the value for
X.
-8.5x – 3.5x = -78
x = 6.5
Describe how Jason can check his answer.
I

Answers

Answer:
Jason can check his answers by plugging in 6.5 in where x is shown.

Explanation:
-8.5x6.5-3.5x6.5
Where the 6.5s are is where x was and it was a multiplication because x is next to the number

Answer:

we know, that  If the x value is a solution to the equation, the x value must satisfy the equation. so It is true.

Step-by-step explanation:

just copy and paste it, its right

Evan is going to the county fair this weekend. The admission to the fair is $5 and the cost per
ride is 50¢. If his parents gave him $20, write and solve a linear equation to find how many
rides he can go on.

Answers

Answer:

I think 40

Step-by-step explanation:

20/.50

Answer:

30 rides

Step-by-step explanation:

First subtract $5 from $20 (20-5) to get $15 now multiply 15 by 2 (which is the same as dividing by 1/2. and you get 30. so your answer is 30 rides

20-5=15       15x2=30     30 rides

any one know the answer plz i will give brainlyest

Answers

Answer:

Step-by-step explanation:

P=2*9+2*4

P=18+8

P=26 in.

64x^2y-y factor the expression

Answers

Answer:

y(8x+1)(8x-1)

Step-by-step explanation:

Solve for g.
2(g - 13) = 12
g

Answers

Answer:

-2

Step-by-step explanation:

Farmer Jane has many hens that have laid many eggs. Before the eggs hatch, Jane wants to
count how many eggs are blue, how many are brown, and how many are white.
Jane counts that, of all the eggs, 6 are blue and 25% are brown.
If 10% of the eggs are blue, how many of the eggs are white?
a) 15
b) 21
c) 39
d) 65

Answers

Answer:

The correct option is;

c) 39

Step-by-step explanation:

The given information are;

The number of eggs that are blue = 6

The percentage of eggs that are brown = 25%

The percentage of eggs that are blue = 10%

Let the number of eggs Jane has = X

Therefore;

10% of X = 10/100 × X = 6

X = 6 × 100/10 = 60

The number of eggs Jane has = X = 60

The percentage of the eggs that are white eggs = 100 - (The percentage of eggs that are brown + The percentage of eggs that are blue)

The percentage of the eggs that are white eggs = 100 - (10 + 25) = 65%

The percentage of the eggs that are white eggs = 65%

∴ The number of  eggs that are white = 65% of X = 65/100 × X= 65/100× 60 = 39 eggs

The number of  eggs that are white = 39 eggs.

Here is the last one.

Answers

$ 190.40 hope it he,lps.

The cost of Veronica's dinner is $13.75 she leaves a tip that is 18% of the cost of dinner how much tip did she leave for her server?

Answers

Answer:

2.48$

Step-by-step explanation:

You can say that the tip is ? of of 13.75 and written as

[tex]\frac{?}{13.75}[/tex] and .18 is [tex]\frac{18}{100}[/tex] cross multiply these so

13.75 x 18 = 100?

247.5 = 100?

2.475 = ?

then round up

Waterco is filling barrels with waste water at the rate of 8 quarts per hour. The recycling facility picks up 150 barrels on each trip, and each barrel holds 15 quarts of wastewater. How many days are between each pick up? Show your work to receive full credit. Round answer to the tenths place 

Answers

Answer:

11.7 days

Step-by-step explanation:

Given that:

Filling rate = 8 quarts per hour

150 barrels picked up per trip

One barrel = 15 quarts of waste water

Barrel picked up per trip = 150 barrels

Number of quarts per barrel = 15 quarts

Total quantity of waste water = (150 * 15) = 2250 quarts

Filling rate = 8 quarts per hour

Time taken = quantity / rate

Time taken in days = 2250 quarts /(8*24) = 11.72

11.7 days

HELP!! Check the following sets that are closed under the given operations!!!!

Answers

Answer:

DONDODA

Step-by-step explanation:

Which of the following is equivalent to 5x-6y=20?

A y=5/6x
B y=5/6x-10/3
C y=6/5x+4
D y=-5/6x​

Answers

Answer:

y =  [tex]\frac{5}{6}[/tex]x - [tex]\frac{10}{3}[/tex]

Step-by-step explanation:

Given expression:

               5x  - 6y = 20

To solve this problem, we make y the subject of the expression:

     Solution

              5x  - 6y = 20

      Add -5x to both sides of the expression;

              -5x + 5x - 6y = 20 + (-5x)

                             -6y  = 20 - 5x

     Now, multiply both sides by [tex]-\frac{1}{6}[/tex] ;

              [tex]-\frac{1}{6}[/tex]  x (-6y) =  [tex]-\frac{1}{6}[/tex] (20 - 5x )

                         y  = [tex]-\frac{20}{6}[/tex] + [tex]\frac{5}{6}[/tex]x

                         y =  [tex]\frac{5}{6}[/tex]x - [tex]\frac{10}{3}[/tex]

What is the value of the expression below when y = 6?
бу — 1

Answers

Answer:

35

Given:

y=6

Step-by-step explanation:

бу — 1

6(6)-1

36-1

35

hope it helps you!

How many quarts are in 583.7 liters?

Answers

Answer:

616.788

   OR

616.79 (rounded answer)

Step-by-step explanation:

Answer:

616.78891

Step-by-step explanation:

1 liter is 1.05669 quarts

Good luck!

OMG PLEASE HELP MEEE!!!!

Answers

Answer:

The slope would be zero i think

Step-by-step explanation:

because it doesnt have a slope just lays horizontally

Answer:

0 (zero)

Step-by-step explanation:

1st and 2nd Avenues are both horizontal lines. The slope of a horizontal line is 0.

Answer: slope = 0

Help help me plsssssSss

Answers

Answer:

Step-by-step explanation:

it is that because it equalls with positives numbers and if u do your calculation maybe youll undestand  

At SMS, students were encouraged to wear school colors of blue and white. 900 Students wore their school colors while 300 students did not. What percent of the school population did not wear school colors?

Answers

Answer:

audududheyeheheh gay

which of the following functions is graphed?

A. y= |x - 2| - 3
B. y= |x + 2| - 3
C. y= |x + 2| + 3
D. y= |x - 2| + 3 ​

Answers

Answer:

c

Step-by-step explanation:

C. Y=lx-2l-3 is the answer

HELPP!!! I need help!

Answers

Answer: c.

Step-by-step explanation:

x^2 + 2x - 5 - (x - 3)

distribute the negative

x^2 + 2x - 5 - x + 3

combine like terms

x^2 + x - 2

Answer:

B

Step-by-step explanation:

You start by Figuring out the answer to each side of the equation by using PEMDAS (parenathes,exponets, mutiplacation, division,addition and subtractoin). then you add your varribles and exponets. Then simplify.

The function y = $14.99 + $1.25x represents the price y for a pizza with x toppings. Which is not a reasonable range value for this function?
A. $18.25
B.$21.24
C.$17.49
D.$14.99

Answers

I think the answer is 14.99
The answer is A. :) brainliest?

It takes Daphne 25 minutes to assemble a model plane. During her work day Daphne takes 30 minutes for lunch and one 15 minute break. Which inequality could Daphne use to determine the number of model planes
she can assemble in her 8 hour work day?
25p - 458

Answers

Answer:

y=25p-45

Step-by-step explanation:

We first of all start by cumulating all the time she spent for break

lunch= 30min

break= 15min

total break= 45min

also the time taken to assemble one model plane 25min

let the number of hours be p

and the total number of model plane be y

The model is

y=25p-45

Answer: 25p +45 <480

Step-by-step explanation:

2(x - 3) = -8

can someone explain to me how to slove this without calculator please and thank you<3​

Answers

The answer is X=-1

Answer:

-1

Step-by-step explanation:

Distribute

2(x-3)=-8

2x-6=-8

2x=-2

DIVIDE 2 on both sides

x=-1

I need Your help plish​

Answers

Answer:

5

Step-by-step explanation:

Because there is zones

Find the slope help plz​

Answers

Answer:

The slope would be 10/15 or 2/3 in simplest form.

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