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
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 highThe 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.
Related Questions
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
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
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
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.
Find the slope help plz
Answers
Answer:
The slope would be 10/15 or 2/3 in simplest form.
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
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° .
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!
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!
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
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
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:
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:
HELP!! Check the following sets that are closed under the given operations!!!!
Answers
Answer:
DONDODA
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
Answer:
-1
Step-by-step explanation:
Distribute
2(x-3)=-8
2x-6=-8
2x=-2
DIVIDE 2 on both sides
x=-1
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
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
I need Your help plish
Answers
Answer:
5
Step-by-step explanation:
Because there is zones
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.
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-45Step-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:
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
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
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.
Solve for g.
2(g - 13) = 12
g
Answers
Answer:
-2
Step-by-step explanation:
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
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
Here is the last one.
Answers
$ 190.40 hope it he,lps.
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]
64x^2y-y factor the expression
Answers
Answer:
y(8x+1)(8x-1)
Step-by-step explanation:
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.
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