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

solve the equation
v-9 =14

Answers

Answer:

the answer for this euqation is 23

Step-by-step explanation:

Answer:

or,v=14-9 ...v=5,so v=5

WILL GIVE BRAINLIEST!!!!!!!!
Use 2 to 3 sentences to name the two pairs of alternate interior angles and explain the difference between alternate interior and alternate exterior angles.

Answers

Answer:

2 and 7 are alternate interior, along with 5 and 4. They are inside the space created by the parallel lines. 1 and 8 are alternate exterior, along with 6 and 3. They are outside the space created by the parallel lines.

Difference:

Alternate exterior angles are created in the space outside the parallel lines on alternating sides; interior angles are created in the space inside the parallel lines.

I hope this helped, please mark Brainliest, thank you!

Big Time Movers charges an initial fee of $24.50, plus $12.75 an hour for their moving services. On holidays, they charge 2.5 times their regular total amount. If they made $188.75 on a job on New Year’s Day, how many hours did they work?

This equation represents the data:

2.5(12.75x + 24.50) = 188.75

Big Time Movers worked
hours on New Year’s Day.

Answers

The answer is:

x = 4hrs

Explanation:

2.5(12.75x + 24.50) = 188.75

31.875x + 61.25 = 188.75

31.875x = 188.75 - 61.25

31.875x = 127.50

x = 127.50/31.874

x = 4

I hope this helps!!!

Passage:

Big Time Movers charges an initial fee of $24.50, plus $12.75 an hour for their moving services. On holidays, they charge 2.5 times their regular total amount.

Question:

If they made $188.75 on a job on New Year’s Day, how many hours did they work?

Answer:

Big Time Movers worked "4" hours on New Year’s Day.

Step-by-step explanation:

I did the instruction on edge 202 and got it right

Help please I’lol really appreciate it

Answers

Answer:

j+z+12

Step-by-step explanation:

3xsquared +13x-10

HELPP PLEASE

Answers

Answer:

(x + 5)(3x - 2)

Step-by-step explanation:

Assuming you require the expression factorised.

3x² + 13x - 10

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 3 × - 10 = - 30 and sum = + 13

The factors are + 15 and - 2

Use these factors to split the x- term

3x² + 15x - 2x - 10 ( factor the first/second and third/fourth terms )

= 3x(x + 5) - 2(x + 5) ← factor out (x + 5) from each term

= (x + 5)(3x - 2) ← in factored form

What’s the sum of u and 15

Answers

Answer:

u + 15

Step-by-step explanation:

Since we don't know the value of u, we have to put the equation like this.

Hope I helped :)

Please consider Brainliest :)

7. Francis made 7 withdrawals of
$75 each from his bank account.
What was the overall change in
his account?

Answers

Answer: -$525

Step-by-step explanation:

7x = how many times he withdrew money * how much money he withdrew.

7 * 75 = $525

Francis ended up removing $525 from his bank account, if we assume that he started off with $0- then the change would be -525 dollars.

need help with this 3 = x+3 - 5x​

Answers

Answer:

x=0 (No solution)

Hope this helps!

Answer:

x=0

Step-by-step explanation:

3=x+3−5x

3=x+3+−5x

3=(x+−5x)+(3)(Combine Like Terms)

3=−4x+3

3=−4x+3

Step 2: Flip the equation.

−4x+3=3

Step 3: Subtract 3 from both sides.

−4x+3−3=3−3

−4x=0

Step 4: Divide both sides by -4.

−4x

−4

=

0

−4

x=0

7/4 ÷ 3/4
Quick please!

Answers

Answer:

.145

Step-by-step explanation:

Answer:

2 1/3

Step-by-step explanation:

the population of Landon woods was 82,500 in 2000 in 2010 the population was 89,100 which is the percent of change in the population ​

Answers

Answer:

sorry I couldn't help but I'm not really sure about this I have done this but I actually did have to ask brainly if you choose a subject if you can go to the top right corner and hit mathematics you will automatically get to answer to it but you can't just ask it to community tab because we don't know

solve this please thankyou ​

Answers

Answer:

second option

Step-by-step explanation:

The left side has a solid circle at - 3 indicating x can equal - 3 denoted by ]

The arrow points left to - ∞

The right side has an open circle at - 1 indicating x cannot equal - 1 denoted by )

The arrow points right to ∞

The feasible region is the union of the 2 parts, that is

( - ∞, - 3 ] U (- 1, ∞ )

Angle ABD is 90 what is the measure of ABC

Answers

Answer:

90 I am guessing. if it's like a square or rectangle

What are the slope and the y-intercept of the line shown in the graph?

A. y-intercept = 2 and slope = -3
B. y-intercept = 2 and slope = 3
C. y-intercept = 3 and slope = 2
D. y-intercept = -3 and slope = 2

Answers

Answer:

A

Step-by-step explanation:

The y intercept is where the line crosses the Y (vertical) axis. In this case, it happens at y=2

The slope is the rate of change. For every 1 space it moves on the horizontal axis, it moves 3 vertical spaces. It is going down, so it is -3

positive decimals less than 2? help meeee

Answers

Answer:

0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, etc.

Step-by-step explanation:

any decimal number that is less than 2 and not a negative number (below 0) will work.

I NEED HELP!!!!!! someone? please?

Answers

Answer:

ok but what is your question?

Answer:

whats the quistion

Step-by-step explanation:

There are 12 boxes of crackers in a carton.
There are 3 packages of crackers in each box.
There are 10 crackers in each package.
The number sentence (12 × 3) × 10 is one way to find the total number of crackers in a carton.
Which number sentence shows another way?

Answers

Answer:

(10x3)x12

Step-by-step explanation:

There can I get brainliest

Answer:

10(12·3)

120·30

Step-by-step explanation:

Just move each part around, undo or redo a few parts as well.

I need help please , it would be nice

Answers

Answer:

cant see the picture

Step-by-step explanation:

I need the answer to ( 56 --7)--3

Answers

The answer to the problem is 15.

First, you must set up the equation.

[tex](\frac{-56}{-7})--7[/tex]

Then, you must eliminate double negatives.

[tex](\frac{-56}{-7})+7[/tex]

Next, divide -56 by -7.

[tex]8+7[/tex]

Finally, add like terms.

[tex]15[/tex]

After 2 hours the Red Cross raises $250 and after 6 hours it raised a total of $785. What's the average rate of change in terms of dollars per
hour?

Answers

Answer:

After 2 hours the Red Cross raises $250 and after 6 hours it raised a total of $785. What's the average rate of change in terms of dollars per hour? Add answer. Log in to add ... If we start with 5 cells, and each cell divides in two every 15 minutes, how many total after 1 hour? if you what 3x +2/w is than you ...

Step-by-step explanation:

Can you help me solve for z

Show your work please

Answers

Answer:

[tex] z = \dfrac{3R}{2xy^2} [/tex]

Step-by-step explanation:

[tex] R = \dfrac{2}{3}xy^2z [/tex]

[tex] \dfrac{2}{3}xy^2z = R [/tex]

[tex] \dfrac{3}{2xy^2} \times \dfrac{2}{3}xy^2z = \dfrac{3}{2xy^2} \times R [/tex]

[tex] z = \dfrac{3R}{2xy^2} [/tex]

The rectangle below has a perimeter of 120 inches. (2x is the length and X is width) What is the measure of the width, x, of the rectangle?

Answers

Answer:

x = 20

Step-by-step explanation:

2x + 2x + x + x = 120

6x = 120

x = 20

Which graph has a slope of 2/3

Answers

Answer:

No. the slope is -2/3

Step-by-step explanation:

Count the spaces from one point (-3, 1) to (0, -1)

1 -(-1) / -3 - 0

- 2/3

Select the correct answer.
The function f(x) is given by the table of values.

x 1 2 3 4
f(x) 1 8 27 64
If f(x) is shifted 4 units up to obtain g(x), which table of values represents the function g(x)?


x 5 6 7 8
g(x) 5 12 31 68


x 1 2 3 4
g(x) 5 12 31 68


x 5 6 7 8
g(x) 1 8 27 64


x 1 2 3 4
g(x) 4 32 108 256

Answers

Answer:

The second answer is correct.

Step-by-step explanation:

So g(x) = f(x) + 4

If f(x) = 1, 8, 27, and 64 then g(x) = 5, 12, 31, and 68.

The solution is Option B.

x = { 1 , 2 , 3 , 4 }

g(x) = { 5 , 12 , 31 , 68 }

The function g ( x ) = x³ + 4

How does the transformation of a function happen?

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units: y=f(x+c) (same output, but c units earlier)

Right shift by c units: y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k × f(x)

Horizontal stretch by a factor k: y = f(x/k)

Given data ,

Let the function be represented as A

Now , the value of A is

when x = 1

f ( x ) = 1

when x = 2

f ( x ) = 8

when x = 3

f ( x ) = 27

when x = 4

f ( x ) = 64

So , the equation will be y = x³   be equation (1)

Now , f(x) is shifted 4 units up to obtain g(x)

So , Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Substituting the values in the equation , we get

when x = 1

g ( x ) = 1 + 4 = 5

when x = 2

g ( x ) = 8 + 4 = 12

when x = 3

g ( x ) = 27 + 4 = 31

when x = 4

g ( x ) = 64 + 4 = 68

Therefore , the function is g ( x ) = x³ + 4

Hence , the function is g ( x ) = x³ + 4

To learn more about transformation of a function click :

https://brainly.com/question/26896273

#SPJ2

Please answer correctly !!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!!

Answers

9514 1404 393

Answer:

D.  Multiply/divide both sides by the same variable expression.No

Step-by-step explanation:

1) Comparing the two equations, we see that the multiplier 'x' is missing from both sides in equation B. That is, it has been divided out:

  (5x)/x = (3x)/x   ⇒   5 = 3

Both sides have been divided by x.

__

2) The equations are equivalent if and only if x ≠ 0. Unfortunately, in equation A, the only solution is x = 0. For equations like the one in A, it is better to subtract one side from both:

  5x -3x = 3x -3x   ⇒   2x = 0

Now, dividing by 2, it is clear that the solution is x = 0.

Equations A and B are not equivalent, because the condition on the division property of equality was violated (you cannot divide by 0).

Simplify:
(Xy/3z/4)/4

Answers

Is your answer for sure
Your answer would be x^4 y^12 z^16

Write the number as a power of 5. 125^3

Answers

Answer:

5^9

Step-by-step explanation:

125=5*5*5

125^3=125*125*125

125*125*125=3*(5*5*5)

the answer 5^9

The number as a power of 5 which is obtained by the number 125^3 using the power rule and simplifying is 5⁹.

What is the power rule?

The power rule states that, when the term is raised with a power which is again raised by another power, then this can be simply written as one power by multiplying both the power.

It has to write the number 125³ as a power of 5. Let the resultant number as a power of 5 is n. Thus,

[tex]n=125^3[/tex]

Rewrite the number with multiples of 125.

[tex]n=(5\times5\times5)^3\\n=(5^3)^3[/tex]

By the power rule, the above expression can be rewritten as,

[tex]n=(5)^{3\times3}\\n=(5)^{9}\\n=5^9[/tex]

Thus, the number as a power of 5 which is obtained by the number 125^3 using the power rule and simplifying is 5⁹.

Learn more about the power rule here;

https://brainly.com/question/819893


What do you notice?
What do you wonder?

Answers

I’m very confused with this....



If the measure of 2 is 68° which statements must be true
Select all that apply

A. The measure of 1 is 68°
B. The measure of 3 is 68°
C. The measure of 5 is 292°
D. The measure of 6 is 112°
E. The measure of 7 is 68°
F. The measure of 8 is 112°

Answers

The answer is going to be B. E. F.

How much interest would $1,000,000 earn at 2% compound daily, in one day?

Answers

Answer:

$54.79 is the answer

Step-by-step explanation:

The perimeter of the rectangle is 48 feet. The length is 16 ft. What is the
width?

Answers

is the length both sides already or just on one side?

because if the 16ft. is only on one side, and the sum of the both sides are 32ft, i think the width of the rectangle must be 16ft, which means 8ft from the first side and 8ft from the second side.

but if the 16ft. is the sum of both sides, which means 8ft from the first length and 8ft from the second length, then the answer for the width is 16ft, for each side of the width. 16 for the first width, and 16 for the second width.

is my explanation too complicated?? sorry hehe.

Answer: 64 ( you add 48 & 16 )

Step-by-step explanation:

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