The center field fence in a ballpark is 10 feet high and 400 feet from home plate. 400 feet from home plate. The ball is hit 3 feet above the ground. It leaves the bat at an angle of $\theta$ degrees with the horizontal at a speed of 100 miles per hour. (a) Write a set of parametric equations for the path of the ball. (b) Use a graphing utility to graph the path of the ball when $\theta=15^{\circ} .$ Is the hit a home run? (c) Use a graphing utility to graph the path of the ball when $\theta=23^{\circ} .$ Is the hit a home run? (d) Find the minimum angle at which the ball must leave the bat in order for the hit to be a home run.

Answers

Answer 1

he parametric equations are: [tex]x(t)[/tex]= 100tcos(theta)

y(t) = [tex]-16t^2[/tex] + 100tsin(theta) + 3

How to determine the parametric equations for the path of the ball, graph the ball's path for different angles, and find the minimum angle required for a home run hit in the given scenario?

(a) To write the parametric equations for the path of the ball, we can use the following variables:

x(t): horizontal position of the ball at time ty(t): vertical position of the ball at time t

Considering the initial conditions, the equations can be defined as:

x(t) = 400t

y(t) = -16t^2 + 100t + 3

(b) To graph the path of the ball when θ = 15°, we substitute the value of θ into the parametric equations and plot the resulting curve. However, to determine if it's a home run, we need to check if the ball clears the 10-foot high fence. If the y-coordinate of the ball's path exceeds 10 at any point, it is a home run.

(c) Similarly, we graph the path of the ball when θ = 23° and check if it clears the 10-foot fence to determine if it's a home run.

(d) To find the minimum angle for a home run, we need to find the angle at which the ball's path reaches a maximum y-coordinate greater than 10 feet. We can solve for θ by setting the derivative of y(t) equal to zero and finding the corresponding angle.

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Related Questions

5. A jewelry supply shop buys silver chains from a manufacturer for $45.00. and then sells the
chains at a 57% markup. What is the retail price of a silver chain?

Answers

the answer is $70.65

if you can help me i’ll make brainliest

Answers

Answer:

help me

Step-by-step explanationok so

Answer:

pts

Step-by-step explanation:

Ronald bought 1.5 pounds of red apples and 0.75 pounds of yellow apples. He bought 1.6 times as many pounds of green apples as red apples and yellow apples combined.

How many pounds of green apples did Ronald buy?

Answers

Answer:

To find the number of green apples he bought, We do the following:

calculate the total mass of red and yellow apples bought 1.5+0.75=2.25 poundsSince the mass of green apples bought was 1.6 times the combined mass of yellow and red apples bought we get;2.25×1.6=3.6pounds He bought 3.6 pounds green apples

A TV has a listed price of $578.98 before tax. If the sales tax rate is 8.25%, find the total cost of the TV with sales tax included.
Round your answer to the nearest cent, as necessary.

Answers

Answer:

$626.75

Step-by-step explanation:

First, we must find how much tax will be added to the TV's price:

Step 1: Convert the percentage to a decimal:

To convert a percentage to a decimal, divide it by 100

8.25/100 = 0.0825

Step 2: Multiply the TV's price by that decimal:

578.98 * 0.0825 = 47.76585

So $47.76585 will be added to the price

Now, we can calculate the total price:

Step 3: Add the tax we jsut calculated to the TV's price to find total price:

578.98 + 47.76585

= 626.74585

Step 4: Round to the nearest cent (2 decimal places)

626.75

So the total price is $626.75

3/8÷5/2
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Answers

Answer:

3/20

Step-by-step explanation:

y=4x+6 2y=8x+12 what’s the solution is it one solution, no solution, or infinitely many solutions

Answers

Answer:

Infinitely many solutions.

Step-by-step explanation:

y=4x+6

2y=8x+12

------------

simplify 2y=8x+12 into y=4x+6

y=4x+6 matches the second equation.

Assume that the lines are parallel.

Answers

Answer:

left ?= 110

right?= 70

Step-by-step explanation:

what is the equation of a line that passes through points (0,7) and( 2,8)write your answer in slope intercept form

Answers

Answer:

(0,7) and (2,8)

slope =8-7=1

          2-0=2

m=1/2 meaning slope

equation=y-7/x-o=1/2

2(y-7)=1(x-0)

2y-14=x -o

2y=1x +14

y =1/2 x +7

Step-by-step explanation:

to get the slope is y 2-y 1 divide by x 2-x 1 to get 1/2

you then take one point as (x,y)  and one of the coordinates =the slope

then you divide by the 2 on both sides in order to get y=mx + c

2 Do the following calculations
a) 55,8965 + 12,443 x 3
b) (6 x 3) - 4 + 26 - 2
c) 44,65 = 3 x 11,11 + 68
d) 24 - 16 + 3 + 5 - 6 + 10 - 2
e) 15 = (2+2)​

Answers

Answer:

a) 93,2255

b)38

c)false

d)18

e)false

Can you help me please

Answers

Answer:

D?

Step-by-step explanation:

if i got it wrong im truly sorry

The answer is A the common ratio is 2

Which expressions are equivalent to 8(-10x+3.5y-7)? Select two options.

Answers

Answer:

[tex] - 8x + 120y - 56[/tex]

Step-by-step explanation:

evaluate the power calculate

[tex]8(1 x + 3 \times 5y - 7[/tex]

the coefficient of 1 doest have to be written but keep the sign

[tex]8( - 1x + 15y - 7[/tex]

remove the parentheses

what is one astronomical unit in inches

Answers

Answer:

5.89E+12

Step-by-step explanation:

Rizwan has 100 ruppees . He spent rs 25 in ice cream . Rs 45 on pizza, and the rest on other things . What percantage did he spend on other things .

Answers

Answer:percantage spent on other things = 30%

Step-by-step explanation:

Percentage spent on other things = Money spent on other things/ Total money x `100/ 1

Money spent on rest things = Total money - ( Money spent on ice cream + Money spent on pizza)

100 -(25+ 45)

100-70= Rs 30

Percentage spent on other things = Money spent on other things/ Total money x `100/ 1

= Rs 30/ Rs 100 x 100

0.3 x 100 = 30%

Factor the expression below.
x2 - 81
O A. (X-9)(x - 9)
O B. (x + 27)(x-3)
O C. (x-27)(x - 3)
O D. (x + 9)(x-9)

Answers

Answer is D (x+9)(x-9)

The area covered by a topic lie plant triples every year. By what factors does the are covered by the plant increase every month?

Answers

Answer:

16.67%

Step-by-step explanation:

If area triples every year :

This means that :

With an initial area of 10;

Area at the end of the year = 3 * 10 = 30

Percentage increase per year :

(30 - 10) / 10 * 100%

(20 / 10) * 100%

2 * 100%

= 200% per year

Therefore, monthly increase %

Yearly % increase ÷ number of months in a year

200% ÷ 12

= 16.666666%

= 16.67%

AYO HELP A MAN OUT PLEASE

Answers

Answer:

I think it's A I'm not sure tho

Step-by-step explanation:

the answer is A and I think C I don't know though ur welcome!:)

Rewrite the function by completing the square.
f(x) = x^2 + 14x + 64

Answers

Step-by-step explanation:

step 1. (x^2 + 14x + 49) + 15

step 2. (x + 7)^2 + 15.

Rashid can do a piece of work in 8 days, which Tipu can finish in 12 days. If they work on alternate days with Rashid Beginning, in how many days, the work will be finished?

Answers

Answer: 9.6 days

Step-by-step explanation:

Rashid can do a piece of work in 8 days. Rashid work rate will then be:

= 1/8 owe day.

Tipu can finish in 12 days. Tipu's work rate will be: = 1/12 owe day.

Their work rate together will then be:

= 1/8 + 1/12

= 3/24 + 2/24

= 5/24

From the calculation, together they will finish the work in:

= 1 ÷ 5/24

= 1 × 24/5

= 24/5 days

= 4.8 days

Busy since they are working on alternate days, then this will be multiplied by 2 which will be:

= 4.8 × 2

= 9.6 days

porfis ayúdenme es para hoy ​

Answers

Answers:

1. V=triangle area × length

V=1/2×8×12×20

V=960in³

2. triangle area × length

Area of the triangle=1/2×4×11

A=22ft²

V=22×6

V=132ft³

3. b, volume always have cubic power (³)

4. d, same reason of question 3

-30=5(x+1) x=?

please help ​

Answers

Answer:

x = -7

-30 = 5(x + 1)

5(x + 1) = -30

5(x + 1)/5 = -30/5

x + 1 = -6

x + 1 - 1 = -6 -1

x = -7

At midnight in Minnesota, the temperature was -59. Over the next three hours, the
temperature dropped 7. What was the temperature at 3:00 a.m.?
A-12
B-5°
C -2°
D 2

PLEASE HELP!!!

Answers

9514 1404 393

Answer:

  A.  -12°

Step-by-step explanation:

The final value is found by adding the change to the initial value.

  final temp = initial temp + change in temp

  final temp = -5° + (-7°) = (-5 -7)°

  3 am temp = -12°

Answer:

A

Step-by-step explanation:

1. Write the equation: -5-7. We get that equation because we start at -5 and then it drops 7 degrees. "dropped" is the keyword that tells us to subtract.

2. Solve the equation: -12 degrees. You can solve it very easily by plugging it into a calculator or mentally.

P.S: You typed the question wrong, you said 56 degrees instead of 5. That really had me stumbled lol.

How many gallons of gas would it take to drive 13,500 miles? (URGENT)

Answers

Answer:

24 gallons :)

Step-by-step explanation:

The graph shows your elevation during a run. Which statement is true about your run?​
A- You were running uphill for the first 15 minutes.
B- You were running uphill between 10 and 20 minutes into the run.
C- You were running downhill for the last 10 minutea.
D- You were running downhill the first 15 minutes.

Answers

Answer:

Its D. You were running downhill the first 15 minutes.

x² + y² = 49
Note: Each column in the table represents an ordered pair. If multiple solutions exist, you only need to identify one.​

Answers

Answer:

1....y=7

2...x=7

3...y=5

4...y=6

5...x=2√10

What is the measure of arc BD?​

Answers

Step-by-step explanation:

step 1. mBD = 63°. The arc angle measures the same from the center of a circle.

Write the answer in its simplest form. -8 + 13​

Answers

Answer:

5

Step-by-step explanation:

-8 + 13 is equal to 5.  It is positive since the larger number is positive.

If f(x) = x2, and
g(x) = x - 1, then
f(g(x)) = ?

Answers

Answer:

f(g(x))=1x^2 +-2x+1

Step-by-step explanation:

your inputs should be

1

-2

1

If f(x) = [tex]x^{2}[/tex], g(x) = [tex]x -1[/tex] then f(g(x)) = [tex]1x^{2} -2x+1[/tex].

What is a function?

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given

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

g(x) = [tex]x -1[/tex]

f(g(x)) = [tex](x-1)^{2}[/tex]

It is in the form of [tex](a-b)^{2}=a^{2} -2(a)(b) +b^{2}[/tex]

= [tex]x^{2} -2(x)(1) +1^{2}[/tex]

= [tex]x^{2} -2x+1[/tex]

f(g(x)) = [tex]1x^{2} -2x+1[/tex]

Hence, If f(x) = [tex]x^{2}[/tex], g(x) = [tex]x -1[/tex] then f(g(x)) = [tex]1x^{2} -2x+1[/tex].

Find out more information about function here

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Choose the two number sentences that are true.
A. 5+7= 11+2
B. 3 + 3 = 20 - 9
C. 5+9 = 19 - 4
D. 12 +7 = 5 + 14
E18 - 6 = 15 - 1

Answers

Answer:

D

because 12+7=19

5+14=19

Other option
D: 15.7

Answers

Answer:

I see a typo in the problem. When it says LR. This triangle isn't in the direction of L its the opposite direction. I think the answer might be C but im not completely sure.

Step-by-step explanation:

Big Brain

Find the measure of arc BC

Answers

Answer:

The measure of the Arc BC is 80

I agree! The BC is 80
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