A baseball is thrown in a parabolic arc. It's position above the ground at a given point in time can be represented by the quadratic function LaTeX: p\left(t\right)=\frac{1}{2}gt^2+v_0t+p_0p ( t ) = 1 2 g t 2 + v 0 t + p 0, where LaTeX: t\ge0t ≥ 0, LaTeX: gg is -32 ft/sec/sec, LaTeX: v_0v 0 is initial velocity, and LaTeX: p_0p 0 is its initial position above the ground. If the ball was thrown straight up at 16 ft/sec when it was 5 ft above the ground, how high did it go?

Answers

Answer 1

Answer:

The baseball reached 9 feet high above the ground

Step-by-step explanation:

The given quadratic function representing the position of the baseball above ground is p(t) = 1/2·g·t² + v₀·t + p₀

Where;

t ≥ 0

g = -32 ft./sec²

v₀ = The initial velocity

p₀ = The initial position

Given that when the ball is thrown, we have;

The initial, straight up, velocity, v₀ = 16 ft./sec

The initial position, p₀ = 5 ft.

Substituting the above values in the quadratic function representing the position of the baseball above ground, we have;

p(t) = 1/2·(-32)·t² + 16·t + 5 = 16·t - 16·t² + 5

At the maximum point, the rate of change of the height with time = 0, therefore;

dp(t)/dt = 0 = d(16·t - 16·t² + 5)/dt = 16 - 32·t

16 - 32·t = 0

16 = 32·t

t = 16/32 = 0.5 seconds

Therefore, the time takes to reach the maximum height = 0.5 seconds

The height (maximum) reached in 0.5 seconds is given as follows;

h(t) = 16·t - 16·t² + 5, from which we have;

h(0.5) = 16 × 0.5 - 16 × (0.5)² + 5 = 9

Therefore, the height baseball reached = 9 ft. above ground

A Baseball Is Thrown In A Parabolic Arc. It's Position Above The Ground At A Given Point In Time Can

Related Questions

3(x+1)-2x=-6
Slove this

Answers

Answer:

x = -9

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Equality Properties

Step-by-step explanation:

Step 1: Define Equation

3(x + 1) - 2x = -6

Step 2: Solve for x

Distribute 3:                    3x + 3 - 2x = -6Combine like terms:       x + 3 = -6Isolate x:                          x = -9

Step 3: Check

Plug in x into the original equation to verify it's a solution.

Substitute in x:                    3(-9 + 1) - 2(-9) = -6Add:                                     3(-8) - 2(-9) = -6Multiply:                               -24 + 18 = -6Add:                                     -6 = -6

Here we see that -6 does indeed equal -6.

∴ x = -9 is the solution to the equation.

How could the statement "12 less than x" be written?

Answers

Answer:

The statment would be written as "12 - x".

in desperate need of help , please help lol

Answers

Answer:

No, the figures are not similar.

Step-by-step explanation:

In order for the figures to be similar, in object B, the line labeled as 20 would need to be 10.

I WILL GIVE BRAINLEST

Angela has 5 fewer quarters than twice the number of her dimes. If d represents
the number of dimes Angela has, which expression represents the total number of
Angela’s quarters and dimes


PLSSS SHOW YOUR WORK PLSSSSSS

Answers

Answer:

2d-5=Q ?

Step-by-step explanation:

Am I supposed to be representing quarters too? I think this should solve it though. Lmk if somethings wrong :)

SAS Congruence Theorem Two Column Proof, Pictures Included.


WILL GIVE BRANIEST

Answers

Answer:

we prove the both triangle

first we profe sides

two years late but hope this helps !!

i need help i don’t understand what it means or what it is asking for

Answers

Answer:

its D btw

Step-by-step explanation:

Find the sale price of the item. Round to two decimal places if necessary. Original price: $238.13 Markdown: 70% The sale price is $

pls help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! due very soon!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

$71.44

Step-by-step explanation:

HELP ASAP NEEDS TO BE DONE TODAY.
Which expression is equivalent to 27 + 45?

A. 8(3+6)

B. 8(19+ 37

C. 9(3+5)

D. 9(18 + 36)​

Answers

Answer:

A

Step-by-step explanation:

if you did 6+3=9

8x(9)=72

"27+45=72"

Answer:

C

Step-by-step explanation:

27 + 45 = 72

9(3 + 5)

9 x 3 = 27

9 x 5 = 45

27 + 45

81-1 1/5 x < 55
please help i need help fast

Answers

Step-by-step explanation:

81 - 1.2x < 55

81 < 55 + 1.2x (add 1.2x to both sides)

1.2x > 26 (subtract 55 from both sides)

x > 21 2/3.

what is the difference between the 11th square number and the 4th square number?

Answers

Answer:1 squared 1

2 squared 4

3 squared 9

4 squared 16

5 squared 25

6 squared 36

7 squared 49

8 squared 64

9 squared 81

10 squared 100

11 squared 121

12 squared 144

13 squared 169

14 squared 196

15 squared 225

16 squared 256

17 squared 289

18 squared 324

19 squared 361

20 squared 400

Step-by-step explanation:

dude just search it up

Answer:

105

Step-by-step explanation:

The 11 th square number is 11² = 121

The 4 th square number is 4² = 16

Their difference is 121 - 16 = 105

Rob was driving his car slowly and then increased its speed by 40.5 miles per hour to reach a top speed of 60 miles per hour. What was his car's initial speed?​

Answers

Answer:

19.5

Step-by-step explanation:

60 - 40.5 = 19.5.

The table shows the balance of Steven's savings account over time. Assuming there are no withdrawals, if you graph the relationship for Steven's monthly balances, which points will lie on the resulting line?

Answers

Answer:

(23, 9,200) (26, 10,400)

those are the only 2

What is the radius and diameter of the following circle?
11 cm

Answers

Answer:

Diameter is 11cm, and the radius is 5.5

Step-by-step explanation:

To get the radius, just divide the size of the circle by 2

Diameter is the same size as the circle

A. 48
B. 44
C. 52
D. 40

6. The sum of the ages of a father and his son is 74. Four years ago the
father's age was twice as old as his son. How old is the father now?​

Answers

Answer:

A (48)

Step-by-step explanation:

let the father's age = x and his son's age = y

according to the question,

the sum of their ages is 74

×+y=74......equation 1

four years ago (i.e x-4 & y-4) father's age was twice as old as his son

x-4=2(y-4)

or, x-4=2y-8

x-2y=-4.......equation 2

now, in equation 1

x+y=74

hence,

x=74-y

substituting the values in equation 2

x-2y=-4

(74-y)-2y=-4

74-y-2y=-4

74-3y=-4

74+4=3y

3y=78

y=78/3

y=26

Hence the kid is 26 years old

x+y=74

x+26=74

x=74-26

x=48

Hence the dad is 48 years old

Answer:

The correct answer is: Option A: 48

Step-by-step explanation:

Let x be the present age of father and y be the present age of son

Given that

"The sum of the ages of a father and his son is 74"

[tex]x+y = 74\ \ \ Eqn\ 1[/tex]

Now

x-4 will be the age of father 4 years ago

y-4 will be the age of son 4 years ago

The equation will be:

[tex]x-4 = 2(y-4)\\x-4 = 2y-8\\x-2y-4 =-8\\x-2y = -8+4\\x-2y = -4\ \ \ Eqn\ 2[/tex]

From equation 1:

[tex]x = 74-y[/tex]

Putting in equation 2

[tex]74-y-2y = -4\\74-3y = -4\\-3y = -4-74\\-3y = -78\\\frac{-3y}{-3} = \frac{-78}{-3}\\y = 26[/tex]

Put y = 26 in equation 1

[tex]x+26 = 74\\x = 74-26\\x = 48[/tex]

The father is 48 years old now.

Hence,

The correct answer is: Option A: 48

tan²A -cot²A = sec²A(1-cot²).Trigonometic Identity​

Answers

your proving is in photo

two supplementary angles are in a ratio of 7:11. find the measures of each angle

Answers

Answer:

70° and 110°

Step-by-step explanation:

Supplementary angles sum to 180°

sum the parts of the ratio, 7 + 11 = 18 parts

Divide 180° by 18 to find the value of one part of the ratio.

180° ÷ 18 = 10° ← value of 1 part, thus

7 parts = 7 × 10° = 70°

11 parts = 11 × 10° = 110°

The 2 angles are 70° and 110°

MATHHHH!!!! PLZZZZ!!! HELP!!!

Answers

113% I think check with your teacher

Five congruent squares are put together without gaps or overlap to form a figure shaped like a plus sign. The
perimeter of the figure is 72 cm. Find the area of the figure, in cm?

Answers

Answer:

180 square centimeters

Step-by-step explanation:

Because the five squares are congruent, the 12 sides of the figure are all equal in length. Then the length of one side is 72/12 = 6 cm. Therefore, the area of each square is 36 sq cm and the area of the figure, 5 x 36, is 180 sq cm.

Help me please due in 30 minutes !

Answers

Answer:

B

Step-by-step explanation:

I NEED HELP ITS TIMED​

Answers

Answer:

Binomial

Step-by-step explanation:

This is because it has two terms

The triangles shown below may not be congruent.

A. True
B. False

Answers

TRUEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE

Answer: B. False.

They are in face Congruent! :)

I’ll mark you brainlist I’ll mark you brainlist

Answers

Answer:

Would be the approx 17.55 or 12p

Step-by-step explanation:

Mark me brainliest because you promised it and have a splended day ( ^ :

The slope is 2/1 or just 2 and usually the slope is also known as rate of change so the answer should be 2

Together, teammates Pedro and Ricky got 2687 base hits last season. Pedro had 281 more hits than Ricky. How many hits did each player​ have? help quick

Answers

Answer:

Let x be the number of hits Ricky has. Then x+277 is the number of hits Pedro has. Adding Ricky's and Pedro's hits give you 2685 hits. Therefore, x+(x+227)=2685 2x+227=2685 2x=2408 x=1204 x+277 1481 Therefore, Ricky has 1204 hits and Pedro has 1481 hits.

Step-by-step explanation:

What is 345 divied by 189 remander2

Answers

Answer:

37

4 remander

Step-by-step explanation:

Step 1:

Start by setting it up with the divisor 5 on the left side and the dividend 189 on the right side like this:

           

   5 ⟌ 1 8 9

Step 2:

The divisor (5) goes into the first digit of the dividend (1), 0 time(s). Therefore, put 0 on top:

       0    

   5 ⟌ 1 8 9

Step 3:

Multiply the divisor by the result in the previous step (5 x 0 = 0) and write that answer below the dividend.

       0    

   5 ⟌ 1 8 9

      0    

Step 4:

Subtract the result in the previous step from the first digit of the dividend (1 - 0 = 1) and write the answer below.

       0    

   5 ⟌ 1 8 9

     - 0    

       1    

Step 5:

Move down the 2nd digit of the dividend (8) like this:

       0    

   5 ⟌ 1 8 9

     - 0    

       1 8  

Step 6:

The divisor (5) goes into the bottom number (18), 3 time(s). Therefore, put 3 on top:

       0 3  

   5 ⟌ 1 8 9

     - 0    

       1 8  

Step 7:

Multiply the divisor by the result in the previous step (5 x 3 = 15) and write that answer at the bottom:

       0 3  

   5 ⟌ 1 8 9

     - 0    

       1 8  

       1 5  

Step 8:

Subtract the result in the previous step from the number written above it. (18 - 15 = 3) and write the answer at the bottom.

       0 3  

   5 ⟌ 1 8 9

     - 0    

       1 8  

     - 1 5  

         3  

Step 9:

Move down the last digit of the dividend (9) like this:

       0 3  

   5 ⟌ 1 8 9

     - 0    

       1 8  

     - 1 5  

         3 9

Step 10:

The divisor (5) goes into the bottom number (39), 7 time(s). Therefore put 7 on top:

       0 3 7

   5 ⟌ 1 8 9

     - 0    

       1 8  

     - 1 5  

         3 9

Step 11:

Multiply the divisor by the result in the previous step (5 x 7 = 35) and write the answer at the bottom:

       0 3 7

   5 ⟌ 1 8 9

     - 0    

       1 8  

     - 1 5  

         3 9

         3 5

Step 12:

Subtract the result in the previous step from the number written above it. (39 - 35 = 4) and write the answer at the bottom.

       0 3 7

   5 ⟌ 1 8 9

     - 0    

       1 8  

     - 1 5  

         3 9

     -   3 5

           4

You are done, because there are no more digits to move down from the dividend.

The answer is the top number and the remainder is the bottom number.

Therefore, the answer to 189 divided by 5 calculated using Long Division is:

37

4 Remainder

QUICK !!!

What is the equivalent form of y +2 = -3(2 – 4) in slope-intercept form?

A) y = -3x + 10

B) y=32 + 10

C) y = 3x – 14

D) y= -3x – 14

Answers

Answer:

Is there any other Answers?

cuz I got y=4

I believe it’s b but I’m not that sure

i need help 10 points

Answers

Answer:

B

Step-by-step explanation:

x intercepts is (- 1/2,0)

y intercepts is (0,2)

If f(x)=7x+2 and x=1 what is the output value? Plzzz help ASAP

Answers

It is 7*1+2=9
The output is 9

If bc+ad=b solve for a

Answers

Answer:

10

Step-by-step explanation:

Answer:

a = c/d

Step-by-step explanation:

ad = b-bc

ad = c

a = c/d

Yo can I get some help with this!

Answers

Answer:

b=56

Step-by-step explanation:

Try

Please help Algebra 1

Answers

Answer:

D

Step-by-step explanation:

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