A ball is thrown directly upward from a height of 3 ft with an initial velocity of 20 ​ft/sec. The function ​s(t)=−16t2+20t+3 gives the height of the​ ball, in​ feet, t seconds after it has been thrown. Determine the time at which the ball reaches its maximum height and find the maximum height.

Answers

Answer 1

Answer:

[tex]t=\frac{5}{8}s[/tex] and [tex]s(\frac{5}{8})=\frac{37}{4}ft[/tex]

Step-by-step explanation:

There are different approaches you can take to solve this problem. You can look at it from the geometric approach or the calculus approach. I will us the geometric approach.

When we analyze the given function for the height of the ball:

[tex]s(t)=-16t^2+20t+3[/tex]

we can see that we are dealing with a quadratic function. This means that the graph will be an inverted parabola, just like the one in the attached picture.

so the idea is to find the vertex of the parabola to find the highest the ball gets to be and the time it gets to be at that height.

In order to do so, we can use the vertex formula, which looks like this:

[tex]t=-\frac{b}{2a}[/tex]

this is use when you have a function with the form:

[tex]f(x)=ax^2+bx+c[/tex]

in this case:

a=-16, b=20 and c=3, so the formula then turns to:

[tex]t=-\frac{20}{2(-16)}[/tex]

which yields:

[tex]t=\frac{5}{8} s[/tex]

which is our first answer. So we can then use this to find the maximum height of the ball, just by substituting t into the original function:

[tex]s(\frac{5}{8})=-16(\frac{5}{8})^2+20(\frac{5}{8})+3[/tex]

which yields:

[tex]s(\frac{5}{8})=\frac{37}{4} ft[/tex]

which is our second answer.

A Ball Is Thrown Directly Upward From A Height Of 3 Ft With An Initial Velocity Of 20 Ft/sec. The Function

Related Questions

When dividing fractions, like 1/5 divided by 3/4 what do we do?

Answers

Answer:

we cry bc math is hard JKK unless ?

but fr we can write out an equation by doing (1/5 ÷ 3/4) and then switch the sign to multiplication and we can keep the first fraction the same (in this case 1/5) and then we flip the second fraction BUT when we flip the second fraction upside-down we have to change the symbol to multiplication (1/5x4/3)

then after that all we do is multiply the denominators and numerators :)

1 x 4 = 4

_______

5 x 3 = 15

answer would be 4/15

A fraction is a way to describe a part of a whole. The result of the division of the fraction is 4/15.

What is a Fraction?

A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.

The division of two fractions is carried out by multiplying the dividend fraction(Numerator) by the reciprocal of the divisor fraction(Denominator).

The divisions of the given fractions are carried out as shown below.

1/5 ÷ 3/4

[tex]=\dfrac{\dfrac{1}{5}}{\dfrac{3}{4}}\\\\\\= \dfrac{1 \times 4}{5 \times3}\\\\=\dfrac{4}{15}[/tex]

Hence, the result of the division of the fraction is 4/15.

Learn more about Fraction here:

https://brainly.com/question/1301963

#SPJ2

Need helps with 45 , picture above

Answers

Answer:

Ok:

Step-by-step explanation:

We know Josh buys 3 oranges for $2 and sells 2 oranges for $3. Let's take the LCM (least common multiple) of 2 and 3. It is 6. If he buys 6 oranges, he needs $4. When he sells 6 oranges he makes $9. That is a total profit of $5. In total that means, if we multiple by 10, that means that if he sells 60 oranges,  he would make $50. Thus C is the answer

can somebody help me pleaseee ?? it’s due soon & im stuck .

Answers

Answer:

a. lenqth=32 , width=2

b. m∠p=100  m∠Q=50  m∠R=30

c. XY=20  YZ=12

d.m∠1=90    m∠2=90

Step-by-step explanation:

a. the area of a rectangle is length×width so to find the possible sizes for L and W we need to list the factors (multiplication of two numbers to get 64) of 64, which are,

1  AND  64   (this answer is suitable but it's better to choose another

one if available for more accuracy)

2  AND  32  (this is a good answer to use)

4  AND 16   (this one already used in the question)

8   AND  8   (this answer will be wrong as the sizes need to be different because it's a rectangle but it will be good for square)

SO we will choose 2 AND 32 for the answer and we can put them in any order we want.

b. first of all acute angles are angles measured less than 90 degrees. so to have at least one angle not acute we use measures up to 90 degrees.

I will put one answer as 100 degrees (note you can use any number above 90 to not be an acute angle) and the other answers will be two numbers add up to be 80 degrees (and again you can choose any numbers for that).

c. the two answers should add up to be 32 so for this counterexample we can choose any two numbers to have the sum of 32 (remember that 16+16 already chosen in the question.

d. two supplementary angles are two angles add up to be 180 degrees so for this question we need to find two angles sum to 180 and not obtuse (that mean 90 degrees or less) and the only answer can appear is 90+90=180.  

HELP ASAP
Jason has $2.25 worth of dimes and quarters. He has twice as many dimes as quarters. Determine the number of dimes and the number of quarters that Jason has.

Answers

Answer:

Step-by-step explanation:

let the number of dimes=x

and number of quarters=y

x=2y

0.10 x+0.25 y=2.25

or 10x+25y=225

divide by 5

2x+5y=45

2 ×2y+5y=45

4y+5y=45

9y=45

y=45/9=5

x=2y=2×5=10

Hence dimes=10

quarters=5

Which could be the first step of an indirect proof of the conditional below?
If x2 = 25, then 5’2= 25 and x = 5,
A. Assume x=5 is true.
B. Assume 52 = 25 is true,
C. Assume x2 + 25 is true.
D. Assume 52.25 and x + 5 are true,

Answers

Answer

Option D

Step-by-step explanation

For further help (727) 335-8234

The first step of indirect proof of the conditional below

If x2 = 25, then 5’2= 25 and x = 5 is assume 5² = 25.

Option B is the correct answer.

What is an equation?

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

Conditions:

x² = 25 then 5² = 25 and x = 5

If we have to prove the above conditions indirectly, we have to prove that x² = 25 using the conditions 5² = 25 and x = 5.

So,

We have to assume,

Step 1:

5² = 25

Step 2:

x = 5

Step 3:

x² = 25

Thus,

The first step of indirect proof of the conditional below

If x2 = 25, then 5’2= 25 and x = 5 is assume 5² = 25.

Option B is the correct answer.

Learn more about equations here:

https://brainly.com/question/27996921

#SPJ2

help me plzzzzzzzzzzz

Answers

1. √8, π, 4
2. 5, π+ 2, 17/3,
3. -2, √2 , 1.7
4. 3/2, √5, 2.5
5. √13, 3.7, π + 1
6. √5/2, π - 2, 5/4

Apologies if I got some wrong

3.46x + 6.38 = -4 the answer

Answers

Answer:

x = -3

Step-by-step explanation:

start with 3.46x + 6.38 = -4. Then take away 6.38 from both sides to get 3.46x=-10.38. Then you divide both sides by 3.46 to get x = -3.

   

Simplify the expression.
74÷(32)

A. −218
B. 218
C. 76
D. −76

Answers

Answer:

Simplify the expression.

Exact Form:

37

16

Decimal Form:

2.3125

Mixed Number Form:

2

5

16

What is the solution to 4 x + 6 less-than-or-equal-to 18?

help
<3

Answers

Answer:

x is less-than-or-equal to 3

Step-by-step explanation:

4(3)+6 =18

I need the answer real quick will someone help me

Answers

More info plz there is no context

Two different linear functions are shown below with two points given from each function Use slope-intercept form Function A has The equation of line A is or point-slope form to find the equation of each.

Linear Function A

Points : (-5, -2), (-5, 7)

Linear Function B

Points : (7, -5), (-2, -5)

Which is true about the following:

1. Function A has...

A: Slope of -7
B: Slope of 0
C: Slope of 9
D: No slope

2. The equation of line A is :

A: X= -5
B: Y= -5
C: X= -2
D Y= 7

Function B has...

A: Slope of -7
B: Slope of 0
C: Slope of 9
D: No slope

The equation of Line B is :

A: X= -5
B: Y= -5
C: X= -2
D: Y= 7

Answers

Answer:

This answer is option 1

Step-by-step explanation:

The awnser is No slope,x=-5,A slope of 0,and y=-5

If f(x) = -2 cos x, findf(-300 º). Do not use a calculator.

Answers

Answer:

- 1

Step-by-step explanation:

Using the trigonometric identity

cos(- x) = cosx and exact value cos60° = [tex]\frac{1}{2}[/tex]

Given

f(x) = - 2cosx , then

f(- 300° )

= - 2cos(- 300)°

= - 2cos(300)°

= - 2cos(360 - 300)°

= - 2cos60°

= - 2 × [tex]\frac{1}{2}[/tex]

= - 1

can you terminate 1/10

Answers

Answer:

Hope this helps...if it dosent, sorry

Step-by-step explanation:

Accrotime is a manufacturer of quartz crystal watches. Accrotime researchers have shown that the watches have an average life of 26 months before certain electronic components deteriorate, causing the watch to become unreliable. The standard deviation of watch lifetimes is 4 months, and the distribution of lifetimes is normal. A button hyperlink to the SALT program that reads: Use SALT. (a) If Accrotime guarantees a full refund on any defective watch for 2 years after purchase, what percentage of total production will the company expect to replace? (Round your answer to two decimal places.) Incorrect: Your answer is incorrect. % (b) If Accrotime does not want to make refunds on more than 6% of the watches it makes, how long should the guarantee period be (to the nearest month)? months

Answers

Answer:

a

   [tex]P(X <  24 )=  21.186\%  [/tex]  

b

    [tex]x =  19.78 \  months[/tex]

Step-by-step explanation:

From the question we are told that

 The mean is   [tex]\mu  =  26 \  months[/tex]

 The standard deviation is  [tex]\sigma  =  4 \  months[/tex]

 Generally 2 year is  equal to  24 months

Generally the percentage of total production will the company expect to replace is mathematically represented as

      [tex]P(X <  24 )=  P(\frac{X - \mu }{ \sigma} <  \frac{24 - 26}{4}  )[/tex]

Generally  [tex]\frac{X - \mu}{\sigma } =Z (The  \ standardized \  value  \  of  \  X )[/tex]

     [tex]P(X <  24 )=  P(Z <  -0.8  )[/tex]

Generally from the z-table  

       [tex]P(Z <  -0.8) =  0.21186[/tex]

So

       [tex]P(X <  24 )=  0.21186[/tex]

Converting to percentage

      [tex]P(X <  24 )=  0.21186  * 100[/tex]

=>    [tex]P(X <  24 )=  21.186\%  [/tex]  

Generally the duration that should be the guarantee period if  Accrotime does not want to make refunds on more than 6% is mathematically evaluated as

    [tex]P(X <  x) =  P(\frac{X - \mu }{\sigma}  < \frac{x - 26}{4} )= 0.06[/tex]

=> [tex]P(X <  x) =  P(Z < \frac{x - 26}{4} )= 0.06[/tex]

From the normal distribution table the z-score for  0.06 at the lower tail  is

       [tex]z = -1.555[/tex]

So

    [tex]\frac{x - 26}{4} = -1.555[/tex]

=> [tex]x =  19.78 \  months[/tex]  

A scale drawing of a rectangular park is 5 inches wide and 7 inches long. The actual park is 280 yards long. What is the area?

Answers

Answer:

315

Step-by-step explanation:

5 x 7 = 35

280 + 35 = 315

There sth answer

Answer:7 inches → 280 yards

1 inch → 280 ÷ 7 = 40 yards

5 inches → 40 x 5 = 200 yards

Area = 280 x 200 = 56 000 yards

hope this help btw i am 12

Step-by-step explanation:

y=-7x+6 in standard form. I’ll give brainliest. Hurry pls

Answers

Answer:

7x+y=6

Step-by-step explanation:

trust

can someone help me x -y =1
and can yall explain how you solved it

Answers

Answer:

x = 1 + y

Step-by-step explanation:

add y to both sides, and that is basically it

i need help answering the questions using distributive property. i already know the answers 3. will give brainliest.

Answers

Answer:

Hello

Step-by-step explanation:

by what i understood the awnser should be c

what is 200 digits of pi​

Answers

Answer:

3.141592653589793238462643383279502884197169399375105820974944592307816406286 208998628034825342117067982148086513282306647093844609550582231725359408128481 117450284102701938521105559644622948954930381964428810975665933446128475648233 786783165271201909145648566923460348610454326648213393607260249141273724587006 606315588174881520920962829254091715364367892590360011330530548820466521384146 951941511609433057270365759591953092186117381932611793105118548074462379962749 567351885752724891227938183011949129833673362440656643086021394946395224737190 702179860943702770539217176293176752384674818467669405132000568127145263560827 785771342757789609173637178721468440901224953430146549585371050792279689258923 542019956112129021960864034418159813629774771309960518707211349999998372978049 951059731732816096318595024459455346908302642522308253344685035261931188171010 003137838752886587533208381420617177669147303598253490428755468731159562863882 353787593751957781857780532171226806613001927876611195909216420198938095257201 065485863278865936153381827968230301952035301852968995773622599413891249721775 283479131515574857242454150695950829533116861727855889075098381754637464939319 255060400927701671139009848824012858361603563707660104710181942955596198946767 837449448255379774726847104047534646208046684259069491293313677028989152104752 162056966024058038150193511253382430035587640247496473263914199272604269922796 782354781636009341721641219924586315030286182974555706749838505494588586926995 690927210797509302955321165344987202755960236480665499119881834797753566369807 426542527862551818417574672890977772793800081647060016145249192173217214772350 141441973568548161361157352552133475741849468438523323907394143334547762416862

Step-by-step explanation:

Answer:3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230664709384460955058223172535940812848111745028410270193852110555964462294895493038196

Step-by-step explanation:teehee

Select the correct answer.
Jason is traveling by car from his home to his office. He has gone 3.5 miles so far. From this point on, he can cover 100 miles every 2 hours. What is the equation of a line that models the total miles traveled, y, in x hours after this point?
A.
y = 100x + 3.5
B.
y = 100x – 3.5
C.
y = 50x + 3.5
D.
y = -50x + 3.5

Answers

9514 1404 393

Answer:

  C.  y = 50x + 3.5

Step-by-step explanation:

100 miles in 2 hours is 100/2 = 50 miles per hour. Multiplying that rate by x hours gives the miles traveled in addition to the 3.5 miles so far. The appropriate equation for miles traveled is ...

  y = 50x +3.5 . . . matches choice C

Answer:

Step-by-step explanation:

5. Do this without using a calculator

Calculate 39 × 63 + 39 × 37

A. 3,510. B. 3,900. C. 4,290. D. 97,812

Answers

Answer:

3900

Step-by-step explanation:

Not really sure how to explain this one.

Libby bought three shirts that cost $6.79, $11.08, and $8.95. How much did all three shirts cost

Answers

6.79+11.08+8.95=26.82

Answer:

$26.82

Step-by-step explanation:

It's just simple addition really. You start with adding 6.79 and 11.08 to get 17.87 and then add 8.95 to 17.87 to get 26.82. Hope this helps.

A ferris wheel can accommodate 70 people in 20 minutes; how many people could ride the ferris wheel in 4 hours?

Proportional Question

Answers

Answer:

840

Step-by-step explanation:

if it can hold 70 in 20 minutes it can hold 210 in 1 hour and 4x210 equals 840

what is the answer to 6y * 88 = 88 * 6y

Answers

Answer:

0 or No solutions

Step-by-step explanation:

hope this helps!

Look at the picture to see question plz help quickly and step by step

Answers

Answer: 16.6

Step-by-step explanation:


The volume, V, of a certain gas varies inversely with the amount of pressure, P. placed on it. The volume of this gas is 175
cm' when 3.2 kg/cm² of pressure is placed on it. What amount of pressure must be placed on 400 cm' of this gas?
2.86 kg/cm2
1.31 kg/cm?
7.31 kg/cm2
1.40 kg/cm2

Answers

Answer:

1.3 kg/cm

Step-by-step explanation:

Write the equation in point-slope form of the line that passes through (7, -6) and has the slope of 1/2.

PLS HELP

Answers

Answer:

y=1/2x-6

Step-by-step explanation:

use the equation y=mx+b

m=slope and b=y-intercept.

we know that the slope is 1/2 and the point is in (x,y) form so for b we can insert the b as -6 , the point that intercepts the y-axis. hope this helps!!

Mikel has a chance to win a trip on a TV game show. All he has to do is win the “Shopping Game". In
this game, Mikel is shown six grocery store items without being shown the prices. He must buy
multiples of items until he has a total between $20 and $21 inclusive. If he doesn't reach $20 with his
first item, he continues buying items and adding to his total, until he either wins by getting an amount
between $20 and $21, or he loses by going over $21 or by buying all items and being less than $20.
First, Mikel buys six bottles of shampoo.
Solve the inequality. Round each answer to the hundredths place.

Answers

Answer:  

$20 <= X < = $21

Step-by-step explanation:

You are told that he loses by going over $21 or by buying all items and being less than $20.

That means the total amount of the items bought must be equal to 20 dollars or 21 dollars or be within the two amount of money.

If Mikel buys six bottles of shampoo,  x represents the total amount for the six bottles of shampoo. Then, the compound inequalities for this expression will be x less than or equal to 21 dollars and x greater than or equal to 20 dollars. That is,

$20 <= X < = $21

HELP NOW PLZZZZZ HELPPPPPPPPPPPP

Answers

Answer:

y = 4/3x -11

Step-by-step explanation:

y = -3/4 x - 8

This is in slope intercept form  

y = mx+b where the slope is -3/4

We want a slope that is perpendicular

Take the negative reciprocal

-1 ( -3/4) = 4/3

The slope of the line that is perpendicular is 4/3

Using the slope intercept form of a line is

y = mx+b

y = 4/3x+b

Substituting the point into this equation

-3 = 4/3(6) +b

-3 = 8+b

Subtract 8 from each side

-3-8 = b

-11 =b

y = 4/3x -11

What number would go into the box?

Answers

8. When dealing with exponents like x^2, multiplication is like addition and division is like subtraction (x^2*x^3=x^5, x^3/x^2=x). So, for this one, we can get rid of the X’s and rewrite as this: p+6-2=12. If we solve this, we see that the answer is 8.
Other Questions
to rebuild Athens,The money collected from the Delian League was used byA. PlatoB. DariusC. PericlesD. Aristotle Not sure about the answer pls help me Which of the following describes a theme or the text the lottery At $0.31 per bushel, the daily supply for wheat is 306 bushels, and the daily demand is 459 bushels. When the price is raised to $0.79 per bushel, the daily supply increases to 546 bushels, and the daily demand decreases to 439 bushels. Assume that the price-supply and price-demand equations are linear. a. Find the price-supply equation. Is 17/5 + square root of 64 greater than 8 + pi? Years later, both the United States and Canada fought against Germany in Choose..., which led to the emergence of two major world powers: the United States and the Soviet Union.A. World War IIB. the Great DepressionC.the Civil Rights MovementD.the Cold War Solve for u.3u = 4.8 I dont know how to find what u equals can someone help me Differentiate between a cloth safety belt and a metal buckle in terms of thermal conductors and insulators. Gcf of 16abc^2, 28abc A deep sea diver descended from a rock that is 45 feet below Which is the best estimate for the width of a typical adult hand? An object with a charge of 1.2 C is located 4.5 m away from a second object that has a charge of 0.36 C. Find the electrical force that the objects exert on each other. Use 8.98810 Nm2/C2 for the value of Coulomb's constant. Give your answer to two decimal places. The diagram below shows the requirements for becoming a naturalized citizenWhich statement completes the diagram? MAKING BRAINLIEST, THANKS AND FIVE STARS TO CORRECT ANSWER!! PLZ AND THANK YOU. HAVE A GREAT DAY :DA sperm cell joins with an egg cell during:fertilizationpollinationmitosisgrowth An Empire is defined as:A civilization in which survival is based on a river.A complex society with three levels of government.A civilization that conquers and rules other civilizations.The rules, meanings, and values that are expressed in the ways people live. if I do this research project how useful will it be to me as a senior high school graduate and to the community where I belong and even to the larger community, the Philippines, ASEAN,and the world? plss....I need answer How was the invasion of zebra mussels in the Hudson River affected one biotic or abiotic factor in the river ecosystem? To render a cloud, an artist should demand a strong, hard quality. TRUE or FALSE what is the missing angle? why is a 5 rupees coin attracted by a magnet? name the metal present in the coin