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:
[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.
Related Questions
is 54/35 a rational number?
Answers
Answer:
54/35 is a rational number!
Have a great rest of your day!
Answer:
Yes and no
Step-by-step explanation:
The number 54 is a rational number if 54 can be expressed as a ratio, as in Rational. A quotient is the result you get when you divide one number by another number. Although the 54 is good the 35 is not due to it if you had to choose if it was or not you can say yes but it determines the question.
The quotient of (x5 - 3x3 - 3x2 - 10x + 15) and a polynomial is (x2 - 5). What is the polynomial?
Answers
Answer:
x^3 + 2x - 3
Just divide x^5-3x^3-3x^2-10x+15 by the quotient and you get the polynomial searched.
Step-by-step explanation:
hope it helps , i am in 6th grade and i have got this answer from an elder student.
In the fraction 11/12 the_is 11
Answers
Answer:
numerator
Step-by-step explanation:
.,.............
Hope this helps
32 is 56% of what number?
Answers
Answer:
About 57.14285714, or 57 1/7 (400/7)
Step-by-step explanation:
Suppose the answer is x. This would mean that x multiplied by 0.56 (56%) would equal 32. To isolate x, you would have to divide both sides by 0.56, making the answer 32/0.56, or About 57 and 1/7
31 SPORTS Sixteen students in Mr. Prank's gym class each
participate in one or more sports as shown in the
table. Examples 2 and 3
Mr. Frank's Gym Class
Basketball Soccer Volleyball
Ayanna Lisa Pam
Ayanna Lisa
Sue
Pion
Shin
Lisa Tyron Mex
Ron
Max
Alda
Max
Aida
Juan
Ito
Evita
Juan
Nela
Percy
Tino
Kai
Percy
Nella
a. Let B represent the set of basketball players, S
represent the set of soccer players, and V represent the
set of volleyball players. Draw a Venn diagram of this
situation.
b. Find Sn V. What does this set represent?
c. Find S. What does this set represent?
d. Find BUV. What does this set represent?
Answers
A local charity collected 163 cans of food
every day for 14 days. How many cans did they collect
in the first 10 days? How many did they collect in the
remaining 4 days? How many cans did they collect in
all? Solve this problem any way you choose!
Answers
Answer:
This was $14 less than twice what she spent for a blouse . How much ... From the first two equations, we have A=12B=12(3C)=32C ... How many days will it require for the son to plow the field alone?
Step-by-step explanation:
bbs.
Which statement best compares the two jobs?
O Job A has a lower salary than job B, but the benefits
make job A a more attractive pay package.
O Job B has a lower salary than job A, but the benefits
make job B a more attractive pay package.
O Job A has a higher salary than job B plus benefits that
make job A a more attractive pay package.
O Job B has a higher salary than job A plus benefits that
make job B a more attractive pay package.
Answers
Answer:
B - Job B has a lower salary than job A, but the benefits
make job B a more attractive pay package.
Step-by-step explanation:
Answer: B
Step-by-step explanation:
4. Write an equation for the table in slope intercept form
Answers
Answer:
y=1.6x-5
Step-by-step explanation:
A power boat travels along a river in which the flow of water is at a constant in one direction. If the boat travels at 40 mph downstream and 30 mph upstream. What is the speed of the boat in still water and the speed of the river?
Answers
Answer:
speed of boat is 35 mph
speed of river is 5mph.
Step-by-step explanation:
Let the speed of boat be u mph
let the speed of river be v mph
When boat travel downstream
in that case flow of river will support the speed of boat hence
speed of river will be added to speed of boat
Thus,
speed of boat in downstream = speed of boat + speed of river = u + v
Given
the boat travels at 40 mph downstream
thus,
u + v = 40 -----1
When boat travel upstream
in that case flow of river will oppose the speed of boat hence
speed of river will be subtracted from speed of boat
Thus,
speed of boat in downstream = speed of boat -speed of river = u - v
Given
the boat travels at 30 mph upstream
thus,
u - v = 30 ----2
adding 1 + 2
we have
u + v = 40
+ u - v = 30
2u = 70
u = 70/2 = 35
Thus,
speed of boat is 35 mph
using u = 35 in u + v = 40
we have
35 + v = 40
v = 40 - 35 = 5
Thus, speed of river is 5mph.
If k(x) = -2x2 – 7, find k(4)
Answers
Answer:
-39
Step-by-step explanation:
Answer:
-23
Step-by-step explanation:
You just plug in 4 for x. So it'd be -2(4)2-7
So, you have -8(2)-7
Then: -16-7, which gives you -23
ben payed $900 for a sofa. The price of the sofa Juana was 2/3 the price ben payed. How much did Juana pay for her sofa?
Answers
Answer: $600
Step-by-step explanation:
Find 2/3 of $900.
To do this, we have to get 9 and divide by 3.
9 ÷ 3 = 3
Multiply 3 by 2. You get 6.
Add two zeros.
You will get $600.
Express the ratio below in its
simplest form.
18:3:9
Answers
Answer:
6:1:3
Step-by-step explanation:
all you need is in the photo
Answers
Answer:
slope is -1, y intercept is 5
Step-by-step explanation:
slope formula is y1-y2 over x1-x2
plug in formula
u get the slope is -1
Answers:
Slope = 4
Y intercept = 5
======================================================
Explanation:
Start at the point (-1,1) which is one point on the line. Then move up 4 units and to the right 1 unit to get to (0,5). This is another point on the line.
Therefore the slope = rise/run = 4/1 = 4.
You could also use the slope formula m = (y2-y1)/(x2-x1)
---------------
The y intercept is 5 since the line crosses the y axis at this location. More specifically this is the point (0,5). For any y intercept, x = 0.
The equation of this line in slope intercept form is y = 4x+5. Compare it to y = mx+b and we have m = 4 as the slope and b = 5 as the y intercept.
help find equation and missing angle
Answers
Answer:
angle V + Angle W = angle U
angle VUF is equal to 94 degrees
Step-by-step explanation:
A speedboat, at full throttle, can go 65.0 miles in 1.5 hours. What is the average speed of the boat?
Answers
Solve the system, by elimination please show all the steps!
-2x+2y+3z=0
-2x-y+z=-3
2x+3y+3z=5
Answers
Answer:
x = 1 , y = 1 , z = 0
Step-by-step explanation:
Solve the following system:
{-2 x + 2 y + 3 z = 0 | (equation 1)
-2 x - y + z = -3 | (equation 2)
2 x + 3 y + 3 z = 5 | (equation 3)
Subtract equation 1 from equation 2:
{-(2 x) + 2 y + 3 z = 0 | (equation 1)
0 x - 3 y - 2 z = -3 | (equation 2)
2 x + 3 y + 3 z = 5 | (equation 3)
Multiply equation 2 by -1:
{-(2 x) + 2 y + 3 z = 0 | (equation 1)
0 x+3 y + 2 z = 3 | (equation 2)
2 x + 3 y + 3 z = 5 | (equation 3)
Add equation 1 to equation 3:
{-(2 x) + 2 y + 3 z = 0 | (equation 1)
0 x+3 y + 2 z = 3 | (equation 2)
0 x+5 y + 6 z = 5 | (equation 3)
Swap equation 2 with equation 3:
{-(2 x) + 2 y + 3 z = 0 | (equation 1)
0 x+5 y + 6 z = 5 | (equation 2)
0 x+3 y + 2 z = 3 | (equation 3)
Subtract 3/5 × (equation 2) from equation 3:
{-(2 x) + 2 y + 3 z = 0 | (equation 1)
0 x+5 y + 6 z = 5 | (equation 2)
0 x+0 y - (8 z)/5 = 0 | (equation 3)
Multiply equation 3 by 5/8:
{-(2 x) + 2 y + 3 z = 0 | (equation 1)
0 x+5 y + 6 z = 5 | (equation 2)
0 x+0 y - z = 0 | (equation 3)
Multiply equation 3 by -1:
{-(2 x) + 2 y + 3 z = 0 | (equation 1)
0 x+5 y + 6 z = 5 | (equation 2)
0 x+0 y+z = 0 | (equation 3)
Subtract 6 × (equation 3) from equation 2:
{-(2 x) + 2 y + 3 z = 0 | (equation 1)
0 x+5 y+0 z = 5 | (equation 2)
0 x+0 y+z = 0 | (equation 3)
Divide equation 2 by 5:
{-(2 x) + 2 y + 3 z = 0 | (equation 1)
0 x+y+0 z = 1 | (equation 2)
0 x+0 y+z = 0 | (equation 3)
Subtract 2 × (equation 2) from equation 1:
{-(2 x) + 0 y+3 z = -2 | (equation 1)
0 x+y+0 z = 1 | (equation 2)
0 x+0 y+z = 0 | (equation 3)
Subtract 3 × (equation 3) from equation 1:
{-(2 x)+0 y+0 z = -2 | (equation 1)
0 x+y+0 z = 1 | (equation 2)
0 x+0 y+z = 0 | (equation 3)
Divide equation 1 by -2:
{x+0 y+0 z = 1 | (equation 1)
0 x+y+0 z = 1 | (equation 2)
0 x+0 y+z = 0 | (equation 3)
Collect results:
Answer: {x = 1 , y = 1 , z = 0
Answer:
x= 1, y = 1, z= 0
Step-by-step explanation
-2x + 2y + 3z = 0
2x + 3y + 3z = 5
-2x - y + z = -3
2x + 3y + 3z = 5
(solving systems)
5y + 6z = 5
2y + 4z = 2
(rewriting)
z = 0
y = 1
-2x + 2 x 1 + 3 x 0
x=1
Nadia charges $5.50 an hour for babysitting. She babysits 17.50 hours the first week of the month and 21 hours the second week of the month.
Suppose Nadia raises her rate by $0.55 an hour. How many hours would she need to work to earn the same amount of money she made in the first two weeks of the month?
Answers
Answer:
about 34 hours
Step-by-step explanation:
Answer:
35 hours.
Step-by-step explanation:
To achieve an answer to this question, we'll have to set two expressions equal to each other.
Let's first start by calculating how much Nadia has made in the first two weeks of the month. We can do this by adding the amount of hours she works in the first and second week together:
[tex]21+17.5[/tex]
[tex]=38.5[/tex]
Let [tex]h[/tex] equal hours.
Set up your first expression:
[tex]5.50h[/tex]
Let's go ahead and substitute 38.5 into the expression to see how much money she will make the first two weeks of the month at a rate of $5.50 an hour:
[tex]5.50(38.5)[/tex]
[tex]=211.75[/tex]
We are told that Nadia raises her rate by $0.55, so we'll need to add 0.55 to 5.50 in order to find her increased rate:
[tex]5.50+0.55[/tex]
[tex]=6.05[/tex]
Set up your second expression:
[tex]6.05h[/tex]
Now, set this equal to how much she made the first two weeks at a rate of $5.50 an hour:
[tex]211.75=6.05h[/tex]
Divide both sides of the equation by the coefficient of [tex]h[/tex], which is [tex]6.05[/tex]:
[tex]35=h[/tex]
Therefore, it will take Nadia 35 hours to earn the same amount of money she made in the first two weeks of the month.
_
Check your work by substituting 35 for [tex]h[/tex] in the equation below:
[tex]211.75=6.05h[/tex]
[tex]211.75=6.05(35)[/tex]
[tex]211.75=211.75[/tex]
Since both sides of the equation are equal to each other, our answer is correct!
Circle A has a diameter of 9 , Circle B has a radius of 5 , how many centimeters larger is it ?
Answers
Answer:
4
Step-by-step explanation:
need help with a question
Answers
Answer:
You need to put the Question to get us to answer it sorry
Step-by-step explanation:
ario made a deposit in an account that earns annual interest. His account balance, in dollars, after t years is represented by the expression 400⋅1.05t . Yvonne made a deposit in an account that earns annual interest. Her account balance, in dollars, after t years is represented by the expression 300⋅1.06t . Which statement describes the situation correctly? A. Mario deposited 100 dollars more than Yvonne, and Yvonne’s account earns 1 percent more annual interest than Mario’s account. B. Yvonne deposited 100 dollars more than Mario, and Mario’s account earns 1 percent less annual interest than Yvonne’s account. C. Mario deposited 100 dollars more than Yvonne, and Yvonne’s account earns 1 percent less annual interest than Mario’s account. D. Yvonne deposited 100 dollars more than Mario, and Mario’s account earns 1 percent more annual interest than Yvonne’s account.
Answers
Answer:
nothing at all.
Step-by-step explanation:
2x+5y=10
Solve for y
Answers
2x+5y=10
Move constant to the left by adding its opposite to both sides
2x+5y-10=10-10
the sum of two opposites equals 0
Answer: 2x+5y-10=0
PLEASE MARK ME AS BRAINLIEST
hans cellphone plan costs $200 to start. Then there is a $50 charge each month
Answers
A LOT OF POINTSS
find the surface area
Answers
Answer:
He used 286.73² in. of wrapping paper.
Answer:
I got 286.73
Step-by-step explanation:
I found the area of all the shapes in the thing and added them.
Pls correct me if I did the adding wrong cuz its 55+20+20+88+103.73
Only smart bros answer
Answers
Answer:
9 :/
Step-by-step explanation:
Answer:9
Step-by-step explanation:
3x9=27
27 divided by 3=9
Below are two parallel line intersecting them
Answers
Answer:
x = 53°
Step-by-step explanation:
alternate exterior angles are equal
Answer:
Step-by-step explanation:
Two lines are parallel.
x = 53
Alternate exterior angles are equal
Which equation represents the line that is parallel to 5x +y = 13 and passes through the point (15,-31)? Show complete working format please
Answers
Answer:
Step-by-step explanation:
y = -5x + 13
y + 31 = -5(x - 15)
y + 31 = -5x + 75
y = -5x + 44
Consider the pairs of ratios given and determine whether or not the ratios form a proportion 8 old rings for every 1 ring 16 old rings for every 2 rings A) Yes B) No Save
Answers
Answer:
b
Step-by-step explanation:
even number less than 12
Answers
Answer:
2,4,6,8,10
Step-by-step explanation:
they are even numbers
Answer: 2, 4, 6, 8, 10
Step-by-step explanation:
any of those are even numbers that are less than 12
Megan scored 80% on a test. She got 20 questions correct. How many questions were on the test?
Answers
Answer:
25
Step-by-step explanation:
I'm writing this to get to the 20 character minimum
Answer:
26 Questions
Step-by-step explanation:
please can you help. i would really appreciate it
Answers
Answer:
The integers that satisfy both inequalities are any number between -4.5 and -12
Step-by-step explanation:
Hope this helps and pls do mark me brainliest if you can:)