Answer:
The ball reaches its maximum height at 2.5 seconds
The maximum height is 100 feet
Step-by-step explanation:
Maximum Value of Functions
We use the derivative of a function to find its maximum or minimum value over a given interval.
Given a function y=f(x), the first derivative criterion establishes if x=a is such that:
f'(a)=0, and f''(a) < 0 then x=a is a maximum of f.
The height h in feet of a ball after t seconds is:
[tex]h(t)=-16t^2+80t[/tex]
Find the first derivative:
[tex]h'(t)=-32t+80[/tex]
Equate to 0:
[tex]-32t+80=0[/tex]
Subtract 80:
[tex]-32t=-80[/tex]
Divide by -32:
[tex]t = -80 / (-32) = 2.5[/tex]
t=2.5 seconds
Find the second derivative:
h''(t)=-32
Since h''(t) is always negative, then
The ball reaches its maximum height at 2.5 seconds
To find the value of the maximum height, substitute t=2.5 into the function:
[tex]h(2.5)=-16(2.5)^2+80*2.5=-100+200 = 100[/tex]
The maximum height is 100 feet
of the students in a school are in sixth grade. a. How many sixth graders are there if the school has 90 students? b. How many sixth graders are there if the school has 27 students? c. If the school has students, write an expression for the number of sixth-graders in terms of. d. How many students are in the school if 42of them are sixth graders? plz help it's my test
Hiyo! the answer is 20 students :D! so first off we gotta find the exact number of sixth graders, next of when we find the number which is 90, we need to divide or multiply to get our answer. mkay I just noticed there is answer a. b. c . but I know the exact answer is 20. Sorry if i'm missing something :D
A camera is able to capture 3/4 of a picture per second. How long will it take a camera to snap 6 pictures
SOMEONE HELP IM STRESSING OUT
Answer: right angles x equals 7 and both m1 and 1 arre 5
Step-by-step explanation:
Answer: CA
Step-by-step explanation:
corresponding angles
90=5x
x=18
m1=90
m2=90
2m - 3 = 13
what is the answer?
Answer:
m = 8
Step-by-step explanation:
2(8) = 16
16 - 3 = 13
Therefore, m = 8
What is the sales tax on a $14,500 truck if the tax rate is 9%. What is the total price of the truck
after the sale tax?
Answer:
15805
Step-by-step explanation:
14,500×9÷100=1,305
14,500+1,305=15,805
The chart below shows Mrs. Thompson's grocery bill. What is the average amount Mrs. Thompson spent on groceries?
A. $58
B. $68
C. $78
D. $340
Answer:$68
Step-by-step explanation:
Add $47+$66+$68+$71+$88. You get $340. Divide this by 5 (because there are 5 weeks). You get $68.
Multiply : 1 2/5 x 1/4
Answer:
0.35
Step-by-step explanation:
Answer:
7/20
Step-by-step explanation:
1 2/5 ×1/4=7/20
In 1-4, write an equation in slope-intercept form to represent each table (just the first 4)
Answer:
Q1 y = 17/2x - 2
Q2 y = -3x + 14
Q3 y = 1/4x
Q4 y = 1/8x + 10
Step-by-step explanation:
See, the problem here is, you did everything to NOT convert the decimals into fractions. You would´ve had the right answers if you just learned to deal with the fractions. I´ll only going to be explaining 2 questions since there´s four of them.
Question Two
You take two points from the table, then you do y2 - y1 over x2 - x1. -1 - 5 / 6 - 3 = -6/3 and 3 divided by -6 is -3. Which should give you "m" the slope. Which the slope for this question is -3. To find "b" our y-intercept, we will need to plug in the points from one of the two points we took in the chart into the format of y = mx + b. I chose to do, 5 = -3(3) + b. Multiply m times the x, 5 = - 9 + b. So now, we add 9 to itself to cancel itself out and add it to 5. Which gives us, 14 = b. So our equation is, y = -3x + 14
Question 3
This one is relatively easy, since looking at the table we know theres no b or m. Just a constant rate times x. The same thing we did the last question, take two points from the equation. y2 - y1 over x2 - x1. 1 - 0 over 4 - 0. Which gives us 1/4. 1/4 is our constant rate of change. y = 1/4x
The equation in slope intercept form to represent each table is
Q1 y = 17/2x - 2 Q2 y = -3x + 14 Q3 y = 1/4x Q4 y = 1/8x + 10What is slope intercept form ?You ought to be familiar with two-variable linear equations. You should specifically be aware that the graph of these equations is a line. Check out our introduction to two-variable equations if this is new to you.Additionally, you should be knowledgeable with the y-intercept, x-intercept, and slope of linear equations.Y = mx + b, where m denotes the slope and b the y-intercept, is how the equation of the line is expressed in the slope-intercept form. We can see that the y-intercept of the line in our equation, y = 7 x + 4, is 4.Q2 : Then, you apply y2 - y1 over x2 - x1 over the two points you took from the table. In other words, 3 divided by -6 is equal to -3. This ought to give you the slope "m". Which means that this question has a slope of -3. We must enter the points from one of the two points we picked from the chart into the formula y = mx + b in order to determine "b," our y-intercept. I decided to do 5 = -3 (3) + b. 5 = - 9 + b when the x is multiplied by m. Thus, we add 9 to itself in order for it to cancel out and then add it to 5. The result is that 14 = b. Our equation is therefore y = -3x + 14.Q3 : This one is quite simple because it is obvious from the table that there is no b or m. just a fixed rate multiplied by x. Take two points out of the calculation, just like we did with the previous question. Over x2 - x1 is y2 - y1. 1 - 0 over 4 - 0. thereby giving us 1/4. Our constant rate of change is 1/4. y = 1/4xLearn more about Slope intercept form refer :
https://brainly.com/question/24907633
#SPJ2
6. You have 220 feet of fencing material to enclose a rectangular area for your pet animals. Let x = the length of the rectangular enclosure. (a) [7 points] Set up the function A(x) that represent the enclosed area. (b) [7 points] What should be the dimensions of the enclosed area? (c) [2 points] What is the maximum area of the enclosed area?
Answer:
I will start with (c)
(c) What is the maximum area of the enclosed area?
the maximum area of a rectangle is always given by a square figure
since the square has 4 equal sides, each side will be 220 / 4 = 55 ft long
maximum area = 55 x 55 = 3,025 ft²
(b) What should be the dimensions of the enclosed area?
the dimensions would be 55 ft in length by 55 ft in width
(a) Set up the function A(x) that represent the enclosed area.
perimeter of the rectangle = 220
we have 4 equal sides, so
A(x) = x²
doing my sister's homework plz help
Answer:
5/14
Step-by-step explanation:
Point: (3,−4)
m: −1
Equation:
please answer will mark brainlest need the equation answer in 1 hour
Answer:
We need to turn the equation into y=mx+b form.
So the equation would be:
y=-1(3)+-4
Step-by-step explanation:
Kenny had 24 pairs of socks before she went on vacation. After vacation she only had 18 pairs. What is the percent decrease of socks from before until after vacation
Answer:
Step-by-step explanation:
25% decrease
What up guys it’s JustinExpert I’m new if you want to learn more follow you don’t have to do it though but I’m assuming ima be popalar so yeah I will be posting nice content
Answer:
okay
:)
Step-by-step explanation:
Answer:
wow cool good luck but maybe change your name if you want to be popular
I need help with this problem someone please help me
Answer:
67
180-46=134
134/2=67
what is the value of this?
Answer:
4
Step-by-step explanation:
I used desmos
[tex]\textsf{Hey there!}[/tex]
[tex]\mathsf{\dfrac{-2(7-15)}{4}}\\\\\mathsf{7-15=-8}\\\\\mathsf{\dfrac{-2(-8)}{4}}\\\\\mathsf{-2(-8)=16}\\\\\mathsf{\dfrac{16}{4} = 4}\\\\\\\boxed{\boxed{\mathsf{Thus,\ your\ answer\ is: \boxed{\boxed{\mathsf{\bf{D.\ 4}}}}}}}\checkmark[/tex]
[tex]\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
Use the information to answer the following questions.
The angle measures of a triangle are shown.
Angle A: (5x – 5) degrees
Angle B: (3x + 3) degrees
Angle C: (5x) degrees
The sum of the measures of the three angles is equal to 180°. What is the measure of Angle B?
Answer:
I don't know i am new
Step-by-step explanation:
Sorry
I beg anybody please
Answer:
if no one answers pic b cuz i got good luck
Step-by-step explanation:
please help thank you
Answer:
B
Step-by-step explanation:
A=4 so its wrong cause the original one is 10-12=-2
what is true about the slopes of perpendicular lines
What is - ( 2)^3?
Help please
It takes 6 cubes to build a staircase with 3 steps. How many cubes will be needed for 11 steps?
Pls show work
Answer:
5 more cubes
Step-by-step explanation:
you just keep on adding the cubes. So i am in honors math and the easiest way to do math like this just use paper so start with the number of cubes and the just keep on adding till you get to the number you need in this case that number is 11.
1) A ratio of 2 to 10 is the same as
*
02/14
2/12
O 1/5
2/5
Answer:1/5
Step-by-step explanation:
Two and ten divided by two equals 1 and 5 so 1/5
Please help me find the area of this!!! 15 points!!
Answer:
[tex]A\approx1608.7\text{ yards}^2[/tex]
Step-by-step explanation:
We can use the alternate formula for the area of a triangle:
[tex]A=\frac{1}{2}ab\sin(C)[/tex]
Where a and b are the side lengths, and C is the angle between the side lengths.
We know that one side length is 60 and the other is 70.
The angle between them is 50°.
So, substitute 60 for a, 70 for b, and 50° for C. This yields:
[tex]A=\frac{1}{2}(60)(70)\sin(50)[/tex]
Evaluate using a calculator. Make sure you’re in Degrees Mode.
Therefore, the approximate area is:
[tex]A\approx1608.7\text{ yards}^2[/tex]
solve for x 3(x-8) = -29.7
Answer:
[tex]x = - 1.9 [/tex]
The answer of this equation is:
1.9
Daniel baked 12 pies in 6 days Rates
(Proportional Relationships)
At a certain elementary school there are 26 students per
classroom. If y represents the total number of students at
the school and x represents the number of classrooms,
which equation is the best representation?
Select one:
y = 26/x
y = 26x
x = 26y
y = 1/26 x
Answer: y =26x
Step-by-step explanation:
Plssss help what is the value of c
Answer:
5
Step-by-step explanation: The Quadratic Formula uses the "a", "b", and "c" from "ax2 + bx + c", where "a", "b", and "c" are just numbers; they are the "numerical coefficients" of the quadratic equation they've given you to solve.
a car travels at a speed of 25 miles per hour. the distance it travels in h hours given by the equation d(h)=25h.
estimate how far he will be 2.5 hours into his trip
Roll a number cube. If the number cube comes up odd, you win the same number of points as the
number on the cube. If the number comes up even, you lose 4 points.
What is the expected number of points per roll?
-0.25
-0.5
0
Oo oo
0.25
0.5
Answer:
-0.5
Step-by-step explanation:
help T^T ion wanna fail this class