Answer:
484feet
Step-by-step explanation:
If the height as a function of time could be modeled by the function h(t)=−16t^2 +16t+480, where t is the time in seconds and h is the height in feet.
The maximum height of Jason occurs when dh/dt = 0 (velocity is zero)
dh/dt = -32t + 16
0 = -32t + 16
32t = 16
t = 16/32
t = 1/2
t = 0.5secs
Get the maximum height
Recall that h(t)=−16t^2 +16t+480
Substitute t = 0.5
h(0.5)=−16(0.5)^2 +16(0.5)+480
h(0.5) = -4 + 8 + 480
h(0.5) = 4 + 480
h(0.5) = 484
Hence the maximum height reached by Jason is 484feet
The maximum height that Jason reaches is h = 484 feet and it will be reached at t = 0.5 sec.
How to find the maximum of a polynomial function?Let the function be denoted by [tex]y = f(x)[/tex]
If it is twice differentiable, then, firstly, we differentiate it with respect to x and equate with 0 to find the critical values.
Let the obtained critical values be [tex]x_1, x_2, ... x_n[/tex]
The second derivative of that function is then evaluated on those critical values.
The [tex]i^{th}[/tex] critical value has got the maximum if [tex]f''(x_i) < 0[/tex]
That means, if at [tex]x = x_i[/tex] , we get
[tex]f'(x-i) = 0\\and\\f''(x_i) < 0[/tex]
Then that point is where function will have maximum.
If [tex]f''(x_i) > 0[/tex], then the point where the function will have minimum
If value of second rate at point [tex]x_i[/tex] is 0, then we go for third rate of function and check the same facts so on for upper rate(if they exist).
For the given case, we're given the height function as:
[tex]h(t) = - 16t^2 + 16t + 480[/tex]
The function is infinitely differentiable as its polynomial(by a theorem).
Its first and second rate with respect to 't', we get;
[tex]h(t) = - 16t^2 + 16t + 480\\h'(t) = -32t + 16\\h''(t) = -32 < 0[/tex]
Thus, all critical points will be maximum points.
The critical points are evaluated by [tex]h'(t) = 0[/tex]
They are calculated as:
[tex]h'(t) = 0\\-32t + 16 = 0\\t = 0.5 \: \rm sec[/tex]
The height at t = 0.5 s is evaluated as:
[tex]h(0.5) = - 16(0.5)^2 + 16(0.5) + 480 = 484 \: \rm feet[/tex]
Thus, at time 0.5, the height function will be at its maximum value(484 feet). That means, the height of Jason will be maximum when time will be 0.5 seconds from initial time.
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Please help if you know the answer thank you
Answer:
a
Step-by-step explanation:
a
Answer: 4 4/10
Step-by-step explanation:
4 4/10 as an Improper fraction is 44/10, 32/10 is less then 44/10.
Please help! 90 x 120 = ? divided by 2
90 x 120 = 10800
10800/2 = 5400
Answer:
21600=xStep-by-step explanation:
so this is the problem:
90x120=x/2
first, you can multiply 90 and 120 to get 10800.
then, your equation looks like this
10800=x/2
you can multiply both sides by 2
2(10800)=(x/2)(2)
then, you get this
21600=x
hope this helped!!!
What are the solutions of the equation (x - 3)2 + 2(x - 3) - 8 = 0? Use u substitution to solve.
Ox= -5 and x = 1
O x= -1 and x = 5
O x= -1 and x = -7
Ox= 1 and x = 7
Given:
The equation is:
[tex](x-3)^2+2(x-3)-8=0[/tex]
To find:
The value of x.
Solution:
We have,
[tex](x-3)^2+2(x-3)-8=0[/tex]
Substitute [tex]x-3=u[/tex].
[tex]u^2+2u-8=0[/tex]
Splitting the middle term, we get
[tex]u^2+4u-2u-8=0[/tex]
[tex]u(u+4)-2(u+4)=0[/tex]
[tex](u-2)(u+4)=0[/tex]
Using zero product property, we get
[tex]u-2=0\text{ and }u+4=0[/tex]
[tex]u=2\text{ and }u=-4[/tex]
Now, substitute [tex]u=x-3[/tex].
[tex]x-3=2\text{ and }x-3=-4[/tex]
[tex]x=2+3\text{ and }x=-4+3[/tex]
[tex]x=5\text{ and }x=-1[/tex]
Therefore, the correct option is b.
The solutions to the equation are x = -1 and x = 5. The correct option is second option x = -1 and x = 5.
Quadratic equationFrom the question, we are to determine the solution of the given equation
(x - 3)² + 2(x - 3) - 8 = 0
First, we will expand the equation and clear the brackets
[tex](x - 3)^{2} + 2(x - 3) - 8 = 0[/tex]
[tex](x - 3)(x - 3) + 2(x - 3) - 8 = 0[/tex]
[tex]x^{2} -6x + 9 +2x - 6 - 8 = 0[/tex]
Simplifying
[tex]x^{2} -4x - 5 = 0[/tex]
Factorizing, we get
[tex]x^{2} -5x +x- 5 = 0[/tex]
[tex]x(x-5)+1(x- 5) = 0[/tex]
[tex](x+1)(x-5)= 0[/tex]
Then,
x + 1 = 0 or x - 5 = 0
x = -1 or x = 5
Hence, the solutions to the equation are x = -1 and x = 5. The correct option is second option x = -1 and x = 5.
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please help!
A restaurant needs a block of ice that is exactly 480 cubic inches in volume.
The height of the ice block must be 10 inches.
Answer:
Step-by-step explanation:
Part A,
99% sure this is D
Part B
It's probably about 4 feet tall.
Part C,
4 in. x 12 in.
2 in. x 24 in.
8 in. x 6 in.
3 in. x 16 in.
Answer:
part A: all the above
partt B: 48
part C: 4 in. x 12 in.
2 in. x 24 in.
8 in. x 6 in.
3 in. x 16 in.
Step-by-step explanation:
A line graph titled Video Rental Stores has year on the x-axis and stores (thousands) on the y-axis. In 2009, there were 4,000 stores.
The line graph shows the number of video rental stores for the years 2005 through 2012.
There were stores in 2009.
Answer:
its 4,000
Step-by-step explanation:
A point is reflected across the x-axis. The new point is located at (4.75, -2.25) Where was the original point located.
Answer:
(4.75, 2.25)
Step-by-step explanation:
Given the coordinate (x,y). If this coordinate is reflected over the x axis, the resulting coordinate will be (x, -y)
Note that the y coordinate was negated.
Let the original point needed be (x, y)
If the new point is located at (4.75, -2.25)
Since the y coordinate was negated, then;
-y = -2.25
y = 2.25
x = 4,75 (x coordinate remains the same)
Hence the original point is (4.75, 2.25)
2.5 ( y + 2/5) = -13
Answer:
y= -5.6
Step-by-step explanation:
Can someone please help me!!!
Answer: x=20
Step-by-step explanation:
If im wrong, sorry
The angles of a triangle add up to 180 degrees.
(3x+5)+(2x+17)+(2x+18)=180
add the ones alike
3x + 2x + 2x=7x
5+17+18=40
so, 7x+40=180
we need to get the variable by itself so we take away 40 first by subtracting it from both sides of the equal sign
7x=140
we take away 7 from x by dividing it- opposite of multiplication is division
x=20
Answer:
x = 20
Step-by-step explanation:
3x+5° + 2x+18° + 2x+17° = 180° (sum of interior angles in a triangle is 180°)
collect like terms
3x + 2x + 2x + 5° + 18° + 17° = 180°
7x + 40° = 180°
solving for x
x = (180 - 40)/7
x = 140/7
x = 20
A teenager has 8 tee shirts, 2 belts, and 5 pairs of jeans. How many different outfits can he wear, assuming that he must wear a belt to keep those pants up and keep that shirt tucked in?
Answer: 80 ways
Step-by-step explanation:
If 8 tee shirts can be worn in 8 ways
similarly for 2 belts = 2 ways
five pair of jeans= 5 ways
so total number of ways=5*2*8=80 ways
Please help me with this question
Answer: 275 cm
volume = length x width x height
v = 6.25 x 8 x 5.5
v = 275
Help will give crown I don’t not get this
Answer:
4 - 0.6 (Repeating) x = 0.75
Step-by-step explanation:
You divide the fractions by each other ex. 2 divided by 3
Answer:
[tex] 48 - 8x = 9[/tex]
Step-by-step explanation:
Multiply both sides by LCM. which is 12.
[tex]12(4 - \frac{2}{3} x) = \frac{3}{4} \times 12[/tex]
[tex]48 - 8x = 9[/tex]
During a blind taste test of 8 different
sodas, some people were asked to choose
a favorite. Each dot represents one person.
Taste Test
.
A
B
С
F
G
H
D E
Soda
If the ratio of people choosing B to people
choosing H stays the same, how many
people will choose H if the number of people
who choose B increases to 20?
F 6
G4
H5
J 3
Answer:
the answer is 5
Step-by-step explanation:
the ratio is 4:1 so if you increase B to 20 you divide by 4 to get 5.
20:5=4:1
Identify the line segment that is a chord.
Answer:
The line segment that is a chord is AE.
Hope it helps :)❤
Plz help ASAP just say give me the answer and the number the answer goes in thank you very much
Answer:
1) 85
2) 95
3) 75
4) 90
5) 120
6) 110
7) 65
8) 130
A writer for a magazine recently did a test to determine which mid-range digital camera takes the best pictures. Her method is described below. Which part of the method describes an area of potential bias? She gathered 20 of the best-selling cameras and used the same photographer to take 100 pictures with each camera. She ensured that the environment and the subject of each picture were consistent across all cameras and used a 10-point scale to determine picture quality. Of the cameras tested, two were from companies who are major advertisers in the magazine.
Answer:
Two were from companies who are major advertisers.
Step-by-step explanation:
Edmentum/ Plato family for the win.
Of the cameras tested, two were from companies that are major advertisers in the magazine.
What is potential bias?Any affiliations, financing, or financial holdings that could be seen as influencing the review's objectivity to give rise to potential bias.
Such elements might consist of, but are not limited to, the following:
Employment, professional associations, paid to consult, and participation in groups that support relevant causes.
Given that:-
She gathered 20 of the best-selling cameras and used the same photographer to take 100 pictures with each camera.
She ensured that the environment and the subject of each picture were consistent across all cameras and used a 10-point scale to determine picture quality.
Of the cameras tested, two were from companies that are major advertisers in the magazine.
The potential bias is In the cameras tested, two were from companies that are major advertisers in the magazine.
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What is the solution to the inequality? -6x > 36
Answer:
x<-6
Step-by-step explanation:
Flip the sign on a negative
Answer:
x < -6
Step-by-step explanation:
Pls I need the answer rn
Answer:
x = 30
Step-by-step explanation:
since 2 sides are equal, that means their angles are also equal.
you do 180-120 to get 60 and then divide 60 by 2 to get 30
Answer:
x=30
Step-by-step explanation:
We know all the angles a triangle combined are 180 the two bottom angles for this one are equal so we can do
(180-120)/2=30
Rewrite the expression, the quotient of k decreased by 4 and 9, using the division symbol and as a fraction.
Answer:
(k - 4) ÷ 9
(k - 4) / 9
Step-by-step explanation:
k decreased by 4 = k - 4
quotient of k decreased by 4 and 9
= (k - 4) ÷ 9 (using division sign)
Or
= (k - 4) / 9 (as a fraction)
[Help asap, will mark brainliest] Find the area of the right triangle.
Be sure to include the correct unit in your answer.
Answer:
45m
Step-by-step explanation:
1. Multiply the two sides.
2. Divide it by 3 (or multiply by 1/3)
3. The answer is your area.
the sum of twice a number and 11 is equal to 55
Answer:
Equation: 2x+11=5
Solving the equation: x=22
Step-by-step explanation:
The sum of twice a number is 2x+
The sum of twice a number and 11 is 2x+11
The sum of twice a number and 11 is equal to 55 is 2x+11=55
Solving the equation: 2x+11-11=55-11
2x=44
2x/2=44/2
x=22
Does this table show a proportional relationship? If so, what is the constant of proportionality? If not, explain.
Answer:
Yes it does
Step-by-step explanation:
This table has a proportion of 4 since from the weeks and height are times by 4
Example from the table:
Week two has a height of 8 since 2 times 4 is 8
What is the equation of the line that passes through the point ( − 0.5 , 8 ) and has a slope of − 5
Answer (assuming that the equation can be written in point-slope form):
[tex]y-8 = -5(x+\frac{1}{2} )[/tex]
Step-by-step explanation:
Use the point-slope formula, [tex]y-y_1 = m (x-x_1)[/tex] , to write the equation of the line in point-slope form. Substitute values for the [tex]m[/tex], [tex]x_1[/tex], and [tex]y_1[/tex] in the formula.
Since [tex]m[/tex] represents the slope, substitute -5 in its place. Since [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of one point the line intersects, substitute the x and y values of (-0.5, 8) into the formula as well. Remember that we can convert -0.5 to a fraction: [tex]-\frac{1}{2}[/tex]. So, substitute [tex]-\frac{1}{2}[/tex] for [tex]x_1[/tex] and 8 for [tex]y_1[/tex]. This gives the following answer and equation:
[tex]y-8 = -5(x+\frac{1}{2} )[/tex]
Can someone plz help me with this one problem plzzzzz!!!!
What should be done to x^2-10x in order to create a perfect square?
A)subtract 25
B)subtract 5
C)add 5
D)add 25
Answer: B)subtract 5
(x-5)^2-25
Step-by-step explanation:
2a=-10
Divide both sides by 2
2a/2=-10/2
Simplify
a=-5
Add and subtract
x^2-10x+(-5)^2-(-5)^2
Complete the square
(x-5)^2-(-5)^2
Simplify;
(x-5)^2-25
Answered by one other than the ONE & Only #QUEEN herself aka #DRIPPQUEENMO!!
HOPE THIS HELPED!!
the circumference of a circle is about 29.202 inches. the circles area is about ___ square inches.
use 3.14 for pi.
round your answer to the nearest tenth.
Answer:
110
Step-by-step explanation:
really Gregg gift vg6
The graph of a function is a line that passes through the points (3,17) and (6,32). What is the equation of this function?
y=__x +__
Answer:
y=9,49
Step-by-step explanation:
y=3,17×+6,32
y=9,49×
Write 67% as a fraction or mixed number
Answer:
67/100
Step-by-step explanation:
basically just put 100 as denominator
1. When Aaron runs the 400 meter dash, his finishing times are normally distributed with a mean of 80 seconds and a standard deviation of 2.5 seconds. Using the empirical rule, determine the interval of times that represents the middle 99.7% of his finishing times in the 400 meter race.
Answer:
(72.5,87.5)
Step-by-step explanation:
The interval of times that represents the middle 99.7% of his finishing times in the 400 meter race is; (73.5, 87.5)
What is the interval from empirical rule?
We are given;
Mean; E(X) = μ = 80 seconds
Standard Deviation; σ = 2.5
From the empirical rule, the probability of obtaining values within one deviation from the mean is 0.68; within two deviations is 0.95 and within 3 deviations from the mean is 0.997.
We have 99.7 % of the values within 3 deviations from the mean in our question and so the intervals are;
μ - 3σ = 80 - 3(2.5) = 73.5
μ + 3σ = 80 + 3(2.5) = 87.5
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A woman is rowing a boat across a 60 wide river from west to east. She can row at 2 mph in still water, but the river's current is 5 mph from north to south. To the nearest foot, how far downstream on the east bank will she land?
Answer:
S, and the other day. I have been a while. I have a great drea the most important things. The may have to pay a fee of the most popular and I will not 66 the most of the most of my life. I was a bit of the best, but the 15th. I have been a while. I am your what is happening in the next couple days 6 the most of the most of the most
Step-by-step explanation:
popular and I will not be hurt by a friend of the day, and the other side, I think I have a great drea, I think I have been a while. I have been in touch. Thanks for the next day delivery. We have a great drea the same time. I was just the right place for the use of the most of the most popular and I am a beautiful person. The comments for your email.
The woman will land on the east bank of the river at a downstream of 37.5 miles.
What is meant by relative velocity ?Relative velocity of an object in motion is defined as the velocity of the object with respect to another object.
Here,
Width of the river, W = 60 miles
Velocity of the boat in still water, Vb = 2 mph
Velocity of river, Vr = 5 mph
Relative velocity of the boat with respect to river in downstream,
Vbr = Vb + Vr
Vbr = 8 mph
Drift of the boat, d = Vr W/Vbr
d = 5 x 60/8
d = 37.5 miles downstream
Hence,
The woman will land on the east bank of the river at a downstream of 37.5 miles.
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Which expression is equivalent to 11(3 + 10x)?
Answer:
33+ 110x
Step-by-step explanation:
open the bracket.
hope it helps!!!
