Answer:
Slope: 2/1 Y-Intercept: 1
Step-by-step explanation:
Jason jumped off a cliff into the ocean in Acapulco while vacationing with some friends. His height as a function of time could be modeled by the function h ( t ) = − 16 t 2 + 16 t + 480 h(t)=−16t 2 +16t+480, where t is the time in seconds and h is the height in feet. What is the maximum height that Jason reaches?
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.
Learn more about maximum and minimum values here:
https://brainly.com/question/13333267
Which one should I choose?
Answer:
∠ 1 = 58°
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
117° is an exterior angle of the triangle, then
∠ 1 + 59° = 117° ( subtract 59° from both sides )
∠ 1 = 58°
How to find Gradient and y intercept
Hey can you help me fast!!!
Answer:
40 square feet
Step-by-step explanation:
I gotcha bro
4 x 12 = 48
48 - 3 x 2 - 1 x 2 = 48 - 6 - 2 = 40
What is the integer closest to the square root of 17
Answer:
4
Step-by-step explanation:
[tex]\sqrt{16}[/tex] = 4
Answer:
4.
Step-by-step explanation:
The square root of 17 is 4.12...
square root of 16 is 4
three teams a,b,c play in a competition
games won by a : games won by b = 3:1
games won by b :games won by c= 5:1
team b has won 10 games
in total how many games have the three teams won
Answer:
25:2
Step-by-step explanation:
Use the 45-45-45-90 triangle relationship to find the missing sides
Answer: A is 8. B is the square root of 128.
Step-by-step explanation: Nah.
Consider this equation.
tan() = -1
If & is an angle in quadrant II, what is the value of sin()?
ΟΑ. .
5734
34
5734
34
ОВ.
O c.
3V34
34
3V34
34
D.
Answer:
I know u saw me before but the answer is B hope it helps! =)
Answer:
the 5v34 without the minus sign
Step-by-step explanation:
if you start at 89 degrees and it decreases 5% each hour what would it be at in 3 hours
Answer:
A = 76.3 degrees after 3 hours
Step-by-step explanation:
An exponential function is needed here:
A = P(1 - 0.05)^3, where this (1 - 0.95) reflects a DECREASE of 5%/hour.
Then: A = (89 degrees)(0.95)^3, or
A = 76.3 degrees after 3 hours
Anyone know how to answer this mathematics question?
Answer:
B: (-2,-8)
Step-by-step explanation:
(-2,-8) works because (-2-5)^2 + (-8+11)^2 = 49 + 9 = 58
Emily and her friends pick 27 lb of blueberries each pound of blueberries contains 195 blueberries how much blueberries been Emily and her friends pic
Please help! I will give you 'Brainliest' if you do!
Answer:
C $126,720
Step-by-step explanation:
First hour: 1280 tickets
Second hour: 20% more than 1280 tickets
20% of 1280 = 0.2 * 1280 = 256
1280 + 256 = 1536
Second hour: 1536 tickets
First & second hour tickets:
1280 + 1536 = 2816
Total sales:
2816 * $45 = $126,720
Answer: C $126,720
Does this line represent a function? Yes or no
Answer:
Yes
Step-by-step explanation:
The line is straight, showing a linear relationship between x and y.
Answer:
yes this does represent a funtion
Step-by-step explanation:
because if we use the vertical line test where you get a pencil and put it the graph verticaly any where thier is no points on the graph that toch the pencil twice
Also can anyone help with these problems too?
Answer:
6. a
------
7. b
------
8. d
------
9. d
------
Neeed helps math help no links or imma report helps 20 points
Can someone answer this soon please
Answer:
the last one i think
Step-by-step explanation:
Distribute then combine like terms in the following: 2(2x - 3y) - 3(x - 2y - 4) 4
I think its:
2(2x-3y)-3(x-2y-4)4
4x-6y-3x-6y(4)
4x-6y-3x-24y
x-30y
The answer of the question
Answer:
123cm
Step-by-step explanation:
becuse
For every 4 of my wonderful nieces, I want to buy 5 Friendly cupcakes. And I have 12 wonderful nieces.
Answer:
15 cupcakes
Step-by-step explanation:
I'm guessing you mean that you want to find out how many cupcakes you'll need to buy.
I NEED HELP I NEED TO PASS THIS
Answer:
A. the area of the large pond is 16 times the area of the small pond
Step-by-step explanation:
let's say 4 is the radius of the small circle, which means the area is 50.26548
if the large circle is 4 times the small circle, that means it's radius is 16 which means the area is 804.24772
so if you divide the big circle area by the small circle area:
804.24772/50.26548
it gives you 16.00000079577 which is rounded to 16
therefore, the bigger circle is 16 times bigger than the smaller circle
can you please answer these questions
PLEASE HELP ASAP NO LINKS PLEASE A relationship between education and income is given in the table. Based on the data, how much more does a person with a bachelor's degree earn than a person with a high school diploma over the course of 15 years?
A)$387,075
B)$398,730
C)$753,585
D)$785,805
Degree of education Income
High school diploma $26,582
Associate's degree $37,955
Bachelor's degree $52,387
Master's degree $59,995
Doctoral degree $76,821
factor: 18x²+39y-15=0
Answer: x = 6
y= 6x2/13 + 5/13
Step-by-step explanation: to solve for and y: Isolate the variable by dividing each side by factors that don't contain the variable
Mhanifa please help this is due soon
Answer:
(27)Rectangle
Interior angles are all 90°
5x - 3° = 90° 5x = 93° x = 93°/5 x = 18.6° (28)Rhombus
All sides are congruent
14 - x = 2x + 5 2x + x = 14 - 5 3x = 9 x = 3 (29)Square
Diagonals are perpendicular
13x + 5.5° = 90° 13x = 84.5° x = 84.5°/13 x = 6.5°In a study of the television viewing habits of children, a developmental psychologist selects a random sample of 300 first graders - 100 boys and 200 girls. Each child is asked which of the following TV programs they like best: The Lone Ranger, Sesame Street, or the Simpsons.
Complete your work in the space provided or upload a file that can display math symbols if your work requires it. Include your calculations and the completed table in your answer.
Answer:
50, 130, 30, 60
Step-by-step explanation:
For the boys row (Simpsons)-20
For the girls row (Simpsons)-70
For the girls row (Lone Ranger)-50
For the total of Sesame Street- 110
Hope this helped!
Using the formula below, calculate the z-score for the listed data points. z-score: zx = x − μ σ z1 = z5 = z6.5 =
Answer:
z1 = -1.95
z5 = 0.05
z6.5 = 0.8
Step-by-step explanation:
The value of the z score for a mean of 4 and standard deviation is 1.
What is Z score?The z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:
z = (x - μ)/σ
Where x is the raw score, μ is the mean and σ is the standard deviation.
Let us assume that μ = 4, σ = 2, hence for x = 6:
z = (6 - 4) / 2 = 1
The value of the z score for a mean of 4 and standard deviation is 1.
Find out more on Z score at: https://brainly.com/question/25638875
Reduce your fraction into lowest terms.
Please help.
For math class
Answer:
x = 30, z = 45, y = 105
Step-by-step explanation:
The lines are straight, so:
x = 30
z = 45
y = 180 - (45 + 30)
So there
Can someone answer this for me please?
x2+8 so the second one Step-by-step explanation:
If h(x) = 2x² - 5 find h(4x²)
Answer:
8x^4-5
Step-by-step explanation:
8x^4-5
Just substitute 4x^2 into x
Answer:
= 32x^4-5
Step-by-step explanation: