A boy is launching a toy rocket he got for his birthday from the top of an 80 ft building. The function representing
the height is f(0) = -16x? +64x + 80 where x represents time in seconds.
How many seconds did it take the rocket to reach it's maximum height?
A
144 sec
B)
2 sec
Eliminate
1.5 sec
D)
128 sec
Answers
Answer:
2 seconds, assuming the "?" in the equation is supposed to be ^2 (the exponent of 2): f(h) = -16x^2 +64x + 80
Step-by-step explanation:
You can either graph the functuion or take the first derivative to find the maximum height. The first derivative will give us the slope for a values of x. The slope at the top height of the rocket is zero, since it has stopped and is starting it's way back down.
First Derivative:
f(x) = -16x^2 +64x + 80
f'(x) = -32x + 64
Set this equal to zero and solve for x
0 = -32x + 64
x = 2 seconds.
Use 2 seconds in the original equation to find the height at 2 seconds.
f(2) = -16x^2 +64x + 80
f(2) = -16(2)^2 +64*(2) + 80
f(2) = 144 feet
Graph:
A graph is attached. You can locate the maximum at (2,144)
Related Questions
Please help me answer this ASAP
Answers
Answer:
1.15x - 0.7x
Step-by-step explanation:
You take the manufacturer’s price and add 15 percent, then subtract 70 percent of the used price from the retail price to get the answer.
Please answer below :) I will mark the brainiest answer
Answers
Answer:The last option is correct.
Step-by-step explanation:
Nina gets paid $200 a week plus an extra $5 per handbag
she sells. Write an equation for this problem, and identify
the slope and y-intercept
Answers
Answer:
y=5x+200
Step-by-step explanation:
x=number of handbags
y-intercept=200
slope=5
please give me brainly since I'm trying to level up!
A single basket basketball match will be organized by forming 3 teams in equal numbers from a group of 9 students. In how many ways can these three teams be formed?
Answers
~combination
[tex] \large \sf C(n,r) = \frac{n!}{(n-r)! .r!} [/tex]
[tex] \large \sf = C(9,3) = \frac{9!}{(9-3)!.3!} [/tex]
[tex] \large \sf = \frac{9!}{6!.3!} [/tex]
[tex] \large \sf= \frac{(9.8.7.6.5.4.3.2.1)}{(6.5.4.3.2.1).(3.2.1)} [/tex]
[tex] \large \sf = \frac{362880}{720.6} [/tex]
[tex] \large \sf = \frac{362880}{4320} [/tex]
[tex] \large \sf = \boxed{84}\: ✓[/tex]
~ nice to help you ^^
given m||n, determine the value of x (4x-7) (3x+9)
Answers
Step-by-step explanation:
7×4-=28-×3×9=27×28-=756-
David was thinking of a number. David doubles it, then adds 3 to get an answer of 81. 6. What was the original number?.
Answers
Answer:
The answer is 39.3
Step-by-step explanation:
81.6 - 3 = 78.6
78.6 ÷ 2 = 39.3
Nick sketches the graph of y = 0.5' for x 20 y 0.5 of Make one criticism of his sketch.
Answers
Answer:
the graph would just be a straight line going up at points (0, 0.5)
Step-by-step explanation:
This would have no slope
what is the coordinates of the point?
Answers
Answer:
Step-by-step explanation:
3,2
Answer:
2,3 because the point is inside the origin or equivalent so the answer has to be 2,3
HELP! HL theorem. Congruent. Geometry algebra. Triangles. Shapes. Math.
Answers
Answer:
x = 3
Step-by-step explanation:
x² + 15 = x² + 5x
15 = 5x
15 ÷ 5 = x
3 = x
a student says that if 5x^2 = 20, then x must be equal to 2. do u agre or disagree with the student? justify your answer.
Answers
Answer:
The student is correct.
Step-by-step explanation:
Given that 5x² = 20:
It is true that the value of x = 2 because 2² = 4, and when you multiply 4 with 5, you'll get a product of 20:
5x² = 20
5(2)² = 20
5(4) = 20
20 = 20
Therefore, the student is correct that x = 2.
Please help me! Bots keeps answering my questions and I really need an answer
Answers
Answer:
D) the bridge is about 381.16 ft. above the river, and the length of the bridge above the arch is 1,792.58 ft
What is the length of segment AB?
A-5
B-6
C-8
D-10
Answers
Nate earns extra money on the weekends mowing lawns. He charges $14.00$ to work for the first hour. He charges $10.50 for each additional hour. Let hh equal the number of hours after the first hour. Which expression represents how much Nate charges?
Answers
Answer:
m=14+10.50h
Step-by-step explanation:
h represents hours. m represents how much he makes
he's going to get 14 dollars, plus 10.50 times however many hours he works.
Sales tax in a certain community is 7%. If the sales tax on a new car was $1,400, what was the selling price of the car
Answers
Answer:
20,000
Step-by-step explanation:
Answer:
%7 1400
100 x
7x=140000
x=20000$
the value of y varies directly with X. Which function represents the relationship between X and Y if y equals 15/6 when x equals 20
Answers
Answer:
y = (1/8)x
Step-by-step explanation:
The relevant basic formula is y = kx, where k is the constant of proportionality.
We must find k. To do this, let y = 15/6 and x = 20 in the above formula:
15/6 = k(20)
We solve for k by dividing both sides by 20: 15/(6*20) = k = 1/8
Then the specific formula for this situation is y = (1/8)x
Enter the value of x that makes the equation 3x + 4 + 2x + 2 = -24
answer? and how would I answer this.
Answers
Answer:
x = -6
Step-by-step explanation:
Combine like terms.
5x + 6 = -24
Subtract 6 from both sides.
5x = -30
Divide by 5 on both sides.
x = -6
Follow Me:-
[tex]3x + 4 + 2x + 2 = - 24 \\ \\ = > 5x + 6 = - 24 \\ \\ = > 5x = - 24 - 6 \\ \\ = > 5x = - 30 \\ \\ = > x = \cancel \frac{ - 30}{5} \\ \\ = > x = - 6[/tex]
Hope This HelpsHaving trouble using logarithmic differentiation!
Answers
Answer:
Having trouble using logarithmic differentiation!
Find the values of x and y.
Answers
Answer:
y= 132, x= 32.6
Step-by-step explanation:
Let me know if this is right!
Hope it helps
Y= 132, X=32.6
what is the slope of the line
Answers
Answer:
slope = 3/2
Step-by-step explanation:
Step 1: Select two points from the graph.
(3,0) and (1,-3) are two points on the graph.Step 2: Apply the formula to find slope- [tex]\frac{y_2-y_1}{x_2-x_1}[/tex].
[tex]\frac{-3-0}{1-3}[/tex] [tex]\frac{-3}{-2}[/tex] [tex]\frac{3}{2}[/tex]Therefore, the slope is 3/2.
Which expressions are equivalent to 35x + 3. Select the TWO that apply.
25x + 315x
45x - 15x + 3
25x + 335x - 1
1 + 35x + 2
1 + x5+ 2
1 + 25x + 3
Answers
And
1+35x+2
What is the value of x in the equation ?
Answers
Answer:
[tex]x=2[/tex]
Step-by-step explanation:
This is our equation
[tex]2.5\left(6x-4\right)=10+4\left(1.5+0.5x\right)[/tex]
First off we can distribute the 2.5 and the 4
Now our equation is [tex]15x-10=10+6+2x[/tex]
subtract [tex]2x[/tex] from both sides
[tex]13x-10=16[/tex]
add [tex]10[/tex] to both sides
[tex]13x=26[/tex]
Divide both sides by [tex]13[/tex]
[tex]x=2[/tex]
On the accompanying grid, draw and label quadrilateral ABCD with points A(1,2), B(6,1), C(7,6), and D(3,7). On the same set of axes, plot and label quadrilateral A′B′C ′D′, the reflection of quadrilateral ABCD in the y-axis. Determine the area, in square units, of quadrilateral A′B′C′D′.
Answers
Answer: Refer to figure 1 for the diagram needed.
A ' = (-1, 2)
B ' = (-6, 1)
C ' = (-7, 6)
D ' = (-3, 7)
Area = 24 square units
============================================================
Explanation:
Start by drawing an xy axis. Plot the given points A,B,C,D on this grid.
To reflect any given point over the y axis, we apply this rule
[tex](x,y) \to (-x,y)[/tex]
which means we change the sign of the x coordinate, but keep the y coordinate the same. For example, a point like A(1,2) moves to A ' (-1,2). The other points are handled in a similar fashion.
After all of the points have been reflected, you'll get what is shown in figure 1.
------------------
To find the area of quadrilateral ABCD, we can form a bounding box as small as possible around the quadrilateral. Refer to figure 2.
The area of rectangle FEHG is 6*6 = 36 square units
Then we subtract off the areas of these four outer triangles
Triangle AED = 5*2/2 = 5Triangle AFB = 1*5/2 = 2.5Triangle BCG = 1*5/2 = 2.5Triangle CDH = 1*4/2 = 2Meaning we'll end up with 36-5-2.5-2.5-2 = 24 as the area of quadrilateral ABCD. Because a reflection is a mirror copy, quadrilateral A'B'C'D' will have the same area as ABCD.
Find the measure of the angle marked with a question mark using inverse trig
functions. Round your answer to the nearest degree. Enter the number only.
I need the answer quick
Answers
Applying the tangent ratio, the value of x in the right triangle is approximately: 5.
What is the Tangent Ratio?Tangent ratio that can be applied to solve a right triangle is expressed as: tan ∅ = opp/adj.
Given the following:
∅ = 63°Opp = 10 Adj. = xtan 63 = 10/x
x = 10/tan 63
x ≈ 5
Learn more about the tangent ratio on:
https://brainly.com/question/4326804
#SPJ1
Your visually impaired friend asked you to enlarge your notes from class so he can study. You took notes on 8.5-inch by 11-inch paper. The enlarged copy has a smaller side with a length of 10 inches. What is the scale factor of this dilation?
Find the scale factor.
Answers
Answer:FINDING A SCALE FACTOR Your visually impaired friend asked you to enlarge your notes from class so be can study. You took notes on 8.5-inch by 11-inch.
Step-by-step explanation:thank you
The scale factor is 20/17.
According to the question, you took notes on a paper with dimensions 8.5 inches × 11 inches.
the breadth of the paper is 8.5 inches
the length of the paper is 11 inches
Now, to make an enlarged copy, you used a paper that has its smaller side dimension of 10 inches.
Which means the breadth of the new paper is 10 inches.
So, if we calculate the ratio of the breadths we get the scale factor.
k = 10 / 8.5
k = 20/17 is the scale factor of dilation.
Learn more about scale factor:
https://brainly.com/question/20341092
Artem drives 12.6 miles in 12 minutes. He passes a sign which gives the speed limit as 50 mph. By how much, in mph, did Artem's average speed exceed the speed limit?
Answers
12 min is .2 hours
So 12.6/.2 gives a value of 63.
63-50 is a value of 13.
This means Artem is driving 13 over the speed limit of 50mph.
There is a proportional relationship between minutes and dollars per minute, shown on a graph of printing expenses. The graph passes through the point (1, 3.40). What is the slope of the graph? What is the unit rate? Complete the explanation.
Answers
Answer:
Below!
Step-by-step explanation:
The slope is 1. The unit rate is $4.75/min If the graph of a proportional relationship passes through the point (1 , R) then r equals the slope and the unit rate. $4.75 per min.
The slope of the graph resembles the unit rate.
The unit rate is the amount it cost per minute.
The graph passes through the point (1, 3.40), which means it is at x = 1, the rate is $4.75.
please someone help. I really need help with this question. I will give brainliest
Answers
Answer:
3/200
Step-by-step explanation:
total medicine = 9/50 liter
evenly divided into 12
so 1 prescription = 9/50 / 12
= 9/50*12
=3/50*4
=3/200
How to convert minutes and seconds into grades.
Answers
Answer:
Step-by-step explanation:
To convert time to time, kernel time with 24 (number of time in a day).
To convert time to minutes, kernel with time with 1440 (number of minutes in a day = 24 * 60).
To convert s to seconds, multiply the time by 86400 (number of s in a day = 24 * 60 * 60).
Richard sold cupcakes and cookies yesterday. Each cupcake sold for $1.75 and each cookie sold for $0.75. At the end of the day, Richard had sold $49.25 worth of cookies and cupcakes. If he sold 35 cupcakes and cookies combined, how many cupcakes were sold and how many cookies were sold?
Answers
Answer:
20 cupcakes
15 cookies
Step-by-step explanation:
20*$1.75=$35
15*$0.75=$14.25
$35+$14.25=$49.25
Answer:
23 cupcakes and 12 cookies
Step-by-step explanation:
(ASAP) I HAVE C- IN MATH RIGHT NOW AND I NEED TO GET UP MY GRADE PLSSS HELP
Answers
Answer:
Step-by-step explanation:
The product of a number, n, and 0.4 is 8:
(n)(0.4) = 8
n = (8/0.4)
n = 20