Answer:
a. 304 feet
b. 425 feet
c. 3.75 seconds
d. It will take the rocket approximately 8.9 seconds to hit the ground
Step-by-step explanation:
1. The given data of the question including the question relationships are listed as follows;
The height of the cliff from which the rocket was launched = 200-ft.
The initial velocity of the rocket, u = 120 feet per second
The equation that models the height of the rocket with respect to time 't' is h(t) = -16·t² + 120·t + 200
a. The height of the rocket after 1 second is given by plugging in t = 1 in the equation that models the height as follows;
h(1) = -16 × (1)² + 120 × (1) + 200 = 304
The height of the rocket after 1 second, h(1) = 304 feet
b. The maximum height can be found by finding the value of the maximum point of the curve of the equation for the height as follows;
At the maximum point, h'(t) = d(-16·t² + 120·t + 200)/dt = 0
∴ d(-16·t² + 120·t + 200)/dt = -32·t + 120 = 0
t = 120/32 = 3.75
At the maximum point, t = 3.75 seconds
The maximum height can also be found by finding the vertex of the parabola formed by the height equation as follows;
At the vertex (the maximum point), t = -b/(2·a) = -120/(2 × (-16)) = 3.75
At the vertex (the maximum point), t = 3.75
The height at the maximum point = h(3.75) = -16 × (3.75)² + 120 × (3.75) + 200 = 425
The height at the maximum point, h(3.75) = 425 feet
c. The time it will take the rocket to reach the maximum point is given by the value of 't' at the maximum point, the vertex, which is t = -b/(2·a) = -120/(2 × (-16)) = 3.75
Therefore;
The time it takes the rocket to reach the maximum point, [tex]t_{max}[/tex] = 3.75 seconds
d. The time it takes the rocket to hit the ground (height h(t)) is given by finding the values of 't' that satisfy the height equation where h(t) = 0 as follows;
At the ground level, h(t) = 0 = -16·t² + 120·t + 200
Therefore, we get;
-16·t² + 120·t + 200 =
t = (-120 ± √(120² - 4×(-16) × 200))/(2 × (-16))
t ≈ 8.9 or t ≈ -1.4
Therefore, the time it takes the rocket to hit the ground is given by the natural number, t ≈ 8.9 seconds.
What form is this quadratic? f(x)=2x^2+5x-10
Answer:
I hope that you thought so.
I recommend to you: Photomath
a cake has a diameter of 5 inch what is the circumference
Answer:
15.7
Step-by-step explanation:
c=d×3.14 which equals 15.7
Answer:
5π or 15.70796327 (I don't know what to round to or if the answer is supposed to be in terms of pi so it could be either).
Step-by-step explanation:
[tex]2\pi(2.5) = 5\pi[/tex]
[tex]5\pi = 15.70796327[/tex]
HELP PLEASE! THANKS :)
Answer:
If im not wrong, it has to be "How much does your dog weigh"
Step-by-step explanation:
And pleaseee This too
Answer:
the correct option is 75
Step-by-step explanation:
The standard notation for how to write tables is in the next way.
[tex]\left[\begin{array}{ccc}inpt&outpt\\x_1&y_1\\x_2&x_2\end{array}\right][/tex]
Where the input values are represented in the x-axis (the horizontal one) and the output values are on the y-axis (the vertical one).
In this case, we want to find the number of (x-value) for the height of 250.
Then we need to look at the vertical axis and find the value y = 250.
Now let's move to the right until you meet with the point.
Once you reach the point, move down to the axis, the value at which you intersect the axis is the x-value.
We can see that the point is on the middle of the x-values:
x = 70 and x = 80
Then the x-value of the point is x = 75
This means that the correct option is 75
Someone please helppp me ! Extra points and brainlest
Answer:
1 notebook cost $2.27
Step-by-step explanation:
Multiply the unit cost of the pencils by how many pencils you have : ( 1.29*3 = 3.87)
Subtract this from the total cost ( 10.68 - 3.87 = 6.81)
Divide this by 3 since there are 3 notebooks
6.81 / 3 = $2.27
Answer:
2.27
Step-by-step explanation:
have a good day
The graph of f(x)=4/x^2-2x-3 is shown. For which values of x is f(x) decreasing?
Answer: (1,3) (3, infinite)
Step-by-step explanation:
i think this is right
The graph of f(x) = 4/(x² - 2x - 3) is decreasing in the values of (-1,3) ∪ (3,∞)
What is graph?A graph can be defined as "pictorial representation or the diagram that represent a data or values in an organized manner".
According to the question,
The graph of function f(x) = 4/(x² - 2x - 3).
The values (-1,3) ∪ (3,∞) substitute in the given function
f(-1) = 4/0 = undefined
f(3)= 4/0 = undefined
f(∞)= undefined
Hence, The graph of f(x) = 4/(x² - 2x - 3) is decreasing in the values of
(-1,3) ∪ (3,∞).
Learn more about graph here
https://brainly.com/question/21276417
#SPJ2
Marissa's work to find the missing
length of the triangle is shown.
Explain Melissa's error.
24 units
az + b2 = c2
102 + 242 = c2
100 + 576 = C2
676 = C2
V676 = 0
338 = C
10 units
Step-by-step explanation:
She has done one mistake at last that under root 676 is not equal to 338, rather it is equal to 26.
Hope it helps ^_^
Write the equation of the line in slope-intercept form
Answer:
y=x
Step-by-step explanation:
m=1 b=0
(1/1) (Rise/run) (0)(y-intercept)
y=1x+0
y=x
I have no idea what the problem was with
Answer:
,,,,,,,,,,,,,,,,,,,,
Answer:
120in
Step-by-step explanation:
Okay, this is going to be a long one so hang onto your hats let's go
So, we first have to find the length that each of the frogs jumped so:
We're going to start with froggy #1, the 2-inch frog:
2 x 20 = 40
So froggy #1 can jump up to 40 inches so we're going to assume that each time our froggies jump, they jump to their full extent:
40 x 3 = 120
So froggy #1 jumped 120 inches
Now, we do the same with froggy #2, the 4-inch frog:
4 x 20 = 80
80 x 3 = 240
So froggy #2 jumped 240 inches
Now, we have to figure out how far ahead froggy #2 is from froggy #1:
240 - 120 = 120
So, the two froggies will end up 120 inches apart
hope this helps:)
After 10 weeks of work, bob has $1200. After 15 weeks of work Bob has $1800. After 20 weeks of work Bob has $2400. Write the firs four terms of a sequence that represents this situation. Writ and equation to model the situation
Answer:
1200,1800,2400,3000
5x = 600x
Step-by-step explanation:
The first four terms would be
1200,1800,2400,3000
As we can see that
After 10 weeks of work bob has $1200
After 15 weeks of work, bob has $1,800
So the more the weeks would be, the more the earnings it is
And, the difference of the earnings is
= $1,800 -$1,200
= $600
The equation would be
5x = 600x
So if we assume x = 1
So
5 = 600
if we assume x = 2
So
10 = 1200
and so on
NO LINKS OR REPORT
Please help!
Find the area of the figure
Answer:
[tex]Aear=2450cm^{2}[/tex]
Step-by-step explanation:
The figure is made up of a rectangle, parallelogram, and square.
Area of the rectangle is 50(15)=750 cm²
Area of the parallelogram is 40 (40)=1600cm²
Area of the square is 10(10)=100 cm²
The total area is 750+1600+100= 2450 cm²
[tex]-------------------[/tex]
hope it helps..
have a great day!!!
a rectangular prism and its dimensions are shown in the diagram.
what is the total surface area of this prism in square inches?
Answer:
Volume is 243.75
Step-by-step explanation:
v=(7.5)(5)(6.5)=243.75
Mark and Henry win some money and share it in the ratio 4:3. Mark gets £9 more than Henry. How much did they get altogether?
A letter is chosen from the word shown.
BELIEVABLE
Which describes the probability of randomly choosing a consonant?
Answer:
That something unexpected is about to happen.
Step-by-step explanation:
A rectangle has a length of 5x + 2 ft and a width of 2x + 11 ft.
Write an expression to model the area of the rectangle.
Show work, please!
Answer:
A = length * width
A = 5 (x+2)
A = 5x+10
I'm SO SORRY
y+8 can be translated as "the
of a number and elght."
quotient
product
difference
sum
Mike is 6.2 feet tall and casts a shadow that is 10.7 feet long. At the same time, a tree casts a shadow that is 37.5 feet long. How tall is the tree to the nearest tenth of a foot?
Answer:
I think it's 38
Can someone help please
Answer:
b-80 d-6
Step-by-step explanation:
100% correct
1. According to the graph the
percentage score of a student that
slept for 8hours is 80%
2. The graph also show that the student which score 90%,the number of hours the student slept is 6hours
Guys pls help me!!!!!
Answer:
1 ten and 5 ones
Step-by-step explanation:
DUE IN 30 MINTUES!!!!!PLEASEEE HELP!!!
You need to purchase supplies for the trip. You have $1000 to spend.
Oxen: $40 each
Food: $0.20 per lb
Clothing: $10 per set.
Matt also charges 9% tax
Purchase at least 2 oxen, 500lbs of food, and 5 sets of clothing. You may want to purchase more.
Select the amount of items and find the total cost including tax
combine like terms 23x + 3y -5x
Answer:
18x + 3y
Step-by-step explanation:
23x - 5x combine to 18x.
Then the given expression becomes 18x + 3y.
Answer:
18x+3y
Step-by-step explanation:
Find the area of the composite figure. Show your work. What is the area of the figure?
Answer:
46 units²
Step-by-step explanation:
The figure can be decomposed into 2 triangles and a rectangle.
Area of rectangle = L*W
W = 4
L = 8
Area = 32 units²
Area of triangle 1:
Area = ½(b*h)
b = 3
h = 4
Area = ½*3*4
Area = 6 in.
Area of triangle 2:
b = 4
h = 4
Area = ½*4*4
Area = 8 units
✅Area of the figure = 32 + 6 + 8
= 46 units²
Someone plzzz tell me this answer i am really stuck on this
Answer:
A
Step-by-step explanation:
Variables mean multiplying and that stonleigh when that multiplies and adds And it will never be even number because it is at 99 sense meaning $50 is greater than Whatever you multiply $3.99 by
Find the circumference of f
Answer:
its kinda hard to explain udisng words but mutiple to get acxorss then plit it and SFF and you should get the asnwer
Step-by-step explanation:
Which of the following angles is not coterminal with the other three?
a.–197º
b.17º
c.523º
d.163º
9514 1404 393
Answer:
b. 17°
Step-by-step explanation:
All of the angles are 2nd-quadrant angles except 17°, which is a 1st-quadrant angle.
17° is the odd angle
__
When you compute ...
mod(angle, 360), you get 163, 17, 163, 163.
A movie club surveyed 150 high school students. The students were asked how often they go to the movies and whether they prefer comedies or dramas. Their responses are summarized in the following table. Twice a month or less 48 Three times a month or more Comedy 24 Drama 57 21 (a) What percentage of the students prefer dramas? (b) What percentage of the students go to the movies twice a month or less?
Answer:a)
a) 68%
b) 44%
Step-by-step explanation: a) (51+51)/150 × 100 = 102/150 × 100
= 17/25 × 100
= 68%
Help me pls TwT I am terrible at math
Answer:
It should be B:)
Step-by-step explanation:
how many months are in 59 days???
1 month 29 days but if the month have 29 days each then the it will be 2 months
Which section or sections represent what is not in set HH?
Answer:
2) Sections 3 and 4
Step-by-step explanation:
Section 1 represents what ONLY applies to set HH, section 2 represents what is in BOTH set HH and Set C. So they are automatically out of the question.
Section 3 and 4, however, apply to either set C, or no set at all!
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Have a nice day fam. Spread The Love.
The recipe called for a ratio of sugar and flour to be 2 lbs to 9 lbs. If the chef used 18 lbs. of flour, how many pounds of sugar are needed?
Answer:
3/8 lb or 6 oz
Step-by-step explanation: