NASA launches a rocket at t = 0 seconds. Its height, in meters above sea level, as a function of time is
given by h(t) = – 4.9t2 + 139t + 185,
Assuming that the rocket will splash down into the ocean, at what time does splashdown occur?
The rocket splashes down after
seconds.
How high above sea level does the rocket get at its peak?
The rocket peaks at
meters above sea level.
Answers
Answer:
the splash down occurs when h(t) = 0
0 = -4,9t2 + 139t + 185
using the quadratic formula,
t = -1.27 or 29.64 seconds
since time can't be negative
t = 29.64 secs
at the peak, h(t) is maximum
applying calculus,
[d{h(t)}}/dt = -9.8t + 139
at h(t) maximum, [d{h(t)}}/dt is 0
0 = -9.8t + 139
9.8t = 139
t = 14.18 secs
substituting,
h(t) = – 4.9t2 + 139t + 185
h(t) = -4.9(14.18^2) + 139(14.18) + 185
= 1170.77 m
Answer:
Step-by-step explanation:
y = ax² + bx + c
D = b² - 4ac
[tex]x_{12}[/tex] = ( - b ± √D ) ÷ 2a
[tex]y_{max}[/tex] = - [tex]\frac{b}{2a}[/tex]
~~~~~~~~~~~~~
h(t) = - 4.9t² + 139t + 185
- 4.9t² + 139t + 185 = 0
D = 139² + 4(- 4.9)(185) = 22947
[tex]t_{12}[/tex] = ( - 139 ± √22947) ÷ 2(- 4.9)
[tex]t_{1}[/tex] ≈ 29.641 ≈ 30 seconds
[tex]t_{2}[/tex] < 0
[tex]h_{max}[/tex] = - 4.9( [tex]-\frac{139}{2(-4.9)}[/tex] )² + 139( [tex]-\frac{139}{2(-4.9)}[/tex] ) + 185 ≈ 1170.7653 ≈ 1171 meters
Related Questions
Evaluate when
a =3 b= 4.5 and h = 6
Answers
Answer:
For Example: Evaluate a2b for a = –2, b = 3, c = –4, and d = 4.
Step-by-step explanation:
To find my answer, I just plug in the given values, being careful to use parentheses, particularly around the "minus" signs. Especially when I'm just starting out, drawing the parentheses first may be helpful:
a2 b
( )2 ( )
(–2)2 (3)
(4)(3)
12
Note how using parentheses helped me keep track of the "minus" sign on the value of a. This was important, because I might otherwise have squared only the 2, ending up with –4, which would have been wrong.
By the way, it turned out that we didn't need the values for the variables c and d. When you're given a big set of expressions to evaluate, you should expect that there will often be one or another of the variables that won't be included in any particular exercise in the set.
Evaluate a – cd for a = –2, b = 3, c = –4, and d = 4.
In this exercise, they've given me extra information. There is no b in the expression they want me to evaluate, so I can ignore this value in my working:
(–2) – (–4)(4)
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please hurry! I need all of these answers really soon it's due
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HELP PLEASE ASAP What is the length of the diagonal of the square shown below?
Answers
Answer:
C) diagonal = 5√2
Step-by-step explanation:
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diagonal² = 50
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diagonal = √25x2
diagonal = 5√2
Answer:
C) diagonal = 5√2
Step-by-step explanation:
diagonal² = 5² + 5²
diagonal² = 50
diagonal = √50
diagonal = √25x2
diagonal = 5√2
What does it mean to say that two groups are homogeneous?
Answers
Answer:
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Step-by-step explanation:
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C) 720°
B) 1800°
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Answers
Answer:
D- I hope I helped you. Good luck.
A store has clearance items that have been marked down by 35%. They are having a sale, advertising an additional 45% off clearance items. What percent of the original price do you end up paying?
Answers
Let’s pretend something at the store is $100. (It will save some math later)
100 - 35% leaves 65% (0.65 as a decimal)
100 x 0.65 = 65
That’s the price after the first discount. If we take 45% off of the sale price, we’ll be left with 55%, 0.55
65 x 0.55 = $35.75
Now normally you’d compare 35.75(sale price)/ 100(original price) to % off (x)/100, but doe this example, it’s unnecessary.
35.75/100 = x%/100
Solve the equation x = 5/3 (pie) (r^3) for r.
Answers
Answer and Step-by-step explanation:
To solve for r, we need to get everything away from r. We can start off by moving five thirds, and pi.
[tex]x = \frac{5}{3} \pi r^{3}[/tex]
Multiply each side by [tex]\frac{3}{5}[/tex], then divide by [tex]\pi[/tex] (pi)
[tex]\frac{3x}{5\pi } = r^{3}[/tex]
Now, take the cubed root of both sides.
[tex]\sqrt[3]{\frac{3x}{5\pi } } = r[/tex]
^^ That is the answer.
#teamtrees #PAW (Plant And Water)
How many pairs of intersecting lines are shown?
D
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Write 0.41 in fraction simplest form
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42 can’t go into 100 an even amount of times
6.
Reason quantitatively. A local bakery sells bagels
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Answers
Given:
Abbie spent ⁵/₈ of her money and saved the rest.
She spent $45.
Question:
How much money did she have at first?
The Process:
The meaning of "Abbie spent ⁵/₈ of her money" is that she has spent 5 of the 8 parts of the money she had at first.
Let us make a pattern of 8 units for the amount of money that Abbie had at first.
Since Abbie spent ⁵/₈ of her money, then we create a pattern of 5 units containing $9 each. Recall that
From the pattern above, we can see that
Let us calculate how much money Abbie had at first.
Thus, the money Abbie had at first is $72.
The complete pattern of Abbie's initial money is as follows:
- - - - - - - - - -
Quick Steps:
Let M as Abbie's initial money.
Both sides are multiplied by ⁸/₅ so that M is the subject alone on the left side.
We crossed out 5 and 45.
Thus, the money Abbie had at first is $72.
work out 2 1/7 + 1 1/4
Answers
Answer:
95/28
Step-by-step explanation:
what is the area of this square (look at the picture)
Answers
Answer:
484
Step-by-step explanation:
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Gabrielle is 13 years older than Mikhail. the sum of their ages is 113. what is mikhails age?
Answers
Step-by-step explanation:
g=m+13
g+m=113
use substitution
Answer:
50 years old
Step-by-step explanation:
Let's say that Mikhail's age is x.
If so, Gabrielle's age would be 13 years older, therefore x + 13
We know that the sum of their ages is 113, so we can form this equation:
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Answers
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Step-by-step explanation:
Write the Whole Number as a Fraction Over One.
Choose A New Denominator.
Multiply Both Numerator and Denominator.
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Answers
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Gabriel buys a plastic pencil case as shown. How much plastic is the case made from?
Answers
At a summer camp, there are 15 counselors, 5 cooks, and 120 campers. 5 points
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Write the following as algebraic expressions:
Joe had $100. He bought m books for n dollars each. How much money does he have left?
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A line passes through the points (5,22) and (7,24). Write a linear function rule in terms of x and y
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Answers
It’s question 2! Please help! An explanation would be amazing.
Answers
Answer:
n = 0
Step-by-step explanation:
n^2-8n+16=n^2+8n+16
16n=0
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correct 89.6162 to two decimal places
Answers
Answer:
89.62
Step-by-step explanation:
Look at the 3rd place of decimals - this is 6 so we add one to the second place.
i tryed my best
The decimal number rounded to 2 decimal places is 89.62
Given data:
The decimal number is represented as 89.6162
To round 89.6162 to two decimal places, we look at the third decimal place.
Non-zero digits are always significant
Zeros between non-zero digits are always significant
Since the digit in the third decimal place is 6, which is greater than or equal to 5, we round up the second decimal place.
Hence, rounding 89.6162 to two decimal places, the number is 89.62
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Which of the following best describes term response variable
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The dependent variable responds to variations in the separate variable manipulated during the experiment. It allows you to understand whereas if changes involved possess or are not significantly linked or whether they are because of certain factors.
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Answers
Answer: It will one year (or 12 months) before Michael is able to ride the roller coaster.
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Answer:
48-42=6, which is how much Michael needs to grow.
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Which statement best describes the expression fraction 1 over 2 x (14 − 6) x 6 + 4?
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Find the product of 6 and 4, subtract the difference between 14 and 6, then multiply by fraction 1 over 2.
i really need help i don't get it
Answers
Answer:
The correct answer is: Find half the difference of 14 and 6, multiply by 6, then add 4.
Step-by-step explanation:
By Hierarchy Rules of Operators, we must follow these steps:
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Answers
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Step-by-step explanation:
What are the directional changes and numerical changes of the vertex of the graph of the equation y=x^2 when it changes the equation y=(x-3)^2 +5
Answers
Answer:
Step-by-step explanation:
subtracting 3 from x shifts the graph right 3 units.
adding the constant 5 shifts the graph up by 5 units.
A right prism is shown below
what is the volume of the right prism height is 15 in width is 8 in length is 10 in
Answers
Answer:
This is your answer ☺️☺️☺️
1/3 x 4/5 = help me out here
Answers
Answer:
kay it's 4/15
Step-by-step explanation:
this friggen took me forever
I made it to a common denominator 15
5/15*12/15
then I kept simplifying it till I got to 4/15
k bye
1•4=3•5
4/15
I dont know how to explain here
I NEED HELP NOW PLZ!!!
Answers
Answer:
c
Step-by-step explanation:
x=-8
y= -5
therefore y=-5
and c is the answer
Y=-5
X=-8
Y=5/8 x
-5=5/8 (-8)
Which is
-5=-5