The vertical height in feet of a projectile on a planet in our solar system at a given time t in seconds is represented by the function h (t) = -4^2 + 24t Re-write h(t) in the form h(t) = a(t – h)^2 + k and determine the maximum height of the projectile. Show all work.
h (t) = -4t^2 + 24t = -4 (t² - 6t)
= -4 [(t - 3)² - 3²]
= -4 (t - 3)² + 36
max (3 ; 36)
(t - 3)² = t² - 2*t*3 + 3² = t² - 6t + 9
so it's why t² - 6t = (t - 3)² - 9
The maximum height of the projectile is 36 feet.
It is given that the projectile on a planet in our solar system at a given time t in seconds is represented by the function:
[tex]\rm h(t) = -4t^2+24t[/tex] can be written as a function:
[tex]\rm h(t) = a(t-h)^2+k\\[/tex]
It is required to determine the maximum height of the projectile.
What are maxima and minima?Maxima and minima of a function are the extrema within the range, in other words, the maximum value of a function at a certain point is called maxima and the minimum value of a function at a certain point is called minima.
The given function:
[tex]\rm h(t) = -4t^2+24t[/tex] for the maximum height of the projectile differentiate the given function with respect to 't' and equate it to zero.
[tex]\rm h(t) = -4t^2+24t\\[/tex]
[tex]\frac{\mathrm{d} }{\mathrm{d} x} [h(t)] = \frac{\mathrm{d} }{\mathrm{d} x}(-4t^2+24t)\\[/tex]
[tex]\frac{\mathrm{d} }{\mathrm{d} x} [h(t)] = \frac{\mathrm{d} }{\mathrm{d} x}(-4t^2)+\frac{\mathrm{d} }{\mathrm{d} x}(24t)\\[/tex]
[tex]\frac{\mathrm{d} }{\mathrm{d} x} [h(t)] = -8t+24\\[/tex]
[tex]\frac{\mathrm{d} }{\mathrm{d} x} [h(t)] = 0 \Rightarrow-8t+24=0\\[/tex]
[tex]\rm -8t+24=0\\\rm t= 3 \ sec[/tex]
Here, [tex]\rm \frac{\mathrm{d}^2 }{\mathrm dx^2} \leq 0[/tex]
It means that at t=3, we get the maximum height of the projectile.
[tex]\rm h(3)= -4(3)^2+24(3)\\\rm h(3) = -36+72\\\rm h(3)= 36 \ Feet[/tex]
Thus, the maximum height of the projectile is 36 feet.
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The leg lengths of a right triangle are 4 cm and 6 cm. What is the length of the missing side?
Answer:
Step-by-step explanation:
What is the surface area of the square pyramid represented by the net?
Answer: 144m
Step-by-step explanation:
6x6=36
(9 x 3) x 1/2 = 13.5
13.5 x 8(bc there are 8 triangles) = 108
108 + 36 = 144
Hope this helps! Please let me know if you need more help or think my answer is incorrect. Brainliest would be MUCH appreciated. Have a wonderful day!
name the polygon below.
Answer:
Parallelogram
Step-by-step explanation:
Since the opposite sides are parallel in the given polygon, it is parallelogram.
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When a construction worker is on a platform 10 feet above the ground, we can describe her elevation as +10 feet.
A construction worker digs down to 30 feet below the platform. What is her elevation?
It is 30 feet BELOW the platform, so the number is -20 because the platform is 10 feet above ground level.
Her elevation is - 20 because she is 10 feet above ground level, which is 10, and she digs 30 feet down so 10 - 30 is -20.
Hope this helps. :)
Answer:
-20 feet
Step-by-step explanation:
Ok, if the construction worker is first at 10 feet above the ground. If the construction worker goes 30 feet below the platform, the equation can be this: 10 - 30 = e or elevation. Remember that it states that the construction worker digs 30 feet below the platform, and not below the ground. Because 10 - 30 is -20, we know that the construction worker's elevation is -20.
I hope this helps :)
solve the equation using the quadratic formula. 3x^2+7x-20=0
Answer:
Step-by-step explanation:
a = co-efficient of x² = 3
b = co-efficient of x = 7
c = constant = -20
Determinant = D = b² -4ac
= 7² - 4*3*(-20)
= 49 + 240
= 289
[tex]x =\dfrac{-b + \sqrt{D}}{2a} ; \ x =\dfrac{-b- \sqrt{D}}{2a}\\\\\\x=\dfrac{-7+\sqrt{289}}{2*3} ; \ x=\dfrac{-3-\sqrt{289}}{2*30}\\\\\\x=\dfrac{-7+17}{6} ; \ x=\dfrac{-7-17}{6}\\\\x=\dfrac{10}{6}; \ x=\dfrac{-24}{6}\\[/tex]
x = 5/3 ; x = -4
The length of a rectangle is shown below: If the area of the rectangle to be drawn is 12 square units, where should points C and D be located, if they lie vertically below A and B, to make this rectangle? A. C(2, −2), D(−1, −2)
B. C(2, −1), D(−1, −1)
C. C(−2, 2), D(−2, −1)
D. C(−1, 2), D(−1, −1)
Answer:
A.
Step-by-step explanation:
Check out the image, hope it helps!
The city of newport is expecting a budget deficit this year of $257,943, which is 30% less than last year. what was last year's deficit?
last year deficit x 0,70 = 257,943
so
last year deficit = 368,490
- 30% = x (1 - 30%) = x 0,70
The coldest temperature ever recorded in Nome, Alaska, is -54°F. The average temperature in Nome during the Serum Run was 34° warmer. What was the average temperature in Nome during the Serum Run?
There are 40 people in a room. The ration of men to women is 2:3. If 5 more men enter the room, what will the new ratio be?
Answer:
16:29
Step-by-step explanation:
2u+3u=5u
40/5=8
Each unit represents 8 people
Hence, number of women:
8 x 2= 16
Number of men:
8 x 3 =24
New number of men:
24 + 5 = 29
New ratio:
16:29
Answer:
7 : 8 (men to women)
Step-by-step explanation:
Ratio = 2 : 3 (men to women)
40 people in all
40 / 5 = 8
2 x 8 = 16 (men)
3 x 8 = 24 (women)
16 + 5 = 21
21 : 24
7 : 8
Hope this helps!
(Let me know if I got something wrong!)
A premedical student at a university was complaining that she had just paid $158. 60 for her human anatomy book, including tax. Find the price of the book before taxes if the university tax rate is 9%
Answer:
145.50
Step-by-step explanation:
158.60 / (1+.09)
158.60 / 1.09 = 145.50458 (Approximately, I assume you have to round. I included extra digits incase they want more.)
Determine the gcf of each set of monomials
35,30a
Answer:
The GCF of 35 and 30a, will be 5.
Step-by-step explanation:
5 is the greatest number that can be factored into 35 and 30a.
Please help!!!! Will mark the brainliest!!!!
Find the circumference of the object. Use 3.14 or
22/7 for . Round to the nearest hundredth if necessary.
Answer:
C = 3.14 ft
Step-by-step explanation:
C = 2πr
Step 1: Define
r = 0.5 ft
Step 2: Substitute and Evaluate
C = 2π(0.5 ft)
C = 1π ft
C = π ft
C = 3.14 ft
Answer:
3.14
Step-by-step explanation:
Kelly really wants to buy a car. She needs a down payment of $6000. If
she deposits $4550 now with interest compounding continuously at 5%,
how many years will it take her to save enough to buy the car?
Answer:
6 years
Step-by-step explanation:
4550 x 1.05⁶= 6097.43516484
Franny wants to spend an equal amount of money
on the presents for her friends. If she has $62, about
how much money can she spend on each present?
With actually answer
Answer:
62/amount of friends= each present
Step-by-step explanation:
Answer:
62 divide by the number of friends present
Help me to answer this.
Answer:
A
Step-by-step explanation:
determine if 2, 8 ,14 ,20 is an arithmetic sequence. If so find the common difference and the next three terms.
Answer:
D=8-2=6,14-8=6,20-14=6 ARE IN AP
Step-by-step explanation:
26,32,38
Asap! I’ll mark you brainlest
What does How many kilometers did Jon run?
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A business has $10,000 in its bank account. In order to build an addition onto its office, it takes out a loan for $30,000 and deposits that money into the bank account. A number line is shown. The number line goes from zero dollars to forty thousand dollars by intervals of five thousand. A point is plotted at ten thousand dollars. What is the new account balance?
Answer:
The new account balance is $40000
Step-by-step explanation:
The number line is not given. However, the question can be solved without it.
Given
[tex]Balance = \$10000[/tex]
[tex]Loan = \$30000[/tex]
Required
Determine the new balance
[tex]New\ Balance = Initial\ Balance + Loan\ Amount[/tex]
[tex]New\ Balance = \$10000 + \$30000[/tex]
[tex]New\ Balance = \$40000[/tex]
Hence:
The new account balance is $40000
The equation of the line that passes through points (0, negative 7) and (2, negative 1) is shown below. What value is missing from the equation?
y = x – 7
Answer:
answer is y= -3x-7
Step-by-step explanation:
Answer:
3x-7
Step-by-step explanation:
PLS HELP ASAP
What is the measure of ZABC?
Enter your answer in the box
the measure of LABC =
Answer:
B = 180 - 85 = 95
∠ABC = 95
Step-by-step explanation:
Which line plot correctly shows the difference between the greatest and least practice times as three fourths hours? (1 point)
A line plot titled 'Piano Practice Times.' The bottom label is time in hours. The numbers on the line are zero, one fourth, one half, three fourths, one, one and one fourth, one and a half, one and three fourths, and two. There are two xs above three fourths, one x above one, three xs above one and a fourth, and one x above one and a half.
A line plot titled 'Piano Practice Times.' The bottom label is time in hours. The numbers on the line are zero, one fourth, one half, three fourths, one, one and one fourth, one and a half, one and three fourths, and two. There is one x above one half, two xs above three fourths, one x above one, two xs above one and one fourth, and one x above one and three fourths.
A line plot titled 'Piano Practice Times'. The bottom label is time in hours. The numbers on the line are zero, one fourth, one half, three fourths, one, one and one fourth, one and a half, one and three fourths, and two. There is one x above one half, one x above three fourths, two xs above one, one x above one and one fourth, one x above one and three fourths, and one x above two.
A line plot titled 'Piano Practice Times.' The bottom label is time in hours. The numbers on the line are zero, one fourth, one half, three fourths, one, one and one fourth, one and a half, one and three fourths, and two. There is one x above one fourth, one x above one half, one x above three fourths, one x above one, two xs above one and one fourth, and one x above two.
The line plot that shows the difference between the greatest and least practice times is D. A line plot titled 'Piano Practice Times.' The bottom label is time in hours.
What is a line plot?A line plot is a type of chart that displays information as a series of data points connected by straight line segments.
Here, the line plot that correctly shows the difference between the greatest and least practice times as three fourths hours is when the numbers on the line are zero, one fourth, one half, three fourths, one, one and one fourth, one and a half, one and three fourths, and two.
Learn more about line plot on:
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2) Tom left the water hose running for 20 minutes to water his lawn. Did he most
likely use 175 cups or 175 gallons of water?
Answer:
175 gallons
Step-by-step explanation:
easy hoses pump a lot of water
Answer:
i dont know i need the answer as well
Step-by-step explanation:
Find the volume of a right circular cone that has a height of 3.2 in and a base with a
diameter of 5.8 in. Round your answer to the nearest tenth of a cubic inch
Answer:
28.18, rounding it, it would be 28.2 cubic inches
Step-by-step explanation:
V=Pir^2(h/3)
Missing numbers on the number line
The blue dot is at what value on the number line?
Answer:
-3
Step-by-step explanation:
the number line is going up by 3's. It would start at -3 then 0 then 3 then 6 then 9 and so on. Hope this helps (:
papsdamatrix here is this picture
Luke tried to use Cavalieri's principle to show that the two figures have the same volume. The base areas are the same. Therefore, corresponding cross-sections have the same area. The prisms have the same height. So the volumes must be the same. What is the first mistake Luke made?
The error Luke made when trying to use Cavalieri's principle to show that the two figrues have the same volume is stating that: "corresponding cross-sections have the same area" which is NOT TRUE.
What is the Cavalieri's Principle?The Cavalieri's principle was named after Bonaventura Cavalieri. The Cavalieri's principle states the volume of two figures are the same if they have the same height and teh same cross-sectional area at every point along the height.
Thus, the two figures have entirely different cross-sectons. Their areas would be diffrent.
Therefore, the error Luke made when trying to use Cavalieri's principle to show that the two figrues have the same volume is stating that: "corresponding cross-sections have the same area" which is NOT TRUE.
Learn more about Cavalieri's principle on:
https://brainly.com/question/2279671
Answer:
the height
Step-by-step explanation:
Answer from cadencewest69. thanks cadencewest69!!! :)
on another training ride,Jana bikes 15 miles in 50 mins.Explain how you could find the number of miles she bikes in 1 hour
Answer:
18 miles
Step-by-step explanation:
Okay first I divided 15 and 50 by 5 this gives me miles for every 10 minutes this gave me 3 miles for every 10 minutes. Then I multiplied this by 6 because there are 60 minutes in an hour and got 18
Solve for x. Round to the nearest tenth, if necessary.
Answer: 20.4
Step-by-step explanation: