Answer:
60
Step-by-step explanation:
The given function is:
The average rate of change of h(t) from t=a to t=b is given by:
We can rewrite this function as:
The maximum height of the rocket is 231 and it occurs at t=3.75
The initial launch occurs at: t=0
and
The average rate of change from the initial launch to the maximum height is
The average rate of change from the initial launch to the maximum height is 59.21 ft/s.
We have a equation that represents the Rocket path.
We have to find the average rate of change from the initial launch to the maximum height.
What do you mean by a Time - varying quantity ?A time varying quantity is the quantity whose absolute value change with time. For example - y = f(t) = 2t - 1 , where y is the displacement and it varies as y = 2t - 1 with time.
According to the question, we have -
Equation → [tex]h(t) = -16t^{2} +120t+6[/tex]
Height of podium → 6 feet.
Initial velocity (u) = 0
Now -
[tex]h(t) = - 16t^{2} +120t+6[/tex]
Differentiating w.r.t time, we get →
[tex]$\frac{dh}{dt} = - 32t + 120[/tex]
For maximum height → [tex]$\frac{dh}{dt} = 0[/tex]
-32t + 120 = 0
32t = 120
t = 3.8 seconds
This means that at t = 3.8 seconds the rocket will reach its maximum height. Therefore, the maximum height will be -
h(t) = - 16 x 3.8 x 3.8 + 120 x 3.8 + 6
h(t) = - 231.04 + 456 + 6
h(t) = 224.96 + 6
h(t) = 230.96 = 231
The maximum height reached by the rocket is 231 feet's.
Now -
Initial height = 6 feet
Initial time = 0 s
Final height (max) = 231
Time at maximum height = 3.8
Therefore, the average rate of change from the initial launch to the maximum height will be -
[tex]$v_{avg} = \frac{231-6}{3.8-0}=59.21[/tex]
v (avg) = 59.21 ft/s
Hence, the average rate of change from the initial launch to the maximum height is 59.21 ft/s
To solve more questions on Motion of Rockets, visit the link below-
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Find the probability of finding number less than or equal to 10.
1 is the answer
Step-by-step explanation:
Number of possible outcomes = 10
Total number of outcome = 10
Probability = [tex] \frac{Number \: of \: possible \: outcomes}{Total \: number \: of \: outcome}[/tex]
[tex] = > \frac{10}{10}[/tex]
[tex] = > 1[/tex]
Hence, the probability of finding number less than or equal to 10 is [tex]1[/tex]
a. 6798,5 ÷ 135
b. 987,46 ÷ 322
c. 567, 6 ÷34
Answer:
A =50,35925926
=50,36
B=3,066645963
=3,07
C=16,69411765
=16,7
Hope this is what u looking for,
I will send a pic give me a minute
What is the solution to f(x)= g(x), if f(x)=-x and g(x)=x
Answer: 0
Step-by-step explanation:
By substituting the f(x) = -x and g(x) = x into the first equation, we get -x = x so the only answer to the question is 0
help me with angle sum theorem please
Answer:
y = 55°
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
100° is an exterior angle of the triangle , then
y + 45° = 100° ( subtract 45° from both sides )
y = 55°
Sofia leans a 28-foot ladder against a wall so that it forms an angle of 67^ with the ground. How high up the wall does the ladder reach? Round your answer to the nearest hundredth of a foot if necessary.
Answer:
23.43 feet
Step-by-step explain
by my accurate accusations
2,367 DIVIDED BY 2 WITH THE REMAINDER
Answer:
1,183.5
Step-by-step explanation:
When dividing 2,367 by 2, the quotient is 1,183 with a remainder of 1 by performing long division by starting with the leftmost digit of the dividend.
To divide a number by another number and find the quotient and remainder, follow these steps:
Step 1: Divide the first number (dividend) by the second number (divisor). In this case, divide 2,367 by 2.
Step 2: Perform long division by starting with the leftmost digit of the dividend. Divide the digit by the divisor and write the quotient above the division bar.
Step 3: Multiply the quotient by the divisor and subtract the result from the current partial dividend.
Step 4: Bring down the next digit of the dividend and continue the division process until all digits have been used.
Step 5: The final quotient is the whole number obtained from the division, and the remainder is the remaining digit.
In the case of 2,367 divided by 2, the long division process would yield a quotient of 1,183 and a remainder of 1.
Therefore, 2,367 divided by 2 gives a quotient of 1,183 with a remainder of 1.
Learn more about long division here:
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solution set of 2x+4 greater than or equal to -8
Step-by-step explanation:
equal because of the 8+7
Answer:
x \geq -6
Step-by-step explanation:
2x+4 \geq -8
-4 -4
2x \geq -12
/2 /2
x \geq -6
AABC with vertices A(-4, 3), B(-2,-1) and C(-1, 3) is translated by 3 units right and 2 units up, then
it is rotated 90° counterclockwise about the origin. The new image of the triangle is represented by
ABC
What are the coordinates of A'?
Answer :
A. (0,-2)
B. (-5,-1)
C. (-5,1)
D (5,0)
Answer:
C
Step-by-step explanation:
(-4, 3) 3 units right = +3x = -1
(-1, 3) 2 units up = +2y = 5
(1, 5) A rotation of 90° counterclockwise around the origin can be described in mathematical terms as (x, y) → (−y, x).
(1, 5) → (-5, 1), or C
Answer:
B. (-5, -1)
Step-by-step explanation:
Since we're solving for A :
A (-4, 3) translated 3 units to the right and 2 units up would be A (-4 + 3, 3 + 2), which is A' (-1, 5). Then, we have to rotate it 90 degrees clockwise. This would be (-5, -1), as the formula states (x, y) -> (-y, x), which means the x stays the same but goes to the 'y' position, and the y sign changes and goes to the 'x' position.
So, it would be (-5, -1) :)
Which of the following shows the true solution to the logarithmic equation 3 log Subscript 2 Baseline (2 x) = 3 x = negative 1 x = 1 x = negative 1 and x = 1 x = 0, x = negative 1, and x = 1.
The equation which shows the true solution to the given logarithmic equation is,
[tex]x=1[/tex]
What is power rule of logarithmic function?The power of the log rule says that the number written in the front of the logarithmic function can be raised to the power of the logarithmic function.
For example,
[tex]n\log_b(M)=\log_b(M)^n[/tex]
Given information-
The logarithmic equation given in the problem is,
[tex]3\log_2(2x)=3[/tex]
Using the power rule of the logarithmic function,
[tex]\log_2(2x)^3=3[/tex]
Using the exponent rule of the logarithmic function the above equation can be written as,
[tex](2x)^3=3[/tex]
Solve it further,
[tex]8x^3=3\\x^3=1\\x=1[/tex]
Hence, the equation which shows the true solution to the given logarithmic equation is,
[tex]x=1[/tex]
Learn more about the rules of logarithmic function here;
https://brainly.com/question/13473114
Answer:
its B on edge
Step-by-step explanation:
what is the slope of the line???
Answer:
slope: 2 as we see, with every increase in x, y increase twice the more.
Step-by-step explanation:
we can can see the y-intercept at 1.so equation: y = 2x + 1The slope of the linear graph in the question obtained using the ratio of the rise and run of the line is 2.
Recall :
Slope = Rise / Run
From the graph :
Rise = y2 - y1 = 5 - (-1) = 5 + 1 = 6
Run = x2 - x1 = 2 - (-1) = 2 + 1 = 3
The slope of the graph can be expressed thus :
Slope = Rise / Run = 6 /3 = 2
Therefore, the slope of the line in the graph attached is 2
What is the exact value for the expression V52 - V13 + V117 ? Simplify if possible. (5 points)
O 413
O V13
O 21/39
O 839
PLS DON'T ANSWER IF YOU DON'T KNOW
Answer:
[tex]4\sqrt{13}[/tex]Step-by-step explanation:
[tex]\sqrt{52} -\sqrt{13} +\sqrt{117} =[/tex][tex]\sqrt{4*13} -\sqrt{13} +\sqrt{9*13} =[/tex][tex]2\sqrt{13}-\sqrt{13} +3\sqrt{13} =[/tex][tex]4\sqrt{13}[/tex]The exact value for the expression √52 – √13 + √117 given in the question above is 4√13
Surd operationa√b + c√b = (a + c)√b
With the above information in mind, we can simplify the express given in the question above.
Data obtained from the question √52 – √13 + √117Simplification =? How to simplify the expression√52 – √13 + √117
Recall
√52 = √(4 × 13) = 2√13
√117 = √(9 × 13) = 3√13
Thus
√52 – √13 + √117 = 2√13 – √13 + 3√13
√52 – √13 + √117 = (2 – 1 + 3)√13
√52 – √13 + √117 = 4√13
Learn more about surd:
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What is the value of x?
What the answer to this is ?
Answer:
a. median 1.5
Step-by-step explanation:
If you sort the numbers from least to greatest, the middle numbers are 1 and 2, so the median is the middle of those, 1.5. And the mean is 2.75, so it can't be the others.
If there are 32 boys and 8 girls in a room, fill out all of the possible ratios of boys to girls that could be made.
Answer:
32 : 8
8 : 2
4 : 1
Step-by-step explanation:
32 : 8
8 : 2 (32/4 = 8, 8/4 = 2)
4 : 1 (32/8 = 4, 8/8 = 1)
Hope this helps!
A person standing in the ground throws a ball onto a flat rooftop. The ball rolls around for several seconds. Then the ball falls off the roof, into a puddle of mud. (Please help asap) it’s due shortly!
Answer:
Graph DStep-by-step explanation:
According to the question, the correct graph is D.
It's not A because, the ball is thrown after some pause and the ball doesn't roll on the roof, falls immediately.
It's not B or C because the ball goes up after reaching the roof but should fall down.
need help ASAP 1st correct answer gets brainliest
Answer:
22 1/2 degrees
Step-by-step explanation:
4 x 5 = 20
(1/2) x 5 = 2.5
Answer: 22.5 degrees
Step-by-step explanation:
If it fell 4.5 degrees each hour, and there were 5 hours, 4.5x5 == 22.5
Please I could use all the help (no URL links)
Answer:
(6, 2)
Step-by-step explanation:
3(6) - 2 = 16
6 - 5(2) = -4
can someone please help me with this
Step-by-step explanation:
sum of all angles = 360
7x-4 = 360
7x= 364
x = 52
angle j = 150
angle k = 62
angle m = 100
(3 x 100) + (7 x 1) + (4 x 1/100) + (8 x 1/1,000) In standard form?
Answer:
300 + 7 + 0.04 + 0.008 = 307.048
Step-by-step explanation:
mia estimated 5/8 + 1/9 by replacing 5/8 with 1 and 1/9 with 0. her estimated sum was 1+0=1. explain why mias estimate is not accurate
Answer/Step-by-step explanation:
5/8 is not close to 1 in this context. If you want to be accurate, don't estimate. Add the 2 numbers.
Brainliest?!
An electrician bought 80 feet of electrical wire and used 55 feet of it. What percent of the wire went unused? 22% 25% 31. 25% 45. 5%.
Answer: it's 31.3 percent.
Step-by-step explanation:
55 feet of 80 is 68 percent, to find the remainder you need to subtract 68 by 100, and with that, you get 31.3 percent.
if you want that in feet it's about 25 feet
5 = 4x + 13
Solve for X
Answer:
5=4x+13
4x+13=5
4x=5-13
4x= -8
x = -8÷4
x = -2
# be careful£
please help i spent all my points on this
Answer:
exact value is 264π and decimal to the thousandths is 829.381m²
Step-by-step explanation:
It gives you the formula.
(pi times 8 times 25) + (pi times 8 squared)
Answer:
A≈829.38
A= pi x 8 x 25 + (pi x 8^2)
A= 200pi + 64 pi
A= 264pi
Answer is 264
Hope this helps!
Please help me with number 11
Answer:
€0.78
Step-by-step explanation:
To find Euros per Dollar, divide euros by dollars:
€175/$225 = 7/9 €/$ ≈ 0.78 €/$
Kareem received about €0.78 for each dollar exchanged.
(3.4 x 10^-15) +(8.1 x 10^-14) help please, show work thank you
Answer:
see below
Step-by-step explanation:
1) Use Negative Power Rule: [tex]x^{-a} =\frac{1}{x^{a} }[/tex].
[tex]3.4x*\frac{1}{10^{15} } +8.1*x*10^{-14}[/tex]
2) Use Negative Power Rule: [tex]x^{-a} =\frac{1}{x^{a} }[/tex].
[tex]3.4x*\frac{1}{10^{15} } +8.1*x*\frac{1}{10^{14} }[/tex]
3) Use this rule: [tex]\frac{a}{b} *\frac{c}{d} =\frac{ac}{bd} .[/tex]
[tex]\frac{3.4x*1}{10^{15} }+8.1*x*\frac{1}{10^{14} }[/tex]
4) Simplify [tex]3.4x*1[/tex] to [tex](3.4)x[/tex].
[tex]\frac{3.4x}{10^{15} } +8.1*x*\frac{1}{10^{14} } }[/tex]
5) Use this rule: [tex]\frac{a}{b} *\frac{c}{d} =\frac{ac}{bd} .[/tex]
[tex]\frac{3.4x}{10^{15} } +\frac{8.1*x*1}{10^{14} }[/tex]
6) Simplify [tex]8.1*x*1[/tex] to [tex]8.1(x)[/tex].
[tex]\frac{3.4x}{10^{15} } *\frac{8.1*x}{10^{14} }[/tex]
PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
14
Step-by-step explanation:
8×7=56
4×?=?
?= 56÷4
?= 14
Answer:
Divide the numerator by the denominator.
Step-by-step explanation:
Solve the following expression and type your result in the empty box provided below as a decimal. 5 3/10 -9/10
Answer:
So the answer is that 5 3/10 as a decimal is 5.3. 9/10 as a decimal is expressed as 0.9.
Step-by-step explanation:
To convert any fraction to its decimal form, we just need to divide the numerator by the denominator.
In this case, we divide 9 by 10, 9 ÷ 10 = 0.9
You can also verify your answer using Cuemath's Fraction to Decimal Calculator.
Hope this helps!
How do I find the slope of the line?
Answer:
Use the following formula:
[tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
Step-by-step explanation:
Use "change in y over change in x"
-> See attached for more
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly.
- Heather
(A) The sum of a number and 12 is at most -8
(B) A number increased by -8 is greater than 12.
(C) -8 less than a number is no more than 12.
The expression -8 less than a number is no more than 12 will be given as x - 8 ≤ 12
How to interprete inequality statamentLet the unknown values be "x"
a) The sum of a number and 12 is expressed as x + 12
If the result is at most -8, the required inequality will be x + 12 ≤ 8
c) If a number is increased by -8, the result will be x - 8. the expression -8 is greater than 12 will be given as x - 8 > 12 greater than 12.
b) If a number is increased by -8, the result will be x - 8. The expression -8 less than a number is no more than 12 will be given as x - 8 ≤ 12
Learn more on inequality here: https://brainly.com/question/24372553
24/63 is equal to what
Answer:
0.38095238095238
Step-by-step explanation:
Therefore, this equation is true: 24/63 = 8/21 If the numerator is greater than or equal to the denominator of a fraction, then it is called an improper fraction.