The speed of the rocket is able to increase with time in the upward
direction because the rocket has an upward acceleration.
[tex]\displaystyle \mathrm{The \ function \ that \ gives \ the \ height \ of \ the rocket \ is \ }\underline{f(t) = \frac{1}{2} \cdot a \cdot t^2}[/tex]Reasons:
The acceleration of the rocket = a
According to Newton's Law of motion, the height reached by the rocket with time can be found by the formula;
[tex]\displaystyle f(t) = u \cdot t - \frac{1}{2} \cdot a \cdot t^2[/tex]
Where;
u = The initial velocity of the rocket = 0
Which gives;
[tex]\displaystyle f(t) = 0 \times t - \frac{1}{2} \cdot a \cdot t^2 = \mathbf{ \frac{1}{2} \cdot a \cdot t^2}[/tex]
[tex]\displaystyle \underline{The \ height \ of \ the \ rocket, \ f(t) = \frac{1}{2} \cdot a \cdot t^2}[/tex]Learn more here:
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Find the GCF of 21m5n2 and 28m4n2.
What is the other 0 of the quadratic function
Answer: Unknown
Step-by-step explanation:
-b+/-√b^2-4ac/2a < plug a b and c into this equation and boom done ez
Mr. Solomon, the art teacher, has 49.6 pounds of clay. If he gives every student 1.6 pounds of clay and has none left, how many students are in his class?
Answer:
He has 31 students
Step-by-step explanation:
You know this because 49.6 ÷ 1.6 = 31
your family have decided to paint your room. It took 1/2 hour to paint 1/8 of your room. How long will it take to paint your whole room?
Answer:
4 hours
Step-by-step explanation:
In 6 hours, J paints 1 room
So, in 1 hour, J paints 1/6 th of the room
Using similar logic, in 1 hour, T paints 1/12 th of the room.
Working together in one hour, they paint (1/6+1/12) th =1/4 of the room.
1/4 of the room is painted in 1 hour
So, 1 room is painted in 1 1/4=4 hours
Answer:
Step-by-step explanation: 1/7
Four less than the product of a number and 8 is twice the sum of the number and 10 what is the number
Answer:
x=4
Step-by-step explanation:
Four less than the product of a number and 8:
8x−4
is twice the sum of the number and 10, so
8x−4=2(x+10)
Simplify.
8x−4=2x+20
Add 4 to both sides, which is
8x=2x+24
Subtract 2x from both sides:
6x=24
Divide 6 from both sides to isolate the x
x=4
-how I got 20
8x-4=2(x+10) x=8 so 8+10=18 18+2=20
also sorry for posting the answer in the comments and then making an answer after you saw i just wanted da points and hope it helped you :)
how do you factor 3x^2-3x-90
3x^2 - 3x -90
=3 (x^2 - x -30)
=3 (x^2 −6x+5x−30)
=3(x(x−6)+5(x−6))
=3(x−6)(x+5)
Help I need to solve A. B. C and D.
Answer:
A) -3 > -5
B) -5 < 0
C) 6 > -1
D) tuesday > wednesday
Step-by-step explanation:
< = lower than
> = greater than
If you split 8 kg of strawberries among yourself and three friends, how many kilograms of strawberries will each person receive?
Answer:
2kg brainliest expected
Step-by-step explanation:
there's 4 people so divide 8 by 4.
each person shall get 2 kg
. The sum of infinity of G.S is 15, 1st term is 3 then the common ratio is.
Step-by-step explanation:
We know ,
=> Sum = a / 1 - r
=> 15 = 3/1-r
=> 15 - 15r = 3
=> 15r = 18
=> r = 18/15
=> r = 6/5
Sixth grade math please in K12
Item 3
Divide.
5892 ÷ 18
327
327 1/18
327 1/3
327 7/18
Help is apricated
Answer:
327r6
Step-by-step explanation:
Too long, if you really need it, comment on this answer.
90 degree angle is divided into two sides
Answers:
3x + 40 =64
4x - 6 =26
Step-by-step explanation:
So we are dealing with 2 complementary angles with both add up to 90 degrees. We can write an equation that shows this:
(3x+40) + (4x-6) = 90
Combine like terms
7x + 34 =90
Isolate x
7x = 56
x = 8
Now that we found x, all we have to do is substitute it in the equations:
3x + 40 = ?
3(8) +40 = ?
24+40 = ?
64 = ?
4x - 6 = ?
4(8) - 6 = ?
32 - 6 = ?
26 = ?
Answer:
3x+40= 66
4x-6= 26
Step-by-step explanation:
3x+40+4x-6=90˚ (because the square on the angle represents a 90˚)
Add 4x and 3x
Which is 7x
40 minus 6 is 34
The equation now looks like this:
7x+34=90˚
Subtract 34 on both sides:
7x=56
Divide 7 on both sides:
x=8
For 3x+40
Substitute x with 8
the equation now looks like this:
24+40 Which is 66
For 4x-6
4 times 8 is 32
32 minus 6 which is 26
Hope this helps!
Which angle is adjacent to <1?
If you spent 24 weeks working on a project for your job and are rewarded with 3 days of vacation write the ratio of time on vacation to time working as a fraction in lowest terms
what's the sum of 14 12 8 6
Answer:
40
Step-by-step explanation:
14 + 12 + 8 + 6 = 40
Answer:
40
Step-by-step explanation:
14+12=26+8=34+6=40
Please answer the question in the picture
Answer:
2x² + 2x - 24
Step-by-step explanation:
We can use the FOIL method to multiply the terms together and then find the values in our trinomial. First, the F in FOIL. It stands for first, and we need to multiply the first terms in the two expressions. These terms are 2x and x. Multiplying 2x by x gives us 2x², so that's our first term.
Next, the O in FOIL. It stands for outside, and we need to multiply the terms on the very left and the very right. These are 2x and -3, and multiplying 2x by -3 gives us -6x. That's our second term.
Now, the I in FOIL. It stands for inside, so we need to multiply the terms in the middle of the expressions. Those are 8 and x, and we multiply those together to get 8x. That's our third term.
Finally, the L in FOIL. This stands for last; we need to multiply the last terms of each expression. Those are 8 and -3, and we can multiply those to get -24. Now we can get all our terms added together and simplify as needed.
2x² - 6x + 8x - 24
We can simplify -6x and 8x since they are like terms.
2x² + 2x - 24
And there is our trinomial. Hopefully that's helpful! :)
After all the taxes are withheld, Jules's take home pay is about 72% of his total earnings. Estimate his take home pay if his total earnings for the pay period are $240.
Answer:
172.8
Step-by-step explanation:
72% of 240 is 172.8
You can estimate it by rounding 172.8 to $173
Jules's take $173 for home pay.
What is Percentage?
A relative value indicating hundredth part of any quantity is called percentage.
Given that;
Total earning of Jules's = $240
He take home pay is about 72%.
Now,
Amount for take home pay = 72% of $240
It can be solve as;
72% of $240
72% × 240
72/100 × 240
72/10 × 24
172.8
After estimating we get;
Amount for take home pay = $173
Thus, Jules's take $173 for home pay.
Learn more about the percentage visit:
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Find the value of y for the given value of I.
y=x/2 + 9;x = -12
9514 1404 393
Answer:
y = 3
Step-by-step explanation:
Put the value where the variable is and do the arithmetic.
[tex]y=\dfrac{x}{2}+9\\\\y=\dfrac{-12}{2}+9=-6+9\\\\\boxed{y=3}[/tex]
10x-6x-4-1=7-12+2x+2x
Any value of
x
makes the equation true.
Always true
Interval Notation:
(−∞,∞)
A machine packs 180 boxes of cereal in a half-hour. It takes 55 minutes to pack 330 boxes. True or False?
Which of the following could be the number shown on the number line?
A. V66
B. V60
C. V63
D. V65
Answer:
A
Step-by-step explanation:
v666
simplify 3 wholes 6/8 + 2 wholes 2/8
Answer:
5/1
Step-by-step explanation:
3.75 + 2.25 = 5
5 = 5/1
If the map distance is 20 cm and the scale is 4 cm = 60 km, what is the actual distance?
Answer:
300
Step-by-step explanation:
1. 60/4=15
2. 15x20=300
Which is a property of an angle?
A-has two sides that each extend forever in both directions
B-has two endpoints
C-has two center points
D-has two rays that share a common endpoint
Solve all of them please u get 30 points
Step-by-step explanation:
from which text book please
In science class, a student is measuring the temperature of a solution in science experiment. The solution
started at -3.4 degrees. After two minutes the temperature had increased 12.4 degrees. After a few more
minutes, the temperature decreased 20.4 degrees. After one more minute the temperature increased by
3.2 degrees. What is the final temperature?
Answer:
-11.8
Step-by-step explanation:
Given:
-3.4 to 12.4 increased (difference = 15.8)
12.4 to 20.4 decreased (difference = 8)
20.4 to 3.2 increased (difference = 17.2)
To find:
Final temperature.
Solution:
As we noticed, this is a pattern of increase, decrease, increase... (and so on and so forth). From this alone, we have gotten the clue that the temperature is going to decrease. But here is the thing, How far will it decrease?
Use the difference of the starting result to find the ending result.
3.2 - 15
= -11.8
Therefore, the final temperature is -11.8.
(20 points!!!)
Alanna is going shopping for Goggles and food.
The cost of Goggles is $15 and the cost of each food item is $5.
If Alanna can spend at most $55, how many food items can be purchased?
Write an inequality of the form Ax + B ≤ C to represent the word problem using your answers for A, B, and C. Solve the inequality and show your work.
Graph the solution to your inequality on a number line or describe, in words, how to graph the inequality on a number line.
Explain what the solution means in the context of the word problem.
Answer:
(20 points!!!)
Alanna is going shopping for Goggles and food.
The cost of Goggles is $15 and the cost of each food item is $5.
If Alanna can spend at most $55, how many food items can be purchased?
Write an inequality of the form Ax + B ≤ C to represent the word problem using your answers for A, B, and C. Solve the inequality and show your work.
Graph the solution to your inequality on a number line or describe, in words, how to graph the inequality on a number line.
Explain what the solution means in the context of the word problem.
George has four boards that are each 43 feet long and two that are 5.75 feet long.
What is the total length of all the boards together? Give your answer as a decimal.
Answer:
183.50 feet
Step-by-step explanation:
43*4=172
5.75*2=11.50
172+11.50=183.50
183.50 feet
A file that is 249 megabytes is being downloaded. If the download is 15.7% complete, how many megabytes have been downloaded? Round your answer to the
nearest tenth ?
Answer:
39.1 megabytes
Step-by-step explanation:
Percentages are out of a hundred, so 15.7% is 15.7 out of 100, aka 15.7/100, which is 0.157.
Now, you just need to multiple this number by 249 megabytes to get 0.157 * 249 = 39.093 which rounds to 39.1
A continuous random variable X has probability density function X. Show how its
moment generating function can be used to determine the variance of this random
variable.
The moment generating function is defined by
[tex]M_X(t) = \mathbb E[e^{tX}][/tex]
Recall the power series expansion for the exponential function:
[tex]\displaystyle \sum_{n=0}^\infty \frac{x^n}{n!} = 1 + x + \frac{x^2}2 + \frac{x^3}6 + \cdots[/tex]
Then by extension, the MGF could be similarly written as
[tex]\displaystyle M_X(t) = \mathbb E \left[1 + Xt + \frac{(Xt)^2}2 + \frac{(Xt)^3}6 + \cdots\right][/tex]
There's a certain theorem (due to Fubini, in case you're interested in learning more about it) that let's us exchange the order of integration (recall the definition of expectation for continuous random variables) and summation, so that
[tex]\displaystyle M_X(t) = \mathbb E[1] + \mathbb E[Xt] + \mathbb E\left[\frac{X^2t^2}2\right] + \mathbb E\left[\frac{X^3t^3}6\right] + \cdots[/tex]
and by the linearity of expectation,
[tex]\displaystyle M_X(t) = 1 + \mathbb E[X] t + \frac12 \mathbb E\left[X^2\right] t^2 + \frac16 \mathbb E\left[X^3\right] t^3 + \cdots[/tex]
and here we see where the name MGF comes from: the coefficient of the n-th order term in the series expansion "generates" the n-th moment, which is defined as E[Xⁿ].
Now, recall the definition of variance:
[tex]\mathrm{Var}(X) = \mathbb E\left[\left(X - \mathbb E[X]\right)^2\right][/tex]
[tex]\mathrm{Var}(X) = \mathbb E\left[X^2\right] - \mathbb E[X]^2[/tex]
and this is exactly the difference between the second moment and the square of the first moment.
So if you know the MGF, then you essentially get the variance for free with little effort. By differentiating the MGF, we get
[tex]\displaystyle M_X''(t) = \mathbb E[X] + \mathbb E\left[X^2\right] t + \frac12 \mathbb E\left[X^3\right] t^2 + \cdots[/tex]
and setting t = 0 lets us recover the first moment, E[X].
Differentiating again gives
[tex]\displaystyle M_X'(t) = \mathbb E\left[X^2\right] + \mathbb E\left[X^3\right] t + \cdots[/tex]
and setting t = 0 once again recovers the second moment.
Then in terms of the MGF, we have
[tex]\boxed{\mathrm{Var}(X) = M_X''(0) - M_X'(0)^2}[/tex]
Write a function that has the following characteristics:
-Exponential decay
-Asymptote is y = -2
-Shifted left 3 units from the parent function
9514 1404 393
Answer:
y = 0.4^(x+3) -2
Step-by-step explanation:
I have chosen the decay function y=0.4^x as the parent function.
Shifting any function f(x) left 3 and down 2 will transform it to ...
y = f(x+3) -2
So, the shifted parent function is ...
y = 0.4^(x+3) -2
