![[Calculus] Analyze Speed From Position. Show Steps, Please!](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/gCgOoPWUwNE8bqF9RxD2quz4Sorj2E63.png)
Answers
Answer:
B
Step-by-step explanation:
We are given that the position of a particle is modeled by the function:
[tex]s(t)=2t^3-24t^2+90t+7[/tex]
And we want to find the times for which the speed of our particle is increasing.
In other words, we want to find the times for which our acceleration is positive (a(t)>0).
So first, we will find our acceleration function. We can differentiate twice.
By taking the derivative of both sides with respect to t, we acquire:
[tex]\displaystyle s^\prime(t)=v(t)=\frac{d}{dt}\big[2t^3-24t^2+90t+7\big][/tex]
Differentiate:
[tex]v(t)=6t^2-48t+90[/tex]
This is our velocity function. We can differentiate once more to acquire the acceleration function. Therefore:
[tex]\displaystyle v^\prime(t)=a(t)=\frac{d}{dt}\big[6t^2-48t+90\big][/tex]
Differentiate:
[tex]a(t)=12t-48[/tex]
If our speed is increasing, our acceleration must be positive. So:
[tex]a(t)>0[/tex]
By substitution:
[tex]12t-48>0[/tex]
Now, we can solve for t:
[tex]12t>48\Rightarrow t>4[/tex]
Therefore, the only interval for which the speed of the particle is increasing (i.e. the acceleration is positive) is for all times t>4.
So, our answer is B.
Related Questions
Help me out here, I'll give brainlist for explanation.
Answers
Answer:
See below.
Step-by-step explanation:
This is focusing on the order of operations.
PEMDAS = Parenthesis, exponents, multiplication, division, addition, subtraction.
40 ÷ [(18 - 9) - (13 - 12)]
40 ÷ [9 - 1]
40 ÷ 8
5
[(13 - 9) · 3] + [(14 - 8) · 2]
[4 · 3] + [6 · 2]
12 + 12
24
One year, the population of a city was 359,000. Several years later it was 355,410. Find the percent decrease.
Answers
Answer:1%
Step-by-step explanation:
Find the zeros of the function and state the multiplicities.
f(x)= -6x^3+26x^2-28x
Answers
Answer:
X=0 {multiplicity of 1}
X=2 {multiplicity of 1}
X=7/3 {multiplicity of 1}
Step-by-step explanation:
Given the relative frequency table below, which of the following is the corresponding cumulative relative frequency table?
Value
Relative Frequency
3
0.04
4
0.4
5
0.12
6
0.24
7
0.2
Answers
The required cumulative relative frequencies are 0.04, 0.44, 0.56, 0.80, and 1 respectively.
What is the relative frequency of the data?The relative frequency of the data is the ratio of the given frequency to the total frequency in the observation.
From the given data,
Relative frequency = given frequency / total frequency
Where total frequency = 0.04 + 0.4 + 0.12 + 0.24 + 0.2 = 1
Value Relative frequency Cumulative frequency
3 0.04/1 = 0.04 0.04
4 0.4/1 = 0.4 0.04 + 0.4 = 0.44
5 0.12 0.44 + 0.12 = 0.56
6 0.24 0.56 + 0.24 = 0.80
7 0.2 0.80 + 0.2 = 1
Thus the required cumulative relative frequencies are 0.04, 0.44, 0.56, 0.80, and 1 respectively.
Learn more about the relative frequency here:
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You and your friend are playing a game with the spinner below. The first player spins. Then the second player spins. The second player wins if he or she lands on the same number as the first player does, If not, the first player wins. What is the probability that the second player will win?
Answers
Answer:
2
Step-by-step explanation:
2
pls answer asap don’t troll and explain why !!
Answers
Answer:
I need help on this same question---_---
yes.
a triangle just needs to have three sides that connect at their ends nothing more
Find the missing angle.
Answers:
40
70
120
110
Please help
Answers
Answer:
65 + 45 + X = 180
110 + X = 180
X = 180 - 110
X = 70°
that means the other angle in the triangle is 70°
then to find the angle on a straight line
70 + y = 180
collect like terms
y = 180 - 70
y = 110°
that means the angle with the question mark is 110°
hope it helps
Please help me answer this :)
Explain your answer
Will give brainiest
Answers
Answer:
A AAAAAAA
Step-by-step explanation:
Please help me solve this challanging question 9 (step by step sulotion) 50 points!
Answers
9514 1404 393
Answer:
10
Step-by-step explanation:
Let L and T represent the initial amounts that Leo and Theo had. Let n represent the number of bills exchanged in the first exchange. Then we have ...
L -20n +50n = T -50n +20n . . . . after the first exchange, each has the same
After the second exchange, amounts trade places:
(L +30n) +6(50) = T
Substituting this into the first equation, we get ...
L +30n = ((L +30n) +300) -30n
30n = 300
n = 10
Leo gave Theo ten $20 bills.
_____
Comment on the amounts
Theo started with $600 more than Leo, including exactly 16 $50 bills. Leo had at least 10 $20 bills, so he could make the initial exchange. Whatever initial amount Leo had in excess of that $200 was matched in Theo's initial amount, but Theo must have had that excess in $20 bills only. For example, Leo may have started with $300 as 10×$20 +2×$50, but Theo's initial $900 would need to be 5×$20 +16×$50.
A spinner has three unequal sections: red, yellow, and blue. The table shows the results of Nolan's spins.
Find the experimental probability of landing on each color. Enter your answers as simplified fractions.
Color
Red: 13
Yellow: 10
Blue: 5
Frequency
The probability of landing on red is
The probability of landing on yellow is
The probability of landing on blue is
Answers
yellow 10
blue 5
What is the answer to this equation?
Answers
Answer:
OQ = 12
Step-by-step explanation:
PQ + OP = OQ
x + 7 + 4x - 10 = 4x
5x - 3 = 4x
x = 3
OQ = 4x = 4(3) = 12
PLEASE ANSWER GIVING 30 POINTS
Answers
Answer:
this is only 15points but ok
Step-by-step explanation:
answer: D)
Answer:
The answer should be 15.
Step-by-step explanation:
[tex]\sqrt[3]{125}[/tex] Factor 125 = [tex]5^{2}[/tex] x 5. Rewrite the square root of the product [tex]\sqrt{5^{2}X5 }[/tex] as the product of square roots. [tex]\sqrt{5^{2} }[/tex] [tex]\sqrt{5}[/tex]. Take the square root of [tex]5^{2}[/tex].
[tex]3[/tex] x [tex]\sqrt[5]{5}[/tex] Multiply 3 and 5 to get 15.
[tex]\sqrt[15]{5}[/tex]
Jenn is preparing brown rice. She needs 1 1 2 cups of brown rice and 2 cups of water. Jenn has only a 1 8 -cup measuring cup. How many 1 8 -cups each of rice and water will Jenn use to prepare the rice?
Answers
Answer:
She will need 12 1/8 cups of brown rice and 16 1/8 cups of water.
Step-by-step explanation:
You will want to convert 1 1/2 cups into an improper fraction, as well as 2 cups.
1 1/2 = 3/2
2 = 2/1
Now that you have done that you will then have to find a common denominator. You will need to list the multiples for 8 and lowest common factor so you don't have to simplify at the end.
The multiples of 8: 1, 2, 4, and 8
As shown above 2 is a multiple of 8. Therefore you will need to multiply the denominator by 4. This is because 2 x 4 equals 8. So now the denominator is 8. You will now need to multiply the numerator by 4 because that is what you multiplied the bottom by. It will be 3 x 4, and will therefore equal 12. The final improper fraction will be 12/8. The numerator then becomes the answer because that is the amount of 1/8 cups that you will need.
You then repeat this with 2/1. However you will need to multiply the denominator by a different number because it is 1. Looking at the multiples of 8 above, you will multiply the 1 by 8, therefore giving you 8 as the denominator. You will then multiply the numerator by 8 as well. This will result in an answer of 16. You will then have a 16/8. You will need 16 1/8 cups of water.
A rectangle is 27 in tall and 18 in wide. If
it is reduced to a height of 3 in, then how
wide will it be?
Answers
Answer: 2in
Step-by-step explanation: 27 divided by 3 is 9, then 18 divided by 9 is 2
Samantha usually makes lemonade with 8 cups of water and 3/4 cup of sugar. For today's picnic, she wants to make 28 cups of lemonade. How much sugar does she need? Show all of your work.
Answers
Answer:
21 cups of sugar
Step-by-step explanation:
3/4 x 28 = 21
What is the exponential expression for the numerical expression 3⋅3⋅3⋅3 ? 43 4⋅34 124 34
Answers
can you help me please I don't understand.
Answers
B. A and b parrel never touch
C. 44
D.136
E.44
Hope this helps a little
What is the difference of
(x-3)-(+24)
5 1
--X+
6
A
5
1
-
4
6
0
11
4
+
1
6
1
11
x
4
6
Answers
Step-by-step explanation:
[tex](x-3)-(+24) = 0 \\ x - 3 - 24 = 0 \\ x - 27 = 0 \\ x = 27[/tex]
Answer: 27
Step-by-step explanation: ..
Solve for X using this system of equations. Then just explain what you would do to solve for Y.
2Y + 2X = 10
Y = 1 + X
Answers
2+2x+2x=10
4x=10-2
4x=8. /:4
x=2
y=1+2
y=3
In 2nd u know y it says y= and then u put it in the 1st one
solve the problem if correct you get brainliest answer.
Answers
Answer:
a= 3
b = -6
c = -1
Step-by-step explanation:
Let's start by expanding, since the original is not in a condensed form.
3(x-1)² - 4
3(x-1)(x-1) - 4
(x-1)(x-1) = x²-2x+1
3(x²-2x+1) - 4
3x²-6x+3-4
3x²-6x-1
a= 3
b = -6
c = -1
Points and Klie on the same line, as shown on the coordinate plane below.
Answer ALL 3 questions. You can type your answers in the box or upload pictures of our work
A) What is the slope of the line passing through points J and K! Show or explain all your work ,
Answers
9514 1404 393
Answer:
1/2
Step-by-step explanation:
The slope can be found from the slope formula:
m = (y2 -y1)/(x2 -x1)
m = (5-3.5)/(6 -3) = 1.5/3 . . . . from the marked points
m = 1/2
The slope of the line through J and K is 1/2.
Can someone help me find the number to complete the square?
Answers
Answer:
this equation cannot be solved by completing the square
Step-by-step explanation:
problems; e.g. 200 bottles of equal capacity hold 350 litres of water.
How much water does each bottle hold?
Answers
Each bottle holds 1.75 liters of water.
To determine how much water each bottle holds, we can divide the total amount of water by the number of bottles.
Given that 200 bottles hold 350 liters of water, we divide 350 liters by 200 bottles:
350 liters / 200 bottles = 1.75 liters per bottle
Therefore, each bottle holds 1.75 liters of water.Therefore, each bottle holds 1.75 liters of water.
This means that if we were to fill each bottle to its maximum capacity, it would hold 1.75 liters of water.
It's important to note that this assumes each bottle has an equal capacity and that the water is evenly distributed among them.
for such more question on amount
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helsea is graphing the function f(x) = 20(One-fourth)x. She begins by plotting the initial value. Which graph represents her first step? On a coordinate plane, the point (0, 0.25) is graphed. On a coordinate plane, the point (0.25, 0) is graphed. On a coordinate plane, the point (0, 20) is graphed. On a coordinate plane, the point (20, 0) is graphed.
Answers
Answer:
C
Step-by-step explanation:
have trust
You have only one question today How tall was the statue of Hercules if the first and second knuckle of his index finger
Answers
Answer:
Thanks!
Step-by-step explanation:
Answer:
The thumb digit has only two phalanges (bones) so it only has one joint. The index finger is more likely to develop arthritis from the pinch force that.The PIP joint is the first joint of the finger and is located between the first two bones of the finger
Step-by-step explanation:
I NEED HELP ASAP!!!!!
Answers
Answer:
Graph and solutions attached
Step-by-step explanation:
what number is 0.001 more than 437.999
Answers
Answer:
437.999 + 0.001 = 438
Step-by-step explanation:
PLS HELP❗️❗️❗️❗️❗️❗️.
Answers
Answer:
9(p-2)(p-4)
Step-by-step explanation:
For integers a, b and k, we know that a >12, b > 20 and a < b. If b=7k, what is the value of k ?
Answers
This question is incomplete, the complete question is;
For integers a, b and k, we know that a > 12, b < 20 and a < b. If b=7k, what is the value of k ?
Answer: the value of k = 2
Step-by-step explanation:
Given that;
a > 12
b < 20
a < b
If b = 7k
Now if k = 1 {b = 7k = 7}
b would be equal to 7 but b has to be greater than 20
IT CANT BE
if k = 2 { b = 7k = 14}
b would be equal to 14, a is greater than 12, b has to be less than b; 14 < 20,
a has to be less than than b ( 12 < 14 )
IT IS
if k = 3 {b = 7k = 21}
b would be equal to 21, so b is greater than 20 and a is less than 21
IT CANT BE
Therefore the value of k = 2
Jessica has a rectangular picture. the picture is similar to a rectangle that measures 4 inches by 6 what could be the dimensions of Jessica's picture?
Answers
Answer:
wheres the picture
Step-by-step explanation: