A particle moves along the x-axis so that its position at time 1 is given by x(t) = t^2 - 6t + 5. For that value of t is the velocity of the particle zero?(A) 1(B) 2(C) 3(D) 4(E) 5
Answers
Position and Velocity
If we are given the function of the position X(t) where t is the time, the velocity function v(t) is the first derivative of X(t).
The position of the particle is given by:
\(X(t)=t^2-6t+5\)The velocity is calculated by finding the first derivative:
\(\begin{gathered} V(t)=X^{\prime}(t) \\ V(t)=(t^2-6t+5)^{\prime} \end{gathered}\)Taking the derivative:
\(V(t)=2t-6\)Now we need to find when the velocity is 0, so we equate the function to 0 and solve for t.
2t - 6 = 0
Adding 6:
2t = 6
Dividing by 2:
t = 3
Answer: (C) 3
Related Questions
Find the equation of the parabola with the following properties. Express your answer in standard form.
Symmetric with respect to the line y = 2
Directrix is the line x = 11
P = -3
Answers
The equation of the parabola with the following properties y = (-1/4)(x+3)^2 -1
What is the equation of the parabola?To find the equation of a parabola, we can use the formula f(x) = ax^2 + bx + c, where a, b and c are congruent vertices.
Alternatively, we can use PF = PM to find the equation of the parabola.
vertex is half way between the focus and directrix
It's a downward opening parabola, general form
y= a(x-h)^2 + k
where (h,k) = vertex= (-3,-1)
plug in another point on the parabola to solve for a which gives
am answer with either x coefficient = -1'/4 or =4 Check the math.
one or the other is right another point is the y intercept = 9a-1
Another point is directly to the right of the focus (-1, -2) It's 2 down from the directrix and 2 to the right of the focus, equidistant. plug that point into y= a(x+3)^2 -1 and solve for "a"
-2 = a((-1+3)^2 -1
-2 = 4a -1
4a = -
a = -1/4
The parabola is y = (-1/4)(x+3)^2 -1
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An aquarium holds 11.35 cubic feet of water, and is 2.6 feet long and 1.1 feet wide. What is its depth? Round your answer to the nearest whole number.
The depth is
feet.
Answers
The depth of the aquarium is approximately 4 feet when rounded to the nearest whole number (since 3.64 is closer to 4 than it is to 3 when rounded to the nearest whole number).
To calculate the depth of the aquarium, we need to use the formula for volume of a rectangular prism,
which is V = lwh where V is the volume, l is the length, w is the width, and h is the height (or depth, in this case).
Given that the aquarium holds 11.35 cubic feet of water, the volume of the aquarium can be represented by V = 11.35 cubic feet.We are also given that the length of the aquarium is 2.6 feet and the width is 1.1 feet.
Substituting these values into the formula for volume,
we get:11.35 = 2.6 × 1.1 × h
Simplifying this expression:
11.35 = 2.86h
Dividing both sides by 2.6 × 1.1,
we get:h ≈ 3.64 feet (rounded to two decimal places)
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Prove the statement below that we explored in class, but prove it differently from the notes, rather do it by applying the “ working backwards” technique:
If x > 0, then x + (1/x) = and > 2
Answers
The solution is, x²-14x+24
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
Given:
x=12, x=2
Solution: In order to determine the quadratic equation we need to move the integers onto the side where x is and then distribute.
Move the integers
Solution #1
x-12 = 0
Solution #2
x-2=0
Create and expression and distribute
(x-12)(x-2)=0
solving we get,
x²-14x+24 = 0
Therefore, after completing the steps we were able to determine that the quadratic equation that will have solutions of x = 12 and x = 2 is x^2 - 14x + 24.
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In the fall semester of 2009, the average Graduate Management Admission Test (GMAT) of the students at a certain university was 500 with a standard deviation of 90. In the fall of 2010, the average GMAT was 570 with a standard deviation of 85.5. Which year's GMAT scores show a more dispersed distribution
Answers
Answer:
Due to the higher coefficient of variation, 2009's GMAT scores show a more dispersed distribution
Step-by-step explanation:
To verify how dispersed a distribution is, we find it's coefficient of variation.
Coefficient of variation:
Mean of \(\mu\), standard deviation of \(\sigma\). The coefficient is:
\(CV = \frac{\sigma}{\mu}\)
Which year's GMAT scores show a more dispersed distribution
Whichever year has the highest coefficient.
2009:
Mean of 500, standard deviation of 90. So
\(CV = \frac{90}{500} = 0.18\)
2010:
Mean of 570, standard deviation of 85.5. So
\(CV = \frac{85.5}{570} = 0.15\)
Due to the higher coefficient of variation, 2009's GMAT scores show a more dispersed distribution
2009's GMAT scores show a more dispersed distribution.
Given that in 2009: Mean = 500 and standard deviation = 90.
In 2010: Mean = 570 and standard deviation = 85.5.
If the standard deviation is higher then the scores will be more dispersed.
Note that: 90 > 85.5. And 90 corresponds to 2009.
So, 2009's GMAT scores show a more dispersed distribution.
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Find the value of x, 6,4, 3x, 4x+1
Answers
Answer:
If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.
6(3x) = 4(4x + 1)
18x = 16x + 4
2x = 4
x = 2
Find the median of the data set. 1470, 1590, 1420, 1215, 1405, 1370, 1465, 1460, 1230
Answers
Answer:
the median is the middle number find the middle number of these and there's your answer
Answer:
1420 is the Median
Step-by-step explanation:
PLEASE PLEASE HURRY What is −12÷2/3? Responses −36 negative 36 −24 negative 24 −18 negative 18 −8 negative 8
Answers
Answer: -18
Step-by-step explanation:
im not 100% sure but good luck :)
Answer: -12/2/3=-2
Step-by-step explanation:
a class of 54 students is divided into equal groups for orientation each group should have at least 7 students but no more than 10 students. What is the group size?
Answers
2 students more were introducced in the class and each group had 8 people
Help me create three polynomials that match the criteria on the left
Answers
Answer:
Symmetry of functions
A function is an even function if its graph is symmetric with respect to the yyy-axis.
Algebraically, fff is an even function if f(-x)=f(x)f(−x)=f(x)f, left parenthesis, minus, x, right parenthesis, equals, f, left parenthesis, x,
Step-by-step explanation:
MARK ME AS A BRAINLIST
if the square is directly proportional to w and z =4 when w =8
Answers
Answer:
when you calculate the value of w is z= 5
Step-by-step explanation:
5. Determine the value of t4 in an arithmetic sequence given that t₁ = 11 and S9 = 243.
Answers
The value of t₄ in the arithmetic sequence is 103/8.To determine the value of t₄ in an arithmetic sequence, we need to use the given information that t₁ = 11 (the first term of the sequence) and S₉ = 243 (the sum of the first 9 terms of the sequence).
We know that the formula for the sum of an arithmetic sequence is Sₙ = (n/2)(2a + (n-1)d), where Sₙ is the sum, a is the first term, n is the number of terms, and d is the common difference.
From the given information, we have S₉ = 243, a = 11, and n = 9. Plugging these values into the sum formula, we can solve for d:
243 = (9/2)(2(11) + (9-1)d)
243 = 9(22 + 8d)
243 = 198 + 72d
45 = 72d
d = 45/72 = 5/8
Now that we have the common difference, we can find t₄ using the formula for the nth term of an arithmetic sequence:
tₙ = a + (n-1)d
t₄ = 11 + (4-1)(5/8)
t₄ = 11 + 3(5/8)
t₄ = 11 + 15/8
t₄ = 88/8 + 15/8
t₄ = 103/8
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someone please answer this its confusing me
Answers
the line AB will be congruent to line DC so 8t + 7 = 9t - 2 which gives you t = 9
line AD will also be congruent to line BC so 4s + 1 = 2s + 25 which gives you s = 12
A tower is 40 ft tall and 20 ft wide. A model of the tower is 5 in. tall. Identify the width of the model in inches.
Answers
Answer:
The width of the model will be 2.5 inches
Step-by-step explanation:
The tower was scaled down by a factor to a smaller size in the model. We are to, first of all, determine this factor and then use it to scale down the width of the model.
Step One: Determine the scale factor from the tower height.
The scale factor is obtained from the formula:
Scale factor = model size / observed size
This will be
Height of model tower/ height of the real tower.
The height of the model tower is 5 inches which is the same as 0.416667 ft
Scale factor = 0.416667 ft/ 40ft = 0.0104
Step two: Multiply the width of the real-life tower by the scale factor to get the model width.
Width of model =20ft X 0.0104 = 0.208ft
Step three: Convert your answer back to inches.
We will now have to convert 0.208 ft back to inches by multiplying by 12
This will be 0.208 X 12 =2.5 inches.
The width of the model will be 2.5 inches
Jen solved the equation 100 minus one-half x equals 92 to determine the number of questions, x, she answered incorrectly on a test. She began by subtracting 100 from both sides, then multiplying both sides by –2. Which best describes the accuracy of Jen’s work?
Incorrect. She needed to add 100 to both sides instead of subtracting 100.
Incorrect. She needed to multiply both sides by –2 first, then subtract 100.
Correct. She could have also subtracted 100 from both sides, then divided by Negative one-half.
Correct. She could have also multiplied both sides by –2 first, then subtracted 100
Answers
Answer:
Correct. She could have also subtracted 100 from both sides, then divided by Negative one-half.
Step-by-step explanation:
Answer:
Option C is the correct answer.
There are 220 students in the middle school. If 60% chose pizza for lunch, how many students chose pizza? Which is the correct proportion to solve if set up as p/w = %/100% *
Answers
I would say 100 kids. I may not be right
Randy is starting a beehive so that he can have fresh
honey. He decides to check the current population of bees
in the hive by marking 160 bees. Later, Randy collects 240
bees and observes that 30 of them are marked. What is the
BEST estimate for the bee population?
Answers
Answer:
1,280
Step-by-step explanation:
A rectangular piece of paper is 44 cm long and 20 cm wide. A cylinder is forms by rolling the paper along its length. Find its volume
ASAP ⠀⠀⠀⠀⠀⠀⠀
Answers
Answer:
3081.24 cm³ (nearest hundredth)
Step-by-step explanation:
Formulas
\(\textsf{Circumference of a circle}=\sf 2 \pi r\quad\textsf{(where r is the radius)}\)
\(\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}\)
If a rectangular piece of paper is rolled along its length to form a cylinder:
circumference = 44 cmheight = 20 cmTo calculate the volume of the formed cylinder, determine the radius by using the circumference formula:
\(\implies \sf 2 \pi r = 44\)
\(\implies \sf r = \dfrac{44}{2 \pi}\)
\(\implies \sf r =\dfrac{22}{\pi}\)
Substitute the round radius into the formula for Volume and solve for V:
\(\implies \sf V=\pi \left(\dfrac{22}{\pi}\right)^2(20)\)
\(\implies \sf V=\pi \left(\dfrac{484}{\pi^2}\right)(20)\)
\(\implies \sf V=\left(\dfrac{484}{\pi}\right)(20)\)
\(\implies \sf V=\dfrac{9680}{\pi}\)
\(\implies \sf V=3081.239698...cm^3\)
Therefore, the volume of the cylinder is 3081.24 cm³ (nearest hundredth).
On a road trip, a family drives 350 miles per day. How many days, d, must they travel to reach a distance of at least 1400?
Solve the inequality. What does the solution represent in this situation?
Activate Window
Answers
Answer:
350d ≥ 1400
Hope it helps
Calculate the value for the for the following scores 20, 60, 30, 50 given:
begin inline style begin display style sum for blank of end style end style x squared =
Answers
The sum of the scores is equal to 160.
What is a mean?In Mathematics, a mean is sometimes referred to as an average and it can be defined as a ratio of the sum of the total number in a data set (population) to the frequency of the data set.
How to calculate the mean for a data set?Mathematically, the mean for this set of scores can be calculated by using the following formula:
Mean = [F(x)]/n
For the total number of scores (data set), we have;
∑x = 20 + 60 + 30 + 50
∑x = 160.
Mean = [F(x)]/n = 160/4 = 40.
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Jayda is older than her 12-year-old sister. Write an inequality for j, Jayda's age.
Answers
The inequality states that Jayda's age (j) is greater than 12 i.e., j > 12.
Let j represent Jayda's age.
Since Jayda is older than her 12-year-old sister, we can write the inequality:
j > 12
Thus, the inequality states that Jayda's age (j) is greater than 12.
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prove that √2 is not a rational number
Answers
Answer:
Because we started the whole process assuming that a/b was simplified to lowest terms, and now it turns out that a and b both would be even. We ended at a contradiction; thus our original assumption (that √2 is rational) is not correct. Therefore √2 cannot be rational.
Step-by-step explanation:
Graciana sold 36 books at £5.20 each, 26 candles at £1.50 each and some pencils at 90p each. She got a total of £244.20. How many pencils did Graciana sell?
Answers
Answer:
20 pencils
Step-by-step explanation:
36*£5.20 = £187.20
26*£1.50 = £39
£187.20+£39 = £226.2
£244.20 - £226.2 = £18
£18÷£0.90 = 20
Answers and step by step explanations please?(Just one example)
Answers
Louis is a pizza delivery driver. He made $72 in tips on Friday night, and earns an hourly wage of $4. Create an equation to represent his earnings.
Answers
Step-by-step explanation: The keyword is hourly. Since the keyword is hourly, the equation is division.
72 / 4
1. 4 goes into 7 once.
1a. 72 / 4 = 1
2. Now we multiply 4 by 1.
2a. 4 x 1 = 4
3. Now, we subtract 7 by 4.
3a. 7 - 4 = 3
4. Now bring down the 2.
4a. 3 = 32
5. Then you repeat the process!
We'll do the last one step-by-step!
1. 2 goes into 4, 8 times.
1a. 72 / 4 = 18
2. Multiply 8 by 4.
2a. 8 x 4 = 32
3. Lastly, subtract 32 by 32.
32 - 32 = 0
Therefore, your answer is 18 R0.
The sum of three times the number n and 6 is, at most, the difference between the number n and 5.
Answers
Step-by-step explanation:
3n+6≤n-5
2n≤-11
n≤-5.5
27L 600mL divided by 6
Answers
Answer:
4 L 600 mL
Step-by-step explanation:
1 L = 1000 mL
so 27 L 600 mL = 27000 + 600 = 27600 mL
27600/6 = 4600 mL
4 L 600 mL.
ANSWER ASAP DONT SEND A FILE. IS THIS SHAPE A ROTATION, REFLECTION,TRANSLATION, DILATION OR NONE????
Answers
Answer:
translation
Step-by-step explanation:
Answer:
I think it's dilation or none
Step-by-step explanation:
Find missing side lengths
Answers
Answer:
\(y=30\sqrt{2}\)
Step-by-step explanation:
\(In\)Δ\(ABC\)
\(tan45=AB/BC\)
\(1=30/BC\) \([tan45=1]\)
\(-------\\BC=30 \\-------\) ⇒ \(OC=30\\\)
\(and\) \(In\) Δ\(ABC\)
\(Cos45=Bc/AC\)
\(1/\sqrt{2} =x/y\)
\(y=\sqrt{2}*x\)
\(y=30\sqrt{2}\)
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hope it helps....
have a great day!!
1 5 1 15 20 25 1 30 O 10 1 35 40 45 50 55 60 Which of the following represents the Inter-Quartile Range of data? O A 26 O B. 50 O c. 56 OD. 10 O E. 16
Answers
1) Enlisting the data orderly
1 5 1 15 20 25 1 30 O 10 1 35 40 45 50 55 60
1 1 5 15
Which statement compares the product 9/9 x 5,208, the product 19/20 x 5,208, and the product 13/6 x 5,208?
Answers
Answer:
C
Step-by-step explanation:
\(\frac{9}{9}=1\)
\(1=\frac{20}{20}\)
\(\frac{19}{20} <\frac{20}{20}\)
\(\frac{13}{6}=2\frac{1}{6}\)
\(1<2\frac{1}{6}\)