2) Object #l's position is given by s1(t) = 2/3t^3 – 2t^2 + 5t + 105. Object #a's position is s2(t)= 3/2t^2 – t – 11/2. (both positions are in metres and time is in seconds). When do the two objects have the same velocity?
Answers
The two objects have the same velocity at t = 3/2 seconds and t = 2 seconds.
To find when the two objects have the same velocity, we need to equate their velocity functions. First, find the derivatives of their position functions:
Object #l: s1(t) = 2/3t^3 - 2t^2 + 5t + 105
s1'(t) = 2t^2 - 4t + 5
Object #a: s2(t) = 3/2t^2 - t - 11/2
s2'(t) = 3t - 1
Now, set their velocities equal to each other and solve for t:
2t^2 - 4t + 5 = 3t - 1
Rearrange the equation:
2t^2 - 7t + 6 = 0
Factor the equation:
(2t - 3)(t - 2) = 0
The solutions are t = 3/2 and t = 2. So, the two objects have the same velocity at t = 3/2 seconds and t = 2 seconds.
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Related Questions
Find the equation of the line that goes through (-8,11) and is perpendicular to x= - 15. Write the equation in the form x = a, y = b, or y = mx + b.
The equation is
(Type the equation using integers or fractions. Simplify your answer.)
Answers
Answer:
y=11
Step-by-step explanation:
Hi there!
We want to find the equation of the line that passes through the point (-8, 11) and is perpendicular to x=-15
If a line is perpendicular to another line, it means that the slopes of those lines are negative and reciprocal; in other words, the product of the slopes is equal to -1
The line x=-15 has an undefined slope, which we can represent as 1/0, which is also undefined.
To find the slope of the line perpendicular to x=-15, we can use this equation (m is the slope):
\(m_1*m_2=-1\)
\(m_1\) in this instance would be 1/0, so we can substitute it into the equation:
\(\frac{1}{0} *m_2=-1\)
Multiply both sides by 0
\(m_2=0\)
So the slope of the new line is 0
We can substitute it into the equation y=mx+b, where m is the slope and b is the y intercept:
y=0x+b
Now we need to find b:
Since the equation passes through the point (-8,11), we can use its values to solve for b.
Substitute -8 as x and 11 as y:
11=0(-8)+b
Multiply
11=0+b, or 11=b
So substitute into the equation:
y=0x+11
We can also write the equation as y=11
Hope this helps!
Jamilla solved the inequality x+ b2 and graphed the solution as shown below. 6 5 4 3 -2 -1 0 1 2 3 4 5 6 What is the value of b and the missing symbol in Jamilla's inequality? Ob=-1,2 O b=-1, s O b = 1,2 O b= 1, g
Answers
The inequality solved to give a solution of x ≥ 1 and x ≤ -3 is |x + 1| ≥ 2.
b = 1, ≥
From the diagram, the solution to the inequality is x ≥ 1 and x ≤ -3
Hence:
|x + b| ≥ 2
x + b ≥ 2 or -(x + b) ≥ 2
x ≥ 2 - b or x ≤ -2 - b
2 - b = 1 and -2 - b = -3
b = 1
Hence |x + 1| ≥ 2
The inequality solved to give a solution of x ≥ 1 and x ≤ -3 is |x + 1| ≥ 2. b = 1, ≥
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Your cousin earns $9.25 an hour at work. Last week she earned $222.00 How many hours did she work last week?
1
F
hour
5
G. 92 hours
OH 24 hours
1. 212.75 hours
Answers
For the supply equations, where X is the quantity supplied in units of a thousand and P is the unit price in dollars,
a. Sketch the supply curve,
b. Determine the price at which the supplier will make 2000 units of the commodity available in the market.
P = x2 + 16x + 40
Answers
b. the price at which the supplier will make 2000 units available in the market is $76.
To sketch the supply curve, we need to determine the relationship between quantity supplied (X) and price (P). The supply equation P = \(x^{2}\) + 16x + 40 represents a quadratic equation. By selecting different values for X and solving for P, we can plot the corresponding points on a graph to visualize the supply curve. We can choose various values for X, such as 0, 1, 2, 3, and so on, and calculate the corresponding values of P using the supply equation. Connecting these points will give us the shape of the supply curve.
To determine the price at which the supplier will make 2000 units available, we substitute X = 2 into the supply equation P = \(x^{2}\) + 16x + 40 and solve for P. By substituting X = 2, we have P = 4 + 16(2) + 40 = 4 + 32 + 40 = 76.
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Based on the only info given it is guaranteed that AD = CD true or false
Answers
Answer:
Can we have a picture or more information, please? Thanks!
Step-by-step explanation:
Matthew wants to take out a loan to buy a car. He calculates that he can make repayments of $35,000 per year. If he can get a six-year loan with an interest rate of 9.25%, what is the maximum price he can pay for the car?
Answers
The maximum price Matthew can pay for the car, considering his repayment capability and the loan terms, is approximately $126,318.29.
To determine the maximum price Matthew can pay for the car, we need to consider his repayment capability and the terms of the loan.
Matthew can make annual repayments of $35,000. Since the loan term is six years, the total amount he can repay over the loan period is $35,000 multiplied by six, which equals $210,000.
To calculate the maximum price of the car, we need to account for the interest rate of 9.25%. The interest rate represents the cost of borrowing and is applied to the loan amount.
Let's assume the loan amount is denoted by P.
The formula to calculate the future value of a loan with interest is:
FV = P(1 + r)^n
Where:
FV = Future value (total amount repaid)
P = Principal amount (maximum price of the car)
r = Interest rate per period (9.25% or 0.0925)
n = Number of periods (six years)
Since Matthew can repay a total of $210,000 over the loan period, we can set up the equation:
$210,000 = P(1 + 0.0925)^6
Now we can solve for P:
P = $210,000 / (1 + 0.0925)^6
Evaluating this expression, we find:
P ≈ $126,318.29
Therefore, the maximum price Matthew can pay for the car, considering his repayment capability and the loan terms, is approximately $126,318.29.
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"The sum of 5% of a number and 9 is 16."
translate the question for me!!
Answers
Answer:
x = 140
Step-by-step explanation:
5% = 5/100 = 0.05
0.05x + 9 = 16
0.05x = 16-9
x = 7/0.05
x = 140
Jeff's preferences can be represented by the following utility function U = In x + In y.
a. What is Jeff's demand function for good x? If Px = 1, Py=2 and W = 200, how much x does he consume?
b. If Px increases to 2, calculate the compensating variation.
c. Calculate the total effect, the substitution effect and the income effect of the price change.
Answers
After considering the given data we conclude that the answer for the sub questions are
a) Jeff consumes 33.33 units of good x.
b) the compensating variation is:
\(CV=W'-W=2(50)-200=-100CV\)
c) The income effect is negative, indicating that Jeff will consume less of good x due to the decrease in purchasing power caused by the price increase.
a. To find Jeff's demand function for good x, we can use the following equation:
\(\frac{\partial U}{\partial x}=\frac{1}{x}=\frac{p_x}{p_y}=\frac{1}{2}\)
Solving for x, we get:
\(x=\frac{1}{2}y\)
Substituting the given values, we get:
\(x=\frac{1}{2}(200/3)=33.33\)
Therefore, Jeff consumes 33.33 units of good x.
b. If Px increases to 2, the new demand function for good x is:
\(x'=\frac{1}{2}y'\)where y' is the amount of good y consumed at the new prices and income. To find the compensating variation, we need to find the amount of income Jeff would need at the original prices to achieve the same level of utility as he does at the new prices. We can use the following equation:
\(W'=W+CV\) where W is the original income, W' is the new income, and CV is the compensating variation.
Substituting the given values, we get:
\(8.51=\ln(33.33)+\ln(66.67)8.51=ln(33.33)+ln(66.67)\)
\(y'=\frac{W'}{2}\)
\(x'=\frac{1}{2}y'\) Solving for y', we get:
y'=100
Solving for x', we get:
x'=50
Therefore, the compensating variation is:
\(CV=W'-W=2(50)-200=-100CV\)
c. To calculate the total effect, substitution effect, and income effect of the price change, we can use the following equations:
\(TE=\frac{\Delta U}{U_0}\)
\(SE=\frac{\Delta x_s}{x_0}\)
\(IE=\frac{\Delta x_i}{x_0}\)where \(\Delta U\)is the change in utility, \(U_0\) is the initial utility,\(\Delta x_s\) is the change in consumption due to the substitution effect, \(x_0\) is the initial consumption, and \(\Delta x_i\) is the change in consumption due to the income effect.
The change in consumption due to the price change can be calculated as:
as:
\(\Delta x=x'-x_0=\frac{1}{2}y'-\frac{1}{2}y_0\)
where \(y_0=2x_0\) and \(y'=2x'\)
Substituting the given values, we get:
\(\Delta x=x'-x_0=50-33.33=16.67\)
The substitution effect can be calculated as:
\(SE=\frac{\Delta x_s}{x_0}=\frac{x_s'-x_0}{x_0}=\frac{1}{2}\frac{y_0-y_s'}{x_0}=\frac{1}{2}\frac{p_x}{p_y}\frac{y_0}{x_0}\)
Substituting the given values, we get:
\(SE=\frac{1}{2}\frac{1}{2}\frac{2x_0}{4x_0}=\frac{1}{4}\)
The income effect can be calculated as:
\(IE=\frac{\Delta x_i}{x_0}=\frac{\Delta W}{W_0}=\frac{CV}{W_0}\)
Substituting the given values, we get:
\(IE=\frac{-100}{200}=-0.5\)
The total effect can be calculated as:
\(TE=SE+IE=\frac{1}{4}-0.5=-0.25\)
Therefore, the total effect of the price change is negative, indicating that Jeff will consume less of good x as a result of the price increase. The substitution effect is positive, indicating that Jeff will consume more of good x due to the relative price change. The income effect is negative, indicating that Jeff will consume less of good x due to the decrease in purchasing power caused by the price increase.
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Which of these is an Irrational number?
А
4.789
В
6.66666...
С
3.14159...
D
7.00000001
Answers
Answer:
the anser and the
Step-by-step explanation:
Answer:
If im wrong just say but i think it B
Step-by-step explanation:
Two cups of coffee are heated to 100 degrees fahrenheit. Cup 1 is then heated an additional 20 degrees centigrade, cup 2 is heated an additional 20 kelvin. Which cup of coffee is hotter?.
Answers
According to the final temperature for each case, the two cups of coffee have the same final temperature.
Which one of two cups is hotter?
In this question we have the case of two cups of coffee that are heated at two different temperatures, one in degrees centigrade and other in Kelvin, after being at the same temperature, both in degrees in Fahrenheit. According to the definitions of the three temperature scales, the following relationship in temperature changes is shown:
Δ °F = (9 / 5) Δ °C = (9 / 5) Δ K
Then, the final temperature of each cup of coffee is now determined:
Cup 1
T₁ = 100 °F + (9 / 5) · (20 ° C)
T₁ = 136 °F
Cup 2
T₂ = 100 °F + (9 / 5) · (20 K)
T₂ = 136 °F
Since T₁ = T₂, then the two cups of coffee have the same final temperature.
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You look over the songs in a jukebox and determine that you like 14
of the 53 songs.
(a) What is the probability that you like the next four songs that are played? (Assume song cannot be repeated.)
(b) What is the probability that you do not like the any of the next four songs that are played? (Assume song cannot be repeated.)
Answers
The probability that all four songs are liked will be 0.03418 and the probability of not liking the next four songs will be 0.99658.
What is probability?The probability of an event occurring is defined by probability.
Probability is also called chance because if you flip a coin then the probability of coming head and tail is nothing but chances that either head will appear or not.
As per the given,
Total songs = 53
Like songs = 14
Probability of selecting and liking the first song = 14/53
Now since repetition is not allowed and one like the song has been chosen out of 14 thus, the remaining songs = 13, and total songs = 43 - 1 = 52
Probability of selecting liking the second song = 13/52
Probability of selecting liking the third song = 12/51
Probability of selecting liking the fourth song = 11/50
a)
The probability of liking all songs will be 14/53 x 13/52 x 12/51 x 11/50 = 0.03418.
b)
The probability of not liking the next four songs =1 - The probability of liking all songs
The probability of not liking the next four songs = 1 - 0.03418 = 0.96582.
Hence "The probability that all four songs are liked will be 0.03418 and the probability of not liking the next four songs will be 0.99658".
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What is an equation for the line that passes through (6,-5) and (-8,16)
Answers
Answer:
y=mx
Step-by-step explanation:
i think thats the equation am pretty sure tho
Show that the set S = {n/2^n} n∈N is not compact by finding a covering of S with open sets that has no finite sub-cover.
Answers
To show that the set S = {n/2^n : n ∈ N} is not compact, we need to find a covering of S with open sets that has no finite subcover. In other words, we need to demonstrate that there is no finite collection of open sets that covers the set S.
Let's construct a covering of S:
For each natural number n, consider the open interval (a_n, b_n), where a_n = n/(2^n) - ε and b_n = n/(2^n) + ε, for some small positive value ε. Notice that each open interval contains a single point from S.
Now, let's consider the collection of open intervals {(a_n, b_n)} for all natural numbers n. This collection covers the set S because for each point x ∈ S, there exists an open interval (a_n, b_n) that contains x.
However, this covering does not have a finite subcover. To see why, consider any finite subset of the collection. Let's say we select a subset of intervals up to a certain index k. Now, consider the point x = (k+1)/(2^(k+1)). This point is in S but is not covered by any interval in the finite subcover, as it lies beyond the indices included in the subcover.
Therefore, we have shown that the set S = {n/2^n : n ∈ N} is not compact, as there exists a covering with open sets that has no finite subcover.
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If a circle has a diameter if (x+3) inches what is its circumference
Answers
Answer:
π (x + 3) inch OR 3.14x + 9.42 inch
Step-by-step explanation:
Diameter (d) = x + 3
Circumference of a circle = πd
=》Circumference of a circle = π (x + 3) inch
If π = 3.14, then,
Circumference = 3.14 (x + 3)
Circumference = 3.14x + 9.42 inch
Hope it helps ⚜
100 points + brainliest for answering correctly, show the work:
(((2367^2 times 12) / -6) - 186734) + ((568531 + 1376^3) times 30)
Answers
so (2367^2•12)=6.7•10^7
The multiply by 12 results to 8.1•10^8
Then divide by (-6) which is -1.3•10^8
You subtract to 186734–> doesnt change anything
On the other side there is
((568531+(1376)^3)=2.6•10^9
Multiply to 30 you get 7.8•10^10
Add those 2 pieces together and bam
7.8•10^10
Answer:
7816422510
Step-by-step explanation:
(((5602689*12)/-6) - 186734) + ((568531+2605285376)*30)
((67232268/-6) - 186734) + (2605853907*30)
( -11205378 - 186734) + 78175617210
−11392112 + (78175617210)
= 7816422510
Last Friday Kali had $22.62. Over the weekend she received some money for cleaning the attic. She now has $33.99. How much money did she receive?
Answers
To find the answer, all you need to do is subtract 22.62 from 33.99. Remember that you need to line up the decimals, or else you will not get the right answer.
33.99
22.62
———
11.37
Bradley Wiggins cycles 2.5km on a warm up. If the diameter of Bradley's bike wheel is 68cm, how many times (to the nearest whole rotation) will Bradley's bike wheel have rotated on this journey?
Answers
Answer:
1171 rotations
Step-by-step explanation:
Given that:
Distance cycled = 2.5km
Diameter of bike wheel, d = 68cm = 0.68m
We obtain the Circumference of the bike wheel:
Circumference, C = πd
C = 3.14 * 0.68
C = 2.1352 m
The number of rotations Bradley's wheel will make will be :
Total distance cycled / Circumference
= (2.5 *1000)m / 2.1352m
= 2500 / 2.1352
= 1170.8505
= 1171 rotations
if an iPad is on sale for $450 and it was originally $500, what was the discount percent?
Answers
Answer:
Step-by-step explanation:
10%
Answer:
It is 90% off.
Step-by-step explanation:
450 / 500 = 0.9
0.9 = 90%
a school district wants to justify building a new elementary school in the district because it believes that the expected number of students will start to exceed the capacity of the schools in the district. which statistical method would be most appropriate? group of answer choices binomial distribution confidence interval hypothesis test regression analysis
Answers
The answer is that regression analysis is the most appropriate method.
The most appropriate statistical method to justify building a new elementary school in the district would be regression analysis. This method can be used to examine the relationship between the expected number of students and the capacity of the schools in the district.
Regression analysis is a statistical method that helps to determine the relationship between two or more variables. In this case, the expected number of students would be the independent variable, while the capacity of the schools in the district would be the dependent variable. By analyzing the relationship between these variables, the school district can make predictions about how many students will need to be accommodated in the future and whether a new elementary school is necessary.
In contrast, binomial distribution is a statistical method that is used to calculate the probability of a specific number of successes in a set of trials, which would not be suitable for this situation. Confidence intervals and hypothesis tests are statistical methods used to draw conclusions about populations based on sample data, but may not be the most appropriate method for this situation.
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need help plssss!!!!
Answers
should I call 911 !!!!!!!!!!!!!!
Algebra 2 - Grade 11
Can anyone please help me soon as possible?
Use synthetic substitution to find f(–3) and f(4) for each function.
f(x) = x^2 – 5x + 10
f(x) = x^3 + 3x^2 + 2x – 50
Answers
Answer:
for the first equation
f(-3) = 34
f(4) = 6
for the 2nd equation
f(-3) = -56
f(4) ÷ 70
Step-by-step explanation:
my work is attached in a picture.
all you do is substitute each x value into each equation
Find the perimeter. Explain what you added together to get your answer. You can get partial credit for explaining steps, even if your final answer is incorrect.
Answers
Answer:
the area of the shape is 7.14
Step-by-step explanation:
First, find the area of the square:
2 in x 2 in = 4 in
then to find the area of the semi- circles add them together to make a circle
To find the area of the circle, use:
pi x radius^2
Since the diameter is 2 divide the diameter by 2 to get radius
3.14 x 1^2 = 3.14
The circle is 3.14 plus 4 ( the square ) = 7.14
(23)/4)-6×69(7+8)0-(5)2897)
Answers
Answer:
If the Question is correct, the correct soln given below
Step-by-step explanation:
(23-24)/4×0-14485
14485 ans
Answer:
-57917/4
Step-by-step explanation:
Place the following fractions in order least to greatest. (-2/3), (20/10), (3/10), (-5/3)
Answers
Answer:
\(-\frac{5}{3}, -\frac{2}{3}, \frac{3}{10} , \frac{20}{10}\)
Step-by-step explanation:
Cup a holds 1/16 and cup b holds 1/8 he has 3/4 gallons of lemonade. How many more cups of lemonade can jagger pour if he uses cup a than cup b?
Answers
He cannot pour any more cups of lemonade using cup A than cup B
Jagger has 96 cups of lemonade (by multiplying 3/4 gallon with 16).
Let us assume Jagger fills "a" cups of lemonade using Cup A.
Jagger can fill 6 cups with each gallon (by multiplying 16 with 1/16).
So Jagger can fill 6 x 3/4 x 16 = 72 cups of lemonade using cup A.
Now, let us assume Jagger fills "b" cups of lemonade using Cup B.
Jagger can fill 8 cups with each gallon (by multiplying 16 with 1/8).
So Jagger can fill 8 x 3/4 x 16 = 96 cups of lemonade using cup B.
Since Jagger has only 96 cups of lemonade, he cannot use Cup A to pour more lemonade than Cup B.
So the answer is "0".
Thus, he cannot pour any more cups of lemonade using cup A than cup B.
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To pour the Jagger completely with lemonade we need 2 cups A and 1 cup of B.
What is a fraction ?A fraction is not a whole number it has some amount of fractional or decimal value to it.
According to the given question, we have;
Jagger has two different sized plastic cups for lemonade. Cup A holds 1/16 gallon. Cup B holds 1/8 gallon. He has 3/4 gallon of lemonade.
The remaining lemonade that has to be filled is
= (1 - 3/4)
= 1/4 gallons.
Now he starts to pour the remaining starting with cup A and then B
= 1/16 + 1/8 + 1/16
= 1/4
So, He needs 2 cups of A and 1 cup of B to full the Jagger of lemonade.
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In order to study some effects of alcohol consumption, Dr. Chu tested the physical coordination skills of 21-year-old men who were first assigned to drink a beverage with either 4, 2, or 0 ounces of alcohol. In this study, the independent variable consisted of:
Answers
Dr. Chu tested the physical coordination skills of 21-year-old men who were first assigned to drink a beverage with either 4, 2, or 0 ounces of alcohol. The independent variable in this study is the amount of alcohol consumed by the men, and the dependent variable is the physical coordination skills of the men.
The independent variable in Dr. Chu’s study is the amount of alcohol consumed by the 21-year-old men before testing their physical coordination skills.
The independent variable is the variable that is being manipulated or changed by the experimenter to test its effect on the dependent variable, which is the variable that is being measured.In this study, the independent variable is the quantity of alcohol consumed by the men.
They were divided into three groups, one was given a beverage containing 4 ounces of alcohol, another group was given a beverage containing 2 ounces of alcohol, and the third group was given a beverage without any alcohol.The dependent variable in this study is the physical coordination skills of the 21-year-old men. The dependent variable is the variable that is being measured to determine the effect of the independent variable. Dr. Chu is studying how alcohol consumption affects the physical coordination skills of the 21-year-old men.
Dr. Chu tested the physical coordination skills of 21-year-old men who were first assigned to drink a beverage with either 4, 2, or 0 ounces of alcohol. The independent variable in this study is the amount of alcohol consumed by the men, and the dependent variable is the physical coordination skills of the men.
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Let f(x) = 4x3 – 5x2 – 8 and
g(x) = -2x3 – 6x² – 9x-5
Find (f-g)(x).
Answers
Answer:
(f - g)(x)
Step-by-step explanation:
6x3 + x2 + 9x - 3
Need this answered NOW please HS geometry
Answers
take your time and stay calm ok
PLEASE ANSWER QUICKLY
Answers
Answer:
A. 16 to 20 is equivalent to ratio 32:40
stay safe healthy and happy..T/F - If A and B are n x n and invertible, then A^-1B^-1 is the inverse of AB.
Answers
The given statement " If A and B are n x n and invertible, then A⁻¹B⁻¹ is the inverse of AB." is true because A and B are invertible matrices, it means that they both have an inverse (A⁻¹and B⁻¹, respectively). The product of A and B, represented by AB, is also an n x n matrix.
To show that A⁻¹B⁻¹is the inverse of AB, we must demonstrate that the product of (AB) and (A⁻¹B⁻¹) results in the identity matrix, which is an n x n matrix with 1s along the diagonal and 0s elsewhere.
To verify this, we'll multiply (AB) with (A⁻¹B⁻¹) and check if the result is the identity matrix:
(AB)(A⁻¹B⁻¹) = A(BA⁻¹)B⁻¹ (associative property of matrix multiplication)
Since B and A^-1 are inverses of each other, their product equals the identity matrix:
A(BA⁻¹)B⁻¹= AI B⁻¹(where I is the identity matrix)
Multiplying A and I doesn't change A:
AI B⁻¹= A B⁻¹
Now, A and B⁻¹are inverses of each other as well, so their product also equals the identity matrix:
A B⁻¹= I
Thus, A⁻¹B⁻¹ is indeed the inverse of AB, as the product of (AB) and (A⁻¹B⁻¹) results in the identity matrix.
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