You are traveling down a country road at a rate of 95 feet/sec when you see a large cow 300 feet in front of you and directly in your lane. The cow is fearless, and staring you down. (Or perhaps she does not understand the gravity of the situation.) Regardless, if you simply hit your brakes, after t seconds, the car will be j(t) = 95t - 9t^2 feet from the point where the brakes were first applied.
1) Must you steer to avoid the cow, or can you rely solely on your brakes? Explain.
2) Graph J(t), j'(t), and j"(t) and Interpret their meanings in context.
3) Is there a time t after which the graphs in part (ii) probably do not accurately model the path of the car?
4) Write a piece-wise function using j(t) that would more accurately model the path of the car on the interval [0, 10], assuming the car did not move after it stopped. Sketch this graph and its derivative.
Answers
Answer:
1) You can rely solely on your brakes because when doing so the car will just travel 250ft from the point you hit your brakes till the point the car stopped completely, leaving you 50ft away from the cow.
2) See attached picture.
j(t) represents the distance from the point you hit the brake t seconds after you hit it in feet
j'(t) represents the velocity of the car t seconds after the brakes have been hit in ft/s.
j"(t) represents the acceleration of the car t seconds after the brakes have been hit in \(ft/s^{2}\)
3) yes, any time after t=5.28 will not accurately model the path of the car since at that exact time the car will reach a velocity of 0ft/s and unless another force is applied to the car, then the car will not move after that time.
4) \(j(t)=\left \{ {{95t-9t^{2}; 0\le t<5.28s} \atop {250.69; 5.28s\leq t \leq 10s}} \right.\)
\(j'(t)=\left \{ {{95-18t; 0\leq t<5.28s} \atop {0 ; 5.28s\leq t \leq 10s}} \right.\)
(see attached picture for graph)
Step-by-step explanation:
1) In this part of the problem we need to find the time when the speed of the car is 0. Gets to a complete stop. For this we will need to take the derivative of the position function so we get:
\(j(t)=95t-9t^2\)
\(j'(t)=95-18t\)
and we set the first derivative equal to zero so we get:
95-18t=0
and solve for t
-18t=-95
\(t=\frac{95}{18}\)
t=5.28s
so now we calculate the position of the car after 5.28 seconds, so we get:
\(j(5.28)=95(5.28)-9(5.28)^{2}\)
\(j(5.28)=250.69ft\)
so we have that the car will stop 250.69ft after he hit the brakes, so there will be about 50ft between the car and the cow when the car stops completely, so he can rely just on the breaks.
2) For answer 2 I take the second derivative of the function so I get:
\(j(t)=95t-9t^{2}\)
\(j'(t)=95-18t\)
j"(t)=-18
and then we graph them. (See attached picture)
j(t) represents the distance from the point you hit the brake t seconds after you hit it in feet
j'(t) represents the velocity of the car t seconds after the brakes have been hit in ft/s.
j"(t) represents the acceleration of the car t seconds after the brakes have been hit in \(ft/s^{2}\)
3) yes, any time after t=5.28 will not accurately model the path of the car since at that exact time the car will reach a velocity of 0ft/s and unless another force is applied to the car, then the car will not move after that time.
4) \(j(t)=\left \{ {{95t-9t^{2}; 0\le t<5.28s} \atop {250.69; 5.28s\leq t \leq 10s}} \right.\)
\(j'(t)=\left \{ {{95-18t; 0\leq t<5.28s} \atop {0 ; 5.28s\leq t \leq 10s}} \right.\)
(see attached picture for graph)
Related Questions
Your taxable wages for Social Security purposes are $1100. How much is your Social Security tax if you have previous taxable wages of $102,000?
Answers
If you have previous taxable wages of $102,000 and your current taxable wages are $1,100, your Social Security tax would be $6,324 for the previous wages and $68.20 for the current wages.
To calculate the Social Security tax, we need to know the tax rate for Social Security and the taxable wages. Let's assume the Social Security tax rate is 6.2% for both the employee and the employer.
Given that your taxable wages for Social Security purposes are $1,100, and your previous taxable wages are $102,000, we can determine the Social Security tax amount.
First, we need to calculate the Social Security tax on the previous taxable wages of $102,000. Multiply $102,000 by 6.2% (0.062) to find the Social Security tax for that amount:
Social Security tax = $102,000 x 0.062 = $6,324
Next, we calculate the Social Security tax on the current taxable wages of $1,100. Multiply $1,100 by 6.2% to find the tax amount:
Social Security tax = $1,100 x 0.062 = $68.20
Therefore, if you have previous taxable wages of $102,000 and your current taxable wages are $1,100, your Social Security tax would be $6,324 for the previous wages and $68.20 for the current wages.
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Give an example of two events that are not mutually exclusive.
Answers
Answer: in the case of rolling a die the event of getting an 'odd-face' and the event of getting 'less than 4' are not mutually exclusive and they are also known as compatible event. The event of getting an 'odd-face' and the event of getting 'less than 4' occur when we get either 1 or 3.
Step-by-step explanation:
also turning ur body (left and right)
6/5+(-5) HELP ME PLZ ASAP THANKS
Answers
Rules
If you have a - and a - it is equal to a plus
If you have a + and a - it is equal to a minus
Plug in the rules
6/5-5= -3.8
So, the answer is -3.8
I hope this helped
Ps.Brianlist would really help
k) v=u+ax make x the subject
Answers
Answer:
x = (v - u) / a
Step-by-step explanation:
v = u + ax.
subtract u from both sides:
v - u = ax.
divide both sides by a:
(v - u) / a = x.
so x = (v - u) / a.
this can also be written v/a - u/a
Which statement about the quadratic equation below is true?
-1.5x2 +54 = 0
A The equation has X = 6 as its only solution.
B The equation has no real solutions.
C The equation has an infinite number of solutions.
D The equation has x = 6 and x = -6 as its only solutions.
Answers
Answer:
x = ± 6
Step-by-step explanation:
1: Subtract both sides by -54
\(-1.5x^2=-54\)
2: Divide both sides by -1.5
\(x^2=36\)
3: Take both sides to the 1/2 power
\(x= 6, -6\)
Carlos arranged his building blocks into 2 rows of 12 blocks. Liz her arranged blocks into 6 rolls of 4 blocks if they use the same number of blocks what two other ways could they arrange their blocks
Answers
1) Gathering the data
Carlos
2 rows of 12 blocks
Liz
6 rows of 4 blocks
2) The divisors of 24: 1,2, 3, 4, 6, 8,12, 24
Since they have 24 blocks they could arrange it in
3 rows of 8 blocks
8 rows of 3 blocks
4 rows of 6 blocks
polygon h is a scaled factor of polygon g using a scale factor of 1/4
Answers
The fraction of the area of polygon H of polygon G's area would be: 1/16.
What are Similar Polygons?When a polygon is formed by enlarging or reducing an original polygon by a scale factor, the new polygon formed is similar to the original polygon.
What is a Scale Factor?The scale factor = new dimension/original dimension
Given that polygon H is the new polygon formed when polygon G is reduced by a scale factor of 1/4, thus, we would have the following:
Area of polygon H/Area of polygon G = square of the side of polygon H/square of the side of polygon G = square of the scale factor of dilation
Area of polygon H/Area of polygon G = 1²/4² = 1/16
This implies that the area of polygon G is 16 units² while the area of polygon H is 1 units².
Thus, the fraction of the area of polygon H of polygon G's area would be: 1/16.
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rewrite -3(5u+5)+10u in simplest form
Answers
Answer:
-5u-15
Step-by-step explanation:
-3(5u+5)+10u
-15u-15+10u
-5u-15
Collect the like term which is -15u and 10u
You get -5u-15 which is your answer
convert 2.64 to a fraction
please don't just give the answer. can please give some explanation
Answers
Answer:
66/25
Step-by-step explanation:
A decimal is the same this as a fraction just in a different form, for example .1 = 1/10 and .01=1/100 so you can turn .64 into 64/100. So now we have 2 and 64/100, which is a mixed number, but you want the whole thing as just a fraction so 2 = 200/100, so add the two together and you get 264/100. Then you just simplify
Answer:66/25
Step-by-step explanation:
To get rid of the decimal point in the numerator, we count the numbers after the decimal in 2.64, and multiply the numerator and denominator by 10 if it is 1 number, 100 if it is 2 numbers, 1000 if it is 3 numbers, and so on.
Therefore, in this case we multiply the numerator and denominator by 100 to get the following fraction:
264 / 100
Then, we need to divide the numerator and denominator by the greatest common divisor (GCD) to simplify the fraction.
The GCD of 264 and 100 is 4. When we divide the numerator and denominator by 4, we get the following:
66 / 25
Therefore, 2.64 as a fraction is as follows:
66 / 25
Find slope of line please no links
Answers
Answer:
Step-by-step explanation:
Using
Point A: x= 1 and y=3
And point B: x=-2 and y=-6
use equation of slope and substitute the values
Slope= YB-YA/Xb-Xa
= -6-3/-2-1
=3
What is the total of 49 1/4+3 3/8
Answers
Answer:
52 5/8
Step-by-step explanation:
To add fractions, you have to make sure both fractions have a common denominator.
As you can see, the fractions have different denominators, so to make both denominators 8, we have to multiply 1/4 by two, which gives us 2/8.
Then, we just add like normal!
49 2/8+ 3 3/8 = 52 5/8!
Hope this helped! :)
What is (-1) - (-3) Pre-Algebra
Answers
Answer:
2
Step-by-step explanation:
-1-(-3) is the same as -1+3, which is 2
you can also rewrite it as 3-1, which is also 2
Which of the following sets of interior angle measures can form a triangle?
Select all that apply.
A. 45, 45, 45*
B. 60, 60, 60°
C. 40.50,90°
D. 30.60.90*
E. 90,90°, 45°
F. 90, 90, 90°
pleaseee helppp
Answers
As per the angle sum property, the interior angles that form the triangle is option
B. 60, 60, 60°
C. 40.50,90°
D. 30.60.90*
Angle sum property
Angle sum property states that the sum of all the interior angles of the triangle is equal to 180 degrees.
Given,
Here we have the list of interior angles
A. 45, 45, 45*
B. 60, 60, 60°
C. 40.50,90°
D. 30.60.90*
E. 90,90°, 45°
F. 90, 90, 90°
Now, we have to find in which for these angle will form the tringle.
As per the definition of the angle sum property, the sum of all the interior angle of the triangle is 180°.
Based on these we have to verify each of the given interior angles,
A) 45 + 45 + 45 = 135
B. 60 + 60 + 60 = 180
C. 40 + 50 + 90 = 180
D. 30 + 60 + 90 = 180
E. 90 + 90 + 45 = 225
F. 90 + 90 + 90 = 270
Therefore, based on these values we have identified that the options (B), (C), and (D) forms the triangle.
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please help khan academy
Answers
The inequality represented by the graph is given as follows:
y > 3x - 4.
How to define a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change.The intercept b represents the value of y when x = 0.The graph crosses the y-axis at y = -4, hence the intercept b is given as follows:
b = -4.
When x increases by 1, y increases by 3, hence the slope m is given as follows:
m = 3.
Hence the equation of the line is:
y = 3x - 4.
The inequality is composed by the values to the right (greater) of the line, and has an open interval due to the dashed line, hence:
y > 3x - 4.
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anielle earns $36.80 for 4 hours of yardwork. MacKenzie earns $50.40 for 6 hours of yardwork.
Who earns more money per hour? How much more? Use the drop-down menus to show your answer.
Answers
Answer:
MacKenzie earns 155.20 more than Anielle
Step-by-step explanation:
f(x) = 6^2+12x -7
please answer and explainnnn!
Answers
Answer:
A) \(x=-1\pm\sqrt{\frac{13}{6}}\)
Step-by-step explanation:
\(\displaystyle x=\frac{-12\pm\sqrt{12^2-4(6)(-7)}}{2(6)}\\\\x=\frac{-12\pm\sqrt{144+168}}{12}\\\\x=\frac{-12\pm\sqrt{312}}{12}\\\\x=\frac{-12\pm2\sqrt{78}}{12}\\\\x=-1\pm\frac{\sqrt{78}}{6}\\\\x=-1\pm\sqrt{\frac{78}{36}}\\\\x=-1\pm\sqrt{\frac{13}{6}}\)
(8,5); perpendicular to 2x - y = 7
Answers
Answer:
brainliest plzzz
Step-by-step explanation:
2x - y = 7 is in standard form, and if it were slope-intercept form that would help you. I got the y term by itself:
y = 2x - 7 slope-intercept form. You already know the slope of the perpendicular line is the *negative reciprocal* of the slope you have. So that's (-1/2). The perpendicular line is something like
y = -(1/2)x + b and if you substitute 8 for x and 5 for y you get 9 for b.
y = -(1/2)x + 9 is your perpendicular line. In slope-intercept form. To get back to standard form, start by getting rid of fractions. Multiply both sides by 2.
2y = -x + 18 then add x to both sides.
x + 2y = 18 done.
Karl was attempting to calculate economic figures. He found the following equation to be true:fp-w=10000If f=5 and w=5+125i, what is p?
Answers
The value of p = (125i + 10005)/5
=> p = 25i + 2001
Now, According to the question:
Let's know:
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.
Karl was attempting to calculate economic figures.
The given equation is:
fp - w = 10000
f = 5 and w = 5 + 125i
To solve for the value of p.
(-125i - 5) + 5 p = 10000
Add 5 + 125i to both sides:
5 p + ((-125 i - 5) + 125 i + 5) = 125 i + 5 + 10000
(-125 i - 5) + (125 i + 5) = 0:
5 p = 10000 + 5 + 125 i
10000 + 5 + 125 i = (10000 + 5) + 125 i = 10005 + 125 i:
5 p = 125 i + 10005
Divide both sides of 5 p = 125 i + 10005 by 5:
(5 p)/5 = (125 i + 10005)/5
p = (125i + 10005)/5
Hence, The value of p = (125i + 10005)/5.
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What percentage of the shape is purple?
Write your answer using a percent sign (%).
Answers
First, we see a rectangle shape with little squares in it. The length is 5 and the width is 4. If we multiply them, we get 20 square units. However, we will use the 20 to solve the question. Also, we see that there are only 3 squares.
3/20
Let's divide the fraction. 3 / 20 is 0.15. We result with 0.15. Now, we multiply the decimal by 100 to get a percent; we are converting from decimal to percent. As a result, we get 15% as our answer.
3/20 = 0.15 x 100 = 15%
Ajar contains four blue marbles and two red marbles. Suppose you choose a marble at random, and do not replace it. Then you choose a second marble.
K Find the probability of the following event.
Both of the selected marbles are red.
The probability that both of the selected marbles are red is
(Round to three decimal places as needed.)
Answers
Answer:
1/15 or 0.0667
Step-by-step explanation:
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bardai
chatgpt
red marble on the first draw is 2/6, or 1/3
red marble on the second draw, given that the first marble was red, is 1/5
(1/3) * (1/5) = 1/15
jalen drew a rectangle with a perimeter of 20 inches. the smaller side measured 3 inches. jalen said the longer side of the rectangle had to be 7 inches. is jalen correct?
Answers
Yes, Jalen is correct because the rectangle has a perimeter of 20 inches with the smaller side measuring 3 inches and the longer side of the rectangle had to be 7 inches.
How to calculate the perimeter of a rectangle?In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);
P = 2(L + W)
Where:
P represent the perimeter of a rectangle.W represent the width of a rectangle.L represent the length of a rectangle.By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following;
P = 2(3 + 7)
20 = 2(10)
20 = 20 (True).
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In a poll of 555 randomly selected students, 40% stated that they enjoyed statisticsa. Identify the number of students who say that they enjoy statistics? Round to the nearest whole student if necessary.b. Construct a 95% confidence interval estimate of the percentage of all students who say that they enjoy statistics.c. Can we safely conclude that majority of students enjoy statistics? Explain.
Answers
Answer:
a
\(N = 222\)
b
\(0.36< p <0.44\)
c
No we can not safely conclude that majority of students enjoy statistics because the upper limit of the confidence level is less than 50%
Step-by-step explanation:
From the question we are told that
The sample size is \(n = 555\)
The percentage that enjoyed statistics is \(\r p = 40% = 0.40\)
Generally the number of student who say they enjoyed statistics is mathematically represented as
\(N = 0.40 * 55\)
=> \(N = 222\)
Given that the confidence level is 95% then the level of significance is mathematically represented as
\(\alpha = ( 100-95)\%\)
=> \(\alpha = 0.05\)
The critical value of \(\frac{\alpha }{2}\) obtained from the normal distribution table is \(Z_{\frac{\alpha }{2} } = 1.96\)
The margin of error is mathematically represented as
\(E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{ \r p (1 - \r p )}{n} }\)
=> \(E = 1.96 * \sqrt{ \frac{0.40 (1- 0.40 )}{ 555} }\)
=>. \(E = 0.04\)
The 95% confidence interval is mathematically represented as
\(\r p - E < p < \r p + E\)
=> \(0.40 - 0.04 < p <0.40 + 0.04\)
=> \(0.36< p <0.44\)
No we can not safely conclude that majority of students enjoy statistics because the upper limit of the confidence level is less than 50%
Help with number ten please
Answers
Hey kid theres no picture for us to see
What is the ratio of drink mix to water
Answers
I cup of water with four teasppons
N + M? N = 9.1 7.9 -2.4 0.2 -5.8 1.4 and M= 8.2 -0.6 -2.8 -1.8 -2.4 -6.1
Answers
Answer:
\(N + M = \begin{pmatrix}17.3&7.3\\ -5.2&-1.6\\ -8.2&-4.7\end{pmatrix}\)
Step-by-step explanation:
\(\begin{pmatrix}9.1&7.9\\ -2.4&0.2\\ -5.8&1.4\end{pmatrix} +\begin{pmatrix}8.2&-0.6\\ -2.8&-1.8\\ -2.4&-6.1\end{pmatrix} =\begin{pmatrix}9.1+8.2&7.9-0.6\\ -2.4-2.8&0.2-1.8\\ -5.8-2.4&1.4-6.1\end{pmatrix}\)
Then
\(\begin{pmatrix}9.1&7.9\\ -2.4&0.2\\ -5.8&1.4\end{pmatrix} +\begin{pmatrix}8.2&-0.6\\ -2.8&-1.8\\ -2.4&-6.1\end{pmatrix} =\begin{pmatrix}17.3&7.3\\ -5.2&-1.6\\ -8.2&-4.7\end{pmatrix}\)
A florist currently makes a profit of $20 on each of her celebration bouquets and sells an average of 30 bouquets every week. She noticed that when she reduces the price such that she earns $1 less in profit from each bouquet, she then sells three more bouquets per week. The relationship between her weekly profit, P(x), after x one-dollar decreases is shown in the graph below.
A graph for p of x is a downward open parabola with its vertex at (5, 725) and passes through the points (negative 10, 0), and (20, 0).
Use the graph to complete each statement about this situation.
The maximum profit the florist will earn from selling celebration bouquets is $.
The florist will break-even after one-dollar decreases.
The interval of the number of one-dollar decreases for which the florist makes a profit from celebration bouquets is ( , ).
Answers
Answer:
The maximum profit the florist will earn from selling celebration bouquets is $725.
The florist will break-even after one-dollar decreases when her profit is zero. From the graph, this occurs at x = 10. So the florist will break-even after 10 one-dollar decreases.
The interval of the number of one-dollar decreases for which the florist makes a profit from celebration bouquets is (0, 10). This is because the profit is positive for values of x between 0 and 10, and becomes negative after 10.
Step-by-step explanation:
A. Each step in this pattern decreases by 1 block. B. Each step in this pattern increases by 1 block. C. Each step in this pattern doubles the number of blocks. D. Each step in this pattern triples the number of blocks.
Answers
Answer: Each one increases by 1 block
Step-by-step explanation:
Do the following calculation according to correct significant figures:
2.9/1.3 +4.0=
Answers
Answer: 6.2
Step-by-step explanation:
2.9/1.3 +4.0=
2.23 + 4.0=
2.2 + 4.0=6.2
The given information is,
→ (2.9/1.3) + 4.0
Let's solve the problem,
→ (2.9/1.3) + 4.0
→ 2.23 + 4 = 6.23
Thus, the answer is 6.23.
2l+2w for l = 5.2 and w = 6.7
Answers
Answer:
23.8
Step-by-step explanation:
2(5.2) + 2(6.7) = 23.8
Answer:
23.8 ...............
Step-by-step explanation:
I asked my alexa.
foreign direct investment helps improve the economic situation of a recipient country by increasing —- opportunities in the country that the company invests in.
Answers
Foreign direct investment helps improve the economic situation of a recipient country by increasing employment opportunities in the country that the company invests in.
When foreign companies invest in a recipient country, they often establish or expand their operations, which requires hiring local workers. This leads to job creation and reduces unemployment rates in the recipient country.
Increased employment opportunities result in more individuals having access to income and improved standards of living.
Foreign direct investment also contributes to the transfer of technology, knowledge, and skills to the recipient country. Multinational companies often bring advanced technologies, production techniques, and management practices that may not have been available or widely adopted in the recipient country.
Furthermore, foreign direct investment stimulates domestic investment and encourages the growth of local businesses. When foreign companies invest in a recipient country, they often form partnerships or engage in supply chain relationships with local firms.
Overall, foreign direct investment increases employment opportunities, fosters technology transfer, and stimulates domestic investment, all of which contribute to improving the economic situation of a recipient country.
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