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 [tex]ft/s^{2}[/tex]
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) [tex]j(t)=\left \{ {{95t-9t^{2}; 0\le t<5.28s} \atop {250.69; 5.28s\leq t \leq 10s}} \right.[/tex]
[tex]j'(t)=\left \{ {{95-18t; 0\leq t<5.28s} \atop {0 ; 5.28s\leq t \leq 10s}} \right.[/tex]
(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:
[tex]j(t)=95t-9t^2[/tex]
[tex]j'(t)=95-18t[/tex]
and we set the first derivative equal to zero so we get:
95-18t=0
and solve for t
-18t=-95
[tex]t=\frac{95}{18}[/tex]
t=5.28s
so now we calculate the position of the car after 5.28 seconds, so we get:
[tex]j(5.28)=95(5.28)-9(5.28)^{2}[/tex]
[tex]j(5.28)=250.69ft[/tex]
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:
[tex]j(t)=95t-9t^{2}[/tex]
[tex]j'(t)=95-18t[/tex]
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 [tex]ft/s^{2}[/tex]
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) [tex]j(t)=\left \{ {{95t-9t^{2}; 0\le t<5.28s} \atop {250.69; 5.28s\leq t \leq 10s}} \right.[/tex]
[tex]j'(t)=\left \{ {{95-18t; 0\leq t<5.28s} \atop {0 ; 5.28s\leq t \leq 10s}} \right.[/tex]
(see attached picture for graph)
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Step-by-step explanation:
Every five years in August, the population of a certain city is recorded. In 2010, the city had a population
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CAN SOMEONE PLEASE HELP ME WITH THIS ITS DUE TODAY
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1. 4 x 31 is 124
2. 7 x 49 is 658
3. 16 x 48 is 608
4. 8(5 + w) is 8w + 40
5. 11(9 + d) is 11d + 99
6. 15(p + 4 + 2) is 15p + 90
7. Let's simplify step-by-step.
2x−4+3x
=2x+−4+3x
Combine Like Terms:
=2x+−4+3x
=(2x+3x)+(−4)
=5x+−4.
8. Let's simplify step-by-step.
4y−1−3y−2
=4y+−1+−3y+−2
Combine Like Terms:
=4y+−1+−3y+−2
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x+2(x−4)
Distribute:
=x+(2)(x)+(2)(−4)
=x+2x+−8
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10. Part A)
The jazz band sells 31 large boxes of fruit and 74 small boxes of fruit.
For each large fruit box, the price is $20 and cost is $x.
Profit is defined as Price - Cost.
So, profit for one large fruit box = 20 - x
Profit for 31 large fruit boxes = 31(20 - x)
Price of each small fruit box is $10 and cost of each small fruit box is $y. The profit for each small fruit box is 10 - y.
Profit for 74 small fruit boxes = 74(10 - y)
The total profit for 31 large boxes and 74 small boxes will be:
Total profit = 31 (20 - x ) + 74(10 - y)
Using distributive property, we can simplify the above equation as:
Total profit = 31(20) - 31x +74(10) - 74y
Total profit = 1360 - 31x - 74y
Part B)
Cost of each large box is given to be $9. This means x = 9
Cost of each small box is given to be $4. This means y = 4
Using the values of x and y in the profit equation we can find the profit of the Jazz Band.
So, Jazz Band's Profit = 1360 - 31(9) - 74(4)
Jazz Band's Profit = $ 785
Thus the profit of Jazz Band will be $785.
Have A good day!! Hope I helped!!! ^-^
A number more than nine is more than twenty.
write as an inequality
Answers
Answer:
I think it is 20 < x > 9. But I am not completely sure.
Please help me with this answer
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Answer: I believe it is c 4
Step-by-step explanation:
but im not sure
Yang is a car salesperson at Honda dealership. He earns monthly salary of $2,400 and an $250 bonus for each vehicle he sells to a customer. 1. Create an equation to represent the total earnings, t, Yang can make selling v, vehicles in one month.
2. How many vehicles does Yang need to sell in a month to earn a total of $5150?
3. How many vehicles does the salesperson need to sell in a month to earn at least $6000? Write an inequality and solve algebraically using inverse operations.
Answers
Answer:
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Step-by-step explanation:
1. 250 is dependent variable
2. 5,150-2400=2750
2750/250=11
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Answers
Explanation: just took a quiz
Answer: Its 15/2(A)
Step-by-step explanation:
2/3-1=4
Multiply both sides of the equation by 3
2x-3=12
You move constant to the right and you change the sign. Like this: 2x=12+3
Then you add the numbers and you get 2x=15
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Answer:
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Award brainliest!!!
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Answer:
Quintrell's number is 9.
Step-by-step explanation:
Let [tex]x[/tex] be equal to Quintrell's number.
"When 35 is added to my number, the answer is 4 times my original number plus 8."
⇒
[tex]35+x=4x+8[/tex]
Subtract both sides by [tex]x[/tex]
[tex]35+x-x=4x+8-x\\35=3x+8[/tex]
Subtract both sides by 8
[tex]35-8=3x+8-8\\27=3x[/tex]
Divide both sides by 3
[tex]\frac{27}{3} =\frac{3x}{3} \\9=x[/tex]
Therefore, Quintrell's number is 9.
I hope this helps!
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Step-by-step explanation:
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Step-by-step explanation:
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Answer:
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Answer:
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B: 5 * 4 = 20 9 * 4 = 36
C: 5 * 6 = 30 9 * 6 = 54
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Answer:
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In ΔGHI, the measure of ∠I=90°, the measure of ∠G=62°, and GH = 96 feet. Find the length of IG to the nearest tenth of a foot.
Answers
Answer:
45.1feet
Step-by-step explanation:
Given the following
∠I=90°
∠G=62°, and
GH = 96 feet = Hypotenuse
Required
IG = Adjacent side
Using the SOH CAH TOA identity
Cos theta = Adj/hyp
Cos 62 =IG/96
IG = 96cos62
IG = 96(0.4695)
IG = 45.1feet
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Step-by-step explanation:
Q. A mechanic has a radiator hose that
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explanation
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(Hope this helps!!)
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false
Step-by-step explanation:
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----------------------------------------------------------------------------------------------------------------
pls can i get brainliest it took soo long to figure out
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Answers
Answer:
10/117 or 8.55% or 0.09
Step-by-step explanation:
5/13 x 2/9 = 10/117
The probability you get orange juice and a ham sandwich is,
⇒ 10/117
What is mean by Probability?The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one
Given that;
In a cooler there are 5 orange juices, 2 apple juices and 6 grape juices. In a large bag there are 2 ham sandwiches and 7 turkey sandwiches.
Hence, Total number of juice in a cooler = 5 + 2 + 6 = 13
And, Total number of sandwiches = 2 + 7 = 9
Thus, The probability you get orange juice and a ham sandwich is,
⇒ 5 / 13 × 2 / 9
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Answer
80oz
Hope
it helps
Agnete consumes 1.68 grams of caffeine in a week.
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
We know that Agnete drinks 3 cups of drip coffee every day, and each cup contains 8 oz of coffee, which is equivalent to 80 mg of caffeine.
To find out how many grams of caffeine Agnete consumes in a week, we can start by calculating the total amount of caffeine she consumes in a day:
Total caffeine in a day.
= 3 cups x 80 mg/cup
= 240 mg
Then, we can multiply this value by 7 to find the total amount of caffeine she consumes in a week:
Total caffeine in a week = 240 mg/day x 7 days/week = 1680 mg
To convert milligrams (mg) to grams (g), we divide by 1000:
Total caffeine in a week = 1680 mg / 1000 = 1.68 g
Therefore,
Agnete consumes 1.68 grams of caffeine in a week.
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Answers
Step-by-step explanation:
when 0: 5 > 25 = false
when 7: -28 + 5 > 25 = -23 > 25 = false
when -7: 28 + 5 > 25 = 33 > 25 = true
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