1. The velocity of a car as it travels over a level crossing is modeled by v = t2 – 4t + 12
for 0 < t < 4 where t is the time in seconds after it reaches the crossing. When does the car reach its minimum speed? What is the minimum speed?
Show your work or strategy:
When does the car reach its minimum speed? _________________
What is the minimum speed? _________________________
Answers
Answer:
At t=2s the car reach its minimum speed
Minimum speed=8m/s
Step-by-step explanation:
We are given that velocity of car
\(v(t)=t^2-4t+12\)
0<t<4
Differentiate w.r.t t
\(v'(t)=2t-4\)
\(v'(t)=0\)
\(2t-4=0\)
\(2t=4\)
\(t=2\)
\(v''(t)=2>0\)
The velocity is minimum at t=2 s
Substitute t=2
\(v(2)=2^2-4(2)+12\)
\(v(2)=8m/s\)
Hence, the speed of car is minimum at t=2 se and minimum speed of car=8m/s
Related Questions
On a coordinate plane, a curved line labeled f of x with a minimum value of (1.9, negative 5.7) and a maximum value of (0, 2), crosses the x-axis at (negative 0.7, 0), (0.76, 0), and (2.5, 0), and crosses the y-axis at (0, 2).
Which statement is true about the graphed function?
F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5).
F(x) > 0 over the intervals (-∞, -0.7) and (0.76, 2.5).
F(x) < 0 over the intervals (-0.7, 0.76) and (2.5, ∞).
F(x) > 0 over the intervals (-0.7, 0.76) and (0.76, ∞).
Answers
The statement that is true about the function is:
F(x) < 0 over the intervals (-∞, -0.7) and (0.76, 2.5).What is the function of a graph?A function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given:
The minimum value of the curve = (1.9, -5.7),
The maximum value = (0, 2)
The point the function crosses the x-axis (the x-intercept) = (-0.7, 0), (0.76, 0), and (2.5, 0)
The point the function crosses the y-axis (the y-intercept) = (0, 2)
The given points can be plotted using MS Excel, from which we have:
F(x) is less than 0 over the interval from x = -∞, to x = -0.7, and the interval from x = 0.76 to x = 2.5.
Hence, the correct option is A.
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Question 1/10 points)
Which expression is equivalent to x2 - 4x – 45?
0
(x– 9) (x - 5)
Oь
(x + 9) (x + 5)
Оe
(x + 9) (x - 5)
Od
(x - 9) (x + 5)
Can somebody please help me with this
Answers
the 2nd expression is the answer
HELP PLEASE! Which reason is the justification for the statement that angle A ≅ angle B?
A) Vertical angles are congruent.
B) Linear angles are equal.
C) Intersecting lines form opposing angles.
D) Lines intersect at one point.
Answers
5.
What is the width of a rectangle if the area is 2x²-x-6 and the length is 2x + 3?
O-x-1--
x-2
3
2x+3
O-x+ 2
MacBook Air
2x²-1
2
Onone of the answer choices
Answers
Answer: x-2
Use A=Lw
A/L=w
if you factor and cancel, you are left wirh x-2.
Simplify the expression completely 3z+9+5z-4
Answers
Answer:8z+5
Step-by-step explanation: Add 3z to 5z which equals 8z and do 9-4 which equals 5 .Lastly add together.
write a real-world situation that could be modeled by the equation 8+2x=6x. Then solve the problem.
Answers
Answer:
x = 2
Step-by-step explanation:
8 = 6x + -2x
8 = 4x
8 = 4x
4 4
2 = x
What is the circumference of the circle in terms of pi? (C = td) О Тл О 147 О 21л * 28 л
Answers
The circumference of the circle with a radius of 10 cm is 20π cm, option (C) is correct.
A circle's perimeter, or the distance encircling it, is known as its circumference. It is determined by multiplying the circle's diameter by pi. But in this case, we are given the radius of the circle, which is half of the diameter.
To get a circle's circumference, use the following formula:
C = 2πr
where;
r = radius of the circle
π = mathematical constant pi (approximately equal to 3.14).
Given the radius of the circle as 10 cm, we can use the formula to find its circumference:
C = 2πr
C = 2π(10 cm)
C = 20π cm
Hence, option C is correct.
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The correct question is:
What is the circumference of the circle with radius = 10 cm (leave your answer of π).
A) 10π cm
B) 5π cm
C) 20π cm
D) 10π cm
which table best classifies the following numbers as rational and irrational?
-4/5, √2, 2.5,0.4,√16
Answers
Answer:
√2 is the only irrational number here. Others are rational
Step-by-step explanation:
When this net is folded into a cube, which
edge joins with edge X?
X
F
A
E
B
D
C
Answers
When edge D connects with edge X, this net is folded into a cube, which is obtained by folding the given figure in cube.
Explain about the cube?A cube is a solid shape with six square faces. Each side of a square has the same side length, so all faces are the same size.
A cube has 12 sides and 8 vertices. Each vertex refers to the angle where the three edges of the cube meet.
Shape Properties of Cube
It is a three-dimensional square shape It has 6 faces, 12 sides and 8 vertices All faces are square All sides are of equal length Every vertex meets three faces and three sides Sides are square All sides are of equal length Each vertex meets three faces and three sides parallel to it All angles of a cube are right anglesThus, when edge D connects with edge X, this net is folded into a cube.
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In the currency pair USD/CAN, USD is what currency?
Answers
So American money
Help help help please
Answers
The probability that the selected pupil studied both Russian and Spanish is 0.24%.
Define the term probability?A probability is just a tabular value of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging form 0% to 100% can be used to describe probabilities.For the stated question-
The probability number of Russian speakers P(R) = 0.50.The probability number of Spanish speakers P(S) = 0.31.Let the probability number of Russian and Spanish speakers P(R∩S).Then , the probability number of not Russian and Spanish speakers P(R'∩S') = 0.23.Total number of speakers P(E): 0.80.Thus,
P(E) = P(R) + P(S) - P(R∩S) + P(R'∩S')
0.80 = 0.50 + 0.31 - P(R∩S) + 0.23
P(R∩S) = 0.24
Thus, the probability that the selected pupil studied both Russian and Spanish is 0.24%.
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4. Compute the unadjusted cost of goods sold for the year. Do not include any underapplied or overapplied overhead in your answer.
5. Assume that the $70,000 ending balance in Work in Process includes $24,000 of direct materials. Given this assumption, supply the information missing below:
Answers
The unadjusted cost of goods sold for the year is calculated by subtracting the ending inventory from the sum of beginning inventory and purchases. The formula is as follows:
Unadjusted Cost of Goods Sold = Beginning Inventory + Purchases - Ending Inventory
Without knowing the values for beginning inventory, purchases, and ending inventory, we cannot compute the unadjusted cost of goods sold for the year.
5. Given that the $70,000 ending balance in Work in Process includes $24,000 of direct materials, we can calculate the missing information as follows:
Direct Labor = Total Work in Process - Direct Materials - Overhead
Direct Labor = $70,000 - $24,000 - Overhead
Without knowing the value for overhead, we cannot compute the direct labor cost. However, we can rearrange the formula to solve for overhead:
Overhead = Total Work in Process - Direct Materials - Direct Labor
Overhead = $70,000 - $24,000 - Direct Labor
Without knowing the value for direct labor, we cannot compute the overhead cost.
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The rate at which a quantity M of a certain radioactive substance decays is proportional to the amount of the substance present at a given time. Which of the following is a differential equation that could describe this relationship?
1. dM/dt = -3.72 t^2
2. dM/dt = -0.11M
3. dM/dt = 0.08 t^2
4. dM/dt = 1.2M
Answers
Answer:
2. dM/dt = -0.11M
Step-by-step explanation:
Differential equations for proportional amouts:
A differential equation for proportional amounts is given by:
\(\frac{dx}{dt} = ax\)
In which a is the constant rate. If the amount increases, a is positive. If it decays, b is positive.
In this question:
Decays, so a < 0.
Proportional to the amount of the substance present at a given time, which means that a multiplies the amount M.
This means that the correct answer is given by option 2.
You can buy a car for $5995.67 cash or pay $759.00 as a down payment and $129.95 a month for 4 years.
How much more does the installment plan cost than paying cash?
A. $1000.93
B. $241.93
C. $507.43
D. $2475.27
E. $99.27
Answers
well, if you had the cash right now, you can put it down cold for 5995.67 bucks
OR
put as a downpayment now 759 and then over 48 months pay 129.95 each month, well, 129.95 48 times is 129.95 * 48 = 6237.6, now let's add the 759 down and that's 6237.6 + 759 = 6996.6.
well, heck if you had the cash it'd be 5995.67, if you don't is 6996.6, their difference is 6996.6 - 5995.67 = 1000.93.
Roberto Alberto rode his bike three-fourths of a mile 3 days in a row. He thinks he rode somewhere
between 2 and 3 miles.
A) Use the number line to show if Roberto Alberto is right or wrong.
Answers
if <1 and <2 are vertical angles. If m<1=(5x +12) and m<2=(6x-11), find m<1
Answers
Answer:
its 23
Step-by-step explanation:
50 pts. Compute the requested operating costs as indicated, based on the preceding table and the following information.
Car: six-cylinder compact
Year driven: second
Miles driven: 14,000
The insurance cost for second year is $
.
If the answer is right, (I will check it,) then I will post a question and give you more points. just get on my prophile, and keep reloading on my "questions' page. 100 extra points.
DONT FLAG. I NEED HELP WITH THIS PROBLEM AND I"M TRYING TO GET A REAL ANSWER.
Answers
From the table , the insurance cost for the second year based on the prescription given is : $1329
Using the prescription table, the six cylinder compact , second year car with a mileage of 14000 falls in the mid table category with the 13000 mileage label .
The operating cost in insurance for the second year is therefore $1329.
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STRUCTURE Two parents each have the gene combination C's. The gene C is for curly hair. The gene s is for straight hair. Any gene combination that includes a cap C results in curly hair. When all outcomes are equally likely, what is the probability of a child having curly hair?
Answers
The probability of a child having curly hair when both parents have the gene combination C's is 3/4, or 75%.
what is probability ?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. An event is any outcome or set of outcomes of a random process or experiment. Probability can be used to quantify the chance of an event occurring, and it is often expressed as a fraction, decimal, or percentage.
To calculate the probability of an event, we can use the formula:
P(event) = number of favorable outcomes / total number of outcomes
According to the question:
When two parents each have the gene combination C's, they can each pass either a C or an s to their child. This gives four possible outcomes for the child's gene combination: CC, Cs, sC, and ss.
Of these four outcomes, three include at least one C and therefore result in curly hair: CC, Cs, and sC. The only outcome that results in straight hair is ss.
Since all outcomes are equally likely, the probability of the child having curly hair is the number of favorable outcomes (CC, Cs, or sC) divided by the total number of outcomes (CC, Cs, sC, or ss):
P(curly hair) = number of favorable outcomes / total number of outcomes
= 3/4
Therefore, the probability of a child having curly hair when both parents have the gene combination C's is 3/4, or 75%.
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Which of the following statements are always true? Justify your answers. a. If A + B = C, then AD' + BD' = CD' b. If A'B + A'C = A'D, then B + C = D c. If A + B = C, then A + B + D = C + D d. If A + B + C = C + D, then A + B = D
Answers
Answer:
a. True
B. False
C. True
D. False
Step-by-step explanation:
a.) A+B = C then AD' + BD' = CD'
AD'+BD' = D'(A+B)
and we already have that A+B = C
such that D'C = C'D
this statement is true
b.) A'B + A'C = A'D then B+C = D
let's have A = 1 and B= 0, C= 0 and D = 1
A'(0) + A'(0) = 1(1)
0+0 = 1
0 = 1
This is false because 0 is not equal to 1
c.) A+ B=C then A+B+D= C+D
If A+B+D= C+D
Then A+B=C
The statement is true
d.) A+B+C=C+D
A+B = D
let's equate A = 0
B= 0
C= 1
D= 1
from a+b = D
We have
0+0 = 1
0 is not equal to 1
The statement is false
Answer:
a. True
B. False
C. True
D. False
Step-by-step explanation:
a.) A+B = C then AD' + BD' = CD'
AD'+BD' = D'(A+B)
and we already have that A+B = C
such that D'C = C'D
this statement is true
b.) A'B + A'C = A'D then B+C = D
let's have A = 1 and B= 0, C= 0 and D = 1
A'(0) + A'(0) = 1(1)
0+0 = 1
0 = 1
This is false because 0 is not equal to 1
c.) A+ B=C then A+B+D= C+D
If A+B+D= C+D
Then A+B=C
The statement is true
d.) A+B+C=C+D
A+B = D
let's equate A = 0
B= 0
C= 1
D= 1
from a+b = D
We have
0+0 = 1
0 is not equal to 1
The statement is false
Step-by-step explanation:
Subtract 7/8−1/12. don't know
Answers
Answer:
See below.
Step-by-step explanation:
Find the Lowest Common Multiple, or LCM of 8 and 12.
8 - 8, 16, 24
12 - 12, 24
7 x 3 = 21
8 x 3 = 24
1 x 2 = 2
12 x 2 = 24
21/24 - 2/24 = 19/24
-hope it helps
If not allowed, 7/8x(12/12) - 1/12x(8/8)
If f(x)=3x-1 find the following f(3) f(2)
Answers
Answer:
(4(f(2)
Step-by-step explanation:
If f(x(=3x-1 then f(3)f(2)
5. The cost of tuition at the public university that Mateo plans to attend is $9,600 for the first year. Mateo's parents will pay for one-third of the tuition. Mateo will use $1,500 from his savings to help pay for tuition. What is the minimum amount of money Mateo will need to save every month to reach his goal of paying off the remaining tuition cost at the end of 12 months? < PREVIOUS 1 0² 3 04 5 06
Answers
Mateo needs to save at least $408.33 every month to reach his goal of paying off the remaining tuition cost at the end of 12 months.
What is fixed expense and variable expense?Rent or a car payment are examples of monthly costs that are fixed expenses. On the other hand, a variable expense is one that can vary from month to month, like food or entertainment. Variable expenses demand greater flexibility in budgeting because the cost can change, but fixed expenses are often easier to prepare for because the amount is constant.
Given that, cost of tuition fee is $9,600 for the first year.
Now, Mateo's parents will pay for one-third of the tuition thus:
1/3 x $9,600 = $3,200
From the saving the money used is $1500 thus the remining cost is:
$9,600 - $3,200 - $1,500 = $4,900
For 12 months in a year we have:
$4,900 / 12 = $408.33
Hence, Mateo needs to save at least $408.33 every month to reach his goal of paying off the remaining tuition cost at the end of 12 months.
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How are the two angles related?
Answers
The two angles are related in that they are supplementary angles
Supplementary angles would add tuo to 180 degrees according to the angle Theorem.
Adding the two given angles :
52+128 = 180These angles are supplementary
The angles aren't vertical in that , vertical angles should have the same vertex. Complementary angles on the other hand add to 90 degrees. While the angles doesn't share the same side, hence, they aren't adjacent.
Hence, the angles are related as they are supplementary angles .
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3x-30 =1.5 plz help me
Answers
Answer:
x = 10.5
Step-by-step explanation:
3x - 30 = 1.5
3x = 31.5
x = 10.5
A passenger car will go 455 miles on 17.5 gallons of gasoline in city driving what is the rate in miles per gallon ?
Answers
Answer:
26 gallons
Step-by-step explanation:
Take the miles and divide by the gallons
455 miles / 17.5 gallons
26 miles per gallon
Help please I don’t get it
Answers
Answer:
Step-by-step explanation:
-5 - 9x = 3-9x-8 (Used distributive property)
-5 - 9x = -9x-5 (-8+3 = -5)
- 9x = -9x (Add 5 to both sides)
0 = 0 (Add 9x to both sides)
Find the equation (in terms of xx ) of the line through the points (-2,4) and (3,-5)
Answers
Given the points (-2, 4) and (3, -5)
We will find the slope-intercept form of the equation of the line that passes through the given points.
The slope-intercept form is: y = m * x + b
where: m is the slope and (b) is the y-intercept
We will find the slope using the following formula:
\(\begin{gathered} slope=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1} \\ \end{gathered}\)So, the slope will be:
\(m=\frac{-5-4}{3-(-2)}=\frac{-9}{5}\)substitute with (m):
\(y=-\frac{9}{5}x+b\)substitute with the point (3, -5) to find the value of b:
\(\begin{gathered} -5=-\frac{9}{5}\cdot3+b \\ -5=-\frac{27}{5}+b \\ b=-5+\frac{27}{5}=\frac{2}{5} \end{gathered}\)Substitute with (m) and (b) into the slope-intercept form:
So, the answer will be:
\(y=-\frac{9}{5}x+\frac{2}{5}\)If $200 is borrowed with an interest of 18.0% compounded monthly, what is the total amount of money needed to pay it back in 1 year? Round your answer to the nearest dollar. Do not round at any other point in the solving process; only round your answer.
Answers
Answer:
$239
Step-by-step explanation:
Use the compound interest formula and substitute the given values:
A=$200(1+0.18/12)\(^{12(1)}\)
Simplify using the order of operations: A=$200(1.015)\(^{12}\)=$200(1.195618171) ≈ $239.
Answer:
239.12
Step-by-step explanation:
A=$200(1+0.1812)12(1).
Simplify using the order of operations: A=$200(1.015)12=$200(1.195618171)≈$239.12.
Sandro would like to retire at age 60 with an income of $1500 per month from his
retirement savings. If he is to receive these payments until he is 90 years old, what
amount would he need in his retirement savings account at age 60, if the account
earns 4.5% compounded monthly?
Answers
The amount (present value at age 60) that Sandro would neet in his retirement savings account in order to have a monthly income of $1,500 until he is 90 years old, compounded at 4.5% monthly is $296,041.74.
How the present value is computed:The present value is computed using an online fiance calculator that discounts the future withdrawals (monthly income) for a 360-months period.
End of withdrawal period = 90 years old
Beginning of withdrawal period = 60 years old
The number of years between 60 and 90 = 30 years
N (# of periods) = 360 months (30 years x 12)
I/Y (Interest per year) = 4.5%
PMT (Periodic Payment) = $-1,500
FV (Future Value) = $0
Results:
Present Value (PV) = $296,041.74
Sum of all periodic payments = $540,000 ($1,500 x 360 months)
Total Interest = $243,958.26
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What happens to the value of the expression 20+a20+a20, plus, a as aaa increases?
Answers
i think it is 60 because 30 divided by 3-4 equals 2Step-by-step explanation:
Answer: Choice A
Step-by-step explanation:
it increases