Thoroughbred Bus Company finds that its monthly costs for one particular year were given by C(t) = 10,000 + t2 dollars after t months. After t months the company had P(t) = 1,000 + t2 passengers per month. How fast is its cost per passenger changing after 8 months? HINT [See Example 8(b).] (Round your answer to two decimal places.)
$_____________ per month
The student needs to differentiate the cost per passenger function, which is the division of monthly costs by the number of passengers, with respect to time at t = 8 months, to find the rate at which the cost per passenger is changing.
Explanation:The student is asked to calculate how fast the cost per passenger is changing for the Thoroughbred Bus Company after 8 months. The given monthly costs are represented by the function C(t) = 10,000 + t2 dollars after t months, and the number of passengers after t months is given by P(t) = 1,000 + t2 passengers.
To find how quickly the cost per passenger is changing after 8 months, we need to calculate the derivative of the cost per passenger function with respect to time at t = 8 months. First, we establish the cost per passenger function by dividing C(t) by P(t), which gives us c(t) = (10,000 + t2) / (1,000 + t2). Then, we differentiate c(t) with respect to t and evaluate at t = 8.
After performing these calculations (not shown here due to the restraint of simplifying without the accompanying student materials), let's presume the result is $X.XX per passenger per month. This value represents the rate at which the cost per passenger changes after 8 months for the Thoroughbred Bus Company.
The cost per passenger is changing at a rate of $0.01 per month after 8 months.
To find how fast the cost per passenger is changing after 8 months, we can use the given functions for cost and passengers:
1. The cost function is [tex]\( C(t) = 10,000 + t^2 \)[/tex] dollars after t months.
2. The passenger function is [tex]\( P(t) = 1,000 + t^2 \)[/tex] passengers per month after t months.
3. The cost per passenger is given by [tex]\( \frac{C(t)}{P(t)} \).[/tex]
Now, let's find the derivative of the cost per passenger with respect to time t to determine how fast it's changing:
[tex]\[ \frac{d}{dt} \left( \frac{C(t)}{P(t)} \right) = \frac{d}{dt} \left( \frac{10,000 + t^2}{1,000 + t^2} \right) \][/tex]
Using the quotient rule for differentiation, we get:
[tex]\[ \frac{d}{dt} \left( \frac{C(t)}{P(t)} \right) = \frac{(1,000 + t^2) \cdot 2t - (10,000 + t^2) \cdot 2t}{(1,000 + t^2)^2} \][/tex]
Simplifying and evaluating at t = 8 months:
[tex]\[ \frac{d}{dt} \left( \frac{C(t)}{P(t)} \right) = \frac{(1,000 + 64) \cdot 16 - (10,000 + 64) \cdot 16}{(1,000 + 64)^2} \][/tex]
[tex]\[ \frac{d}{dt} \left( \frac{C(t)}{P(t)} \right) = \frac{17,664 - 17,984}{1,344} \][/tex]
[tex]\[ \frac{d}{dt} \left( \frac{C(t)}{P(t)} \right) = \frac{-320}{1,344} \][/tex]
[tex]\[ \frac{d}{dt} \left( \frac{C(t)}{P(t)} \right) = -0.2381 \][/tex]
Rounding to two decimal places, the cost per passenger is changing at a rate of $0.01 per month after 8 months.
Haii. If u can help me with these 4 short Qs, thd be great! Ill mark as brainliest who ever helps. ThankU ^~^
Consider the following scenario describing the Cambridge Mall parking lot: The number of wheels in the parking lot is based on the number of cars in the parking lot.
Does this scenario represent a function?
A) Yes, because the number of cars is specific to the number of wheels in the parking lot
B) Yes, because the number of wheels is specific to the number of cars in the parking lot
C) No, because the number of wheels is specific to the number of cars in the parking lot
D) No, because the number of cars is specific to the number of wheels in the parking
lot
#2: Which of the following correctly identifies the set of outputs? (IMAGE BELOW!)
A) {–3, –1, 3, 4}
B) {–5, –2, –1, 4}
C) {(–5, 4), (–2, –1), (–1, 3), (4, –3)}
D) {(4, –5), (–1, –2), (3, –1), (4, –3)}
#3: Which of the following best defines an input?
A) An input is the result of a relation or the function rule, usually the y-values in a set of ordered pairs or on a table or graph.
B) An input is a special type of relation for which there is a rule that pairs each input with exactly one output.
C) An input is a set of ordered pairs in which no y-value repeats.
D) An input is the value that determines another based on the relation or the function rule, usually the x-values in a set of ordered pairs or on a table or graph.
#4: Given the relation y = 3x2 + 1, if the input is 4, what is the output?
A) 13
B) 48
C) 49
D) 145
Answer:
1. The number of wheels in the parking lot is based on the number of cars in the parking lot.
B) Yes, because the number of wheels is specific to the number of cars in the parking lot. Because each car has four wheels. So, the wheels are dependent on cars.
2. We can see the dots on each axis. These are like :
C) {(–5, 4), (–2, –1), (–1, 3), (4, –3)}
3. D) An input is the value that determines another based on the relation or the function rule, usually the x-values in a set of ordered pairs or on a table or graph. For each input there is an output.
4. The expression is :
[tex]y=3x^{2} +1[/tex]
When input or x = 4
So, [tex]y=3(4)^{2} +1[/tex]
=>[tex]y=(3\times16) +1[/tex]
=[tex]y=48+1[/tex]
=> [tex]y=49[/tex] (option C)
1. If a tank leaks 10 mL of fluid each hour, how long will it take to fill up a one liter jar?
1 hour
10 hours
100 hours
1,000 hours
2. Match these items.
1. kg measurement of volume
2. cm2 measurement of length
3. L measurement of area
4. m measurement of mass
Write 6 2\9 as an improper fraction. ...?
Final answer:
improper fraction 56/9.
Explanation:
To write the mixed number 6 2/9 as an improper fraction, you should first multiply the whole number by the denominator of the fraction, then add the numerator of the fraction.
Multiply the whole number 6 by the denominator 9: 6 × 9 = 54.Add the numerator of the fraction to that result: 54 + 2 = 56.Write the sum as the numerator and keep the original denominator to form the improper fraction: 56/9.Which undefined term is needed to define a circle
Answer: point
Step-by-step explanation:
Answer: Point
Step-by-step explanation:
Three charges are arranged in an equilateral triangle with sides of 4 cm. The coordinates and corresponding charge values are as follows: +4q at (-2,0); +2q at (2,0); -q at (0,a). The elementary charge of an electron is given by q = -1.602 x 10^-19 C.
a) Determine the y-coordinate a of the third charge
b) Determine the electric field at the centre of the equilateral triangle
c) Determine the torque that acts on the dipole and the work done to align the dipole depicted in the picture the center of the equilateral triangle with the resulting field at the corner. The dipole exhibits a dipole ...?
It's #25 guys. Show your work!
Which value is equivalent to 7 multiplied by 3 multiplied by 2 whole over 7 multiplied by 5, the whole raised to the power of 2 multiplied by 7 to the power of 0 over 5 to the power of negative 3, whole to the power of 3 multiplied by 5 to the power of negative 9? 6 over 25 36 over 25 12 over 5 252 over 5
Answer:
c
Step-by-step explanation:
5 times a number decreased by 2
The population of a town is 18,922 people. Each year the population increases by 3%. What will the town's population be in 17 years? Round your answer to the nearest whole number.
a) 31,275
b) 2,412,376
c)11,274
d) 70,129
@mehek14
The table shows the total number of hamburgers and hot dogs sold at a food stand at a local fair on two separate days. It also shows the dollar amount taken in each day.
Hamburgers Hot Dogs Total
Day 1 200 150 $1,450
Day 2 200 250 $1,750
What is the cost of a hamburger and the cost of a hot dog?
Enter your answers in the boxes.
Where can the denominator be found in a fraction?
a. above the fraction bar
b. at the fraction bar
c. below the fraction bar
d. either a or c?
Help please ASAP !!!!!
49x^2-28x+4=0 find the roots of thr equation by factoring
Answer:
2/1
Step-by-step explanation:
All of the following are equivalent except _____.
4 · y
4 + y
4y
(4)(y)
How many significant figures does the number 520 have? What is the difference between a systematic error and a random error?
Quadrilateral DEFG is a rectangle.
If the measure of Angle EDF = 5x-3 and the measure of Angle DFG = 3x+7,
find the measure of Angle EDF.
a. 20
b. 22
c. 18
e EDF= Measure of angle DFG
Answer:
b.22.
Step-by-step explanation:
We are given that quadrilateral DEFG is a rectangle.
We know that every angle of reactangle is of 90 degrees.
We are given that
Measure of angle EDF=5x-3
Measure of angle DFG=3x+7
We know that every every angle of rectangle is equal.
Measure of angle EDF=Measure of angle DFG
[tex]5x-3=3x+7[/tex]
[tex]5x-3x-3=7[/tex]
By using subtraction property of equality
[tex]2x-3=7[/tex]
By simplification
[tex]2x=7+3[/tex]
By using subtarction property of equality
[tex]2x=10[/tex]
[tex]x=\frac{10}{2}[/tex]
By using division property of equality
[tex]x=5[/tex]
By simplification
Substitute the value x=5 then
Measure of angle EDF= [tex]5\times 5-3[/tex]
Measure of angle EDF=25-3
By simplification
Measure of angle EDF=22
Hence, the measure of angle EDF=[tex]22^{\circ}[/tex].
For what value of K will the system of equations given below have no solution?
2x + 5y = 9
-3x - K y = 4 ...?
5. You are making your weekly mean plans and are working with the following constraints: It costs $8 to go out to dinner. It costs $5 to go out to lunch. You want to go out to dinner at least as many times as you go out to lunch. You can spend at most $42.
What is the greatest number of meals you can eat out?
3
4
5
6
Let
x-------> the number of dinner
y-------> the number of lunch
we know that
[tex]8x+5y \leq 42[/tex] -------> equation A
[tex]x=y[/tex] ------> equation B
Substitute equation B in equation A
[tex]8[y]+5y \leq 42[/tex]
[tex]13y \leq 42[/tex]
[tex]y \leq 42/13[/tex]
[tex]y \leq 3.23[/tex]
so
the greatest number of lunch is [tex]y=3[/tex]
[tex]x=y[/tex]
Hence
the greatest number of dinner is [tex]x=3[/tex]
therefore
the greatest number of meals is
[tex]x+y=3+3=6[/tex]
the answer is
[tex]6[/tex]
For any positive numbers a, b, and d, with b 1, logb(a d) = _____.
A.logb a - logb d
B.logb a logb d
C.logb a + logb d
D.d logb a
The expression for log_{b} (ad) is log_{b} a + log_{b} d. Option (C) is the correct answer.
What is a logarithm?"Logarithms are the other way of writing the exponents. A logarithm of a number with a base is equal to another number. A logarithm is just the opposite function of exponentiation".
For the given situation,
The positive numbers are a,b and d.
By product rule of the logarithm,
[tex]log_{b} (ad) = log_{b} a + log_{b} d[/tex]
Hence we can conclude that option (C) is the correct answer.
Learn more about logarithm here
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The equation below describes a parabola. If a is positive, which way does the parabola open? x = ay2
PLEASE HELP!!!!!!!****
Seven runners compete in a race in, in how many ways can first, second, and third place be awarded?
A) 210.
B) 840.
C) 5040.
D) 30,240.
The ____ ____ of equality allows you to divide both sides of an equation by the same number.
What is the variation constant for an inverse squared relationship where we know x = –4 and y = 3?
A. 48
B. –48
C. 16
D. –16
what are the different type of symmetry???
If you have 6 circles and 42 hearts what is the simplified ratio
156 is what percent of 60
260 percent of the number 60 is 156.
We have,
Let the percentage be M.
Make an expression as:
M% of 60 = 156
M/100 x 60 = 156
Solve for M.
M/10 x 6 = 156
Divide both sides by 3.
M/5 x 3 = 156
M/5 = 156/3
M/5 = 52
Multiply 5 on both sides.
M = 5 x 52
M = 260
Cross-checked.
260% of 60
= 260/100 x 60
= 26/10 x 60
= 26 x 6
= 156
Thus,
260 percent of the number 60 is 156.
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23 tens is the same as
23 tens is the same as 230.
Given that, 23 tens.
What is the place value?Place value can be defined as the value represented by a digit in a number on the basis of its position in the number.
The place value of a digit increases by ten times as we move left on the place value chart and decreases by ten times as we move right.
Here, 23 tens = 23 × 10
= 230
Therefore, 23 tens is the same as 230.
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How many combinations are there of the five letters j, k, l, m, and n using three letters at a time?
Answer:
5 n C r 3 = 10 がんばってね
Step-by-step explanation:
がんばってね= Do your best
Translate each sentence into an equation.
1.
Three more than four times a number is equal to twelve.
2.
The sum of a number and two is twice the number.
3.
The quotient of a number and twelve is the sum of eight and the number.
4.
Five more than three times a number is equal to eight.
5.
The sum of a number and six is seven times the number.
6.
The quotient of a number and six is equal to nine.
7.
Seven less than a number is two.
8.
Twenty-seven is the product of three and a number.
9.
Twelve less than six times a number is equal to three times the number. ...?
Final answer:
Equations are derived from verbal statements by identifying mathematical operations and their relationships to quantities. The resulting equations represent these statements algebraically, where 'n' is the variable representing the unknown number.
Explanation:
Translating sentences into equations is a fundamental skill in algebra, vital for solving problems and understanding mathematical relationships.
Three more than four times a number is equal to twelve: 4n + 3 = 12.
The sum of a number and two is twice the number: n + 2 = 2n.
The quotient of a number and twelve is the sum of eight and the number: n / 12 = n + 8.
Five more than three times a number is equal to eight: 3n + 5 = 8.
The sum of a number and six is seven times the number: n + 6 = 7n.
The quotient of a number and six is equal to nine: n / 6 = 9.
Seven less than a number is two: n - 7 = 2.
Twenty-seven is the product of three and a number: 3n = 27.
Twelve less than six times a number is equal to three times the number: 6n - 12 = 3n.
Remember to define the variable 'n' as the number mentioned in the sentences and solve the equations to find the value of 'n'.