Determine the x values that cause the function to be (a) Zero, (b) Positive and (c) Negative, then d) sketch a graph of the function.
Answers
find roots
determine intervals between roots for which function is positive or negative
sketch
or use calculus either way
Related Questions
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
Answers
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.
In an experiment, a ball is drawn from an urn containing 7 orange balls and 12 red balls. If the ball is orange, three coins are tossed. Otherwise two coins are tossed. How many elements of the sample space will have a orange ball ?
Answers
Answer:
84
Step-by-step explanation:
When an orange ball is picked, you toss 3 coins and there are 2^3 = 8 permutations for tossing 3 coins. Now since we have 7 orange balls there will be 7 * 8 = 56 sample spaces with orange balls.
In the experiment, if the ball drawn is orange, three coins are tossed. Otherwise, two coins are tossed. The sample space will have 12 elements with an orange ball.
Explanation:To determine the number of elements in the sample space that have an orange ball, we need to consider two cases: when the ball drawn is orange and when the ball drawn is not orange (red).
If the ball drawn is orange, three coins are tossed. The sample space in this case will have 23 = 8 elements, representing all possible outcomes of the coin tosses.
If the ball drawn is not orange (red), two coins are tossed. The sample space in this case will have 22 = 4 elements, representing all possible outcomes of the coin tosses.
Therefore, the total number of elements in the sample space that have an orange ball is 8 (when the ball is orange) + 4 (when the ball is not orange) = 12.
For what value of K will the system of equations given below have no solution?
2x + 5y = 9
-3x - K y = 4 ...?
Answers
K=5 which makes y=0
Plug in -16 for x which means y=7
Therefore, - 16,7 will be the value of x,y that has no solution.
k=5
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?
Answers
It's #25 guys. Show your work!
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That is in the form [tex]y-y_{1} = m(x-x_{1})[/tex] which is point slope form
In this case,
m = 1/2 is the slope
(x1,y1) = (7,-8) is the point the line goes through
Write 6 2\9 as an improper fraction. ...?
Answers
_ _
9 9
54 + 2
_ _
9 9
56
= _
9
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.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
Answers
For an inverse squared proportion the formula is y = k/x^2
Insert values of y and x into the formula.
3 = k/(-4)^2
3(-4)^2 = k
k = 3(16)
k = 48
Hope this helps. :)
How many significant figures does the number 520 have? What is the difference between a systematic error and a random error?
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Now, the difference between a systematic error and a random error is that a systematic error occurs over and over again, whereas a random error is random and may never be repeated.
Find the missing angle measures. The diagram is not to scale
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and x is equal to 114
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. ...?
Answers
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'.
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
Answers
10 ml is for 1 hours
1l is for x hours
1l = 1000 ml
So, make a proportion:
10 ml is for 1 hours
1000 ml is for x
10 ml : 1h = 1000 ml : x
x = 1h * 1000 ml : 10 ml = 100 hours
Q2. The answers are:
1. kg - measurement of mass
2. cm² - measurement of area
3. L - measurement of volume (1L = 1 dm³)
4. m - measurement of length
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
Answers
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].
Please help me? I'm almost certain it is only option A but I want a second opinion.
Aimee is comparing three investment accounts offering different rates.
Option A: APR of 7.79% compounding monthly
Option B: APR of 7.70% compounding quarterly
Option C: APR of 7.685% compounding daily
She would like to earn at least an 8% annual yield. Which account(s) will give Aimee the yield she wants?
Answers
Answer: option A only
Step-by-step explanation:
@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.
Answers
y=cost per hot dog
200x+150y=1450
200x+250y=1750
we can multiply first equation by -1 and add to 2nd
-200x-150y=-1450
200x+250y=1750 +
0x+100y=300
100y=300
divide both sides by 100
y=3
sub back
200x+150y=1450
200x+150(3)=1450
200x+450=1450
minus 450 both sides
200x=1000
divide both sides by 200
x=5
the cost of a hamburgur is $5
the cost of a hot dog is $3
Hope I helped you!
A group of children, 6 to 10 years old, were asked how many video games they owned. The scatter plot shows the results.
What is the range of video games owned for the cluster?
Answers
Answer:
8 to 10
Step-by-step explanation:
5 times a number decreased by 2
Answers
If you have 6 circles and 42 hearts what is the simplified ratio
Answers
6/42....which reduces to 1/7......so ur simplified ratio of circles to hearts is 1 to 7 or 1:7 or 1/7
for a population of 800000 subway riders, the numbers of subway trips taken per rider last january are approximately normally distributed with a mean of 56 trips and a standard deviation of 13 trips. approximately how many of the riders took between 30 and 43 trips last january??? ...?
Answers
Calculating the number of subway riders who took between 30 and 43 trips involves finding z-scores for these trip numbers, looking up the corresponding probabilities in the normal distribution table, and multiplying the difference by the total population of riders.
Explanation:The question relates to normal distribution and requires calculating the number of individuals in a given population that fall within a specific range of values. The population in question is 800,000 subway riders whose number of trips are normally distributed with a mean (μ) of 56 and a standard deviation (σ) of 13. The task is to find out how many riders took between 30 and 43 trips last January.
To solve this, we first find the z-scores for the values 30 and 43. The z-score is calculated by subtracting the mean from the value and dividing the result by the standard deviation. This will give:
Z for 30 = (30 - 56) / 13 = -2Z for 43 = (43 - 56) / 13 = -1Next, we look up these z-scores in a standard normal distribution table to find the probabilities corresponding to these z-scores. The difference between these probabilities will give us the proportion of riders who took between 30 and 43 trips. Finally, we multiply this proportion by the total population of riders (800,000) to get the number of riders. Assume that the probabilities from the z-table are 0.0228 for z = -2 and 0.1587 for z = -1.
The calculation would be approximately:
Number of riders = 800,000 * (0.1587 - 0.0228) = 800,000 * 0.1359 = 108,720 riders
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.
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Multiply these numbers together to get your answer: 7 x 6 x 5 = 210
Help please ASAP !!!!!
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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
Answers
Bianca took out a $2,600 unsubsidized Stafford loan. She will be attending school for four years, and she wishes to have the loan paid off five years before its normal ten-year duration is finished. The loan has an interest rate of 6.2%, compounded monthly. How much will she have to pay monthly to avoid interest capitalization?
Answers
Answer:
Bianca need to pay $13.43 monthly to avoid interest capitalization.
Step-by-step explanation:
Principal value = $2600
Time = 10 years = 120 months
Interest rate = 6.2% = 0.062
Now, Find amount of payment by using the formula :
[tex]Payment = \frac{Rate\times Principal}{1-(1+rate)^{-time}}\\\\\implies Payment = \frac{0.062\times 2600}{1-(1+0.062)^{-120}}\\\\\implies Payment = \$ 161.32 [/tex]
Total payment is to be paid in 1 year :
[tex]\text{So, Monthly payment = }\frac{161.32}{12}=\$13.43[/tex]
Hence, Bianca need to pay $13.43 monthly to avoid interest capitalization.
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
Answers
Answer:
c
Step-by-step explanation:
156 is what percent of 60
Answers
I hope this helps! :)
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.
Learn more about percentages here:
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Which undefined term is needed to define a circle
Answers
Answer: point
Step-by-step explanation:
Answer: Point
Step-by-step explanation:
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
Answers
Since 8 times 4 would be $24 in total, and 5 x 3 would be $15 in total, so the overall would be $39. Hope this is the answer that you are looking for.
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
Answers
[tex]log _{2} 20 = log _{2} ( 4 * 5 ) = \\ = log _{2} 4 + log _{2} 5[/tex]
[tex]log_{b}( a d ) = log _{b}a +log _{b}d [/tex]
Answer:
C ) log(b) a + log(b) d
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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what are the different type of symmetry???
Answers
translation symmetry
reflection symmetry
(there is also glide reflection symmetry but that's for selective classes)
What is slope between the points (-5,7) and (4,-8)?
Answers
Give an example of an even function and explain algebraically why it is even.
Answers
Final answer:
An even function has the property f(x) = f(-x), exemplified by the quadratic function f(x) = x². To prove it's even, substituting -x for x results in f(-x) = (-x)², which simplifies to f(-x) = x² equaling the original function, confirming its evenness and y-axis symmetry.
Explanation:
An example of an even function is the quadratic function f(x) = x². An even function is defined by the property that f(x) = f(-x). Here's a step-by-step explanation to show that f(x) = x² is even:
Take the function f(x) = x².Substitute -x for every x in the function, so f(-x) = (-x)².Since (-x)² = x², we see that f(-x) = f(x), which satisfies the criteria of an even function. Therefore, x² is even.This even property shows symmetry about the y-axis since the function's graph appears the same on either side of the y-axis. Understanding this helps in various mathematical applications, such as simplifying expectation-value calculations in quantum mechanics or solving geometry problems using the Pythagorean theorem.