Use the quotient rule to find the derivative of the given function. 5+2 - 31 3t+ 8 f'(t) =
Answers
The derivative of the given function f(t) = (5t^2 - 31)/(3t + 8) is f'(t) = (30t^2 + 248t + 93)/(3t + 8)^2.
The quotient rule is a formula used to find the derivative of a function that is the quotient of two other functions. In calculus, the derivative of a function measures how much the function changes as its input changes.
To find the derivative of f(t) using the quotient rule, we use the formula:
f'(t) = [(denominator)(numerator)' - (numerator)(denominator)']/(denominator)^2
where numerator' denotes the derivative of the numerator.
Using this formula, we get:
f'(t) = [(3t + 8)(10t) - (5t^2 - 31)(3)]/(3t + 8)^2
Simplifying this expression, we get:
f'(t) = (30t^2 + 248t + 93)/(3t + 8)^2
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Related Questions
3x+5x-4y+9 pls help bro
Answers
Solution: 8x-4y+9
Step-by-step explanation:
Combine like terms
3x + 5x - 4y + 9
8x - 4y + 9
To find the x-intercept, substitute 0 for y and solve for x. To find the y-intercept, substitute 0 for x and solve for y.
x-intercept(s): (−9/8,0)
y-intercept(s): (0,9/4)
nobody likes to peel the potatoes for Granny's famous mashed taters however someone has to do it Ronnie puts a blocks in a bag for red three green and one yellow she makes all the grandkids take a block if you think renewal potato peeler you pick first what is the probability you will pick a Green Block
Answers
Probability is given by the expression:
\(P=\frac{Numb\text{er of favourable outcome}}{\text{total number of favourable outcomes}}\)Since, you are the first one to pick a block, the probability would be:
3/8, or 37.5% or 0.375. All that values are the same.
5. Oshaunda buys a car that costs $21,000. It depreciates at 8.2% per year. a. Write an equation for the value of the car. V=21,000(1-0.082) V-21,000(0.918) B. Oshaunda tries to sell the car 4 years later. What is the car worth when it is 4 years old? Hint: Use your formula for part (a), and plug in t = 4. Use GEMA to finish the math.
Answers
Answer:
a.
\(f(t) = 21000( {.918}^{t} )\)
b.
\(f(4) = 21000( {.918}^{4}) = 14913.86\)
What is the domain and range of this graph?
Answers
Answer:
Domain: 4 is greater than x and x is greater than or equal to -5
range: -2,1,3
Function: yes, discontinue function
Step-by-step explanation:
A bag contains colored tiles.
.
3 tiles are red
6 tiles are green
3 tiles are blue
.
A tile will be randomly selected from the bag. What is the probability in decimal form that the
tile selected will be green?
0.05
5.0
0.50
0.55
Answers
Answer:
0.50
Step-by-step explanation:
3+3+6=12
6 is half of 12
50% in decimal form is .50
Question Help 2.4.PS-9 The equation P=5s represents the perimeter P of a regular pentagon with side length s. What is the perimeter of a regular pentagon with side length 3 cm? The perimeter is c cm. Enter your answer in the answer box and then click Check Answer. Check Ansa Clear All All parts showing of 7 Back Next Review progress Question 3
Answers
Answer:
Perimeter = 15 cm
Step-by-step explanation:
The equation P=5s represents the perimeter P of a regular pentagon with side length s.
We need to find the perimeter of a regular pentagon with side length of 3 cm.
To find it, put s = 3 cm in the given equation.
P = 5(3) cm
= 15 cm
Hence, the perimeter of the regular pentagon of side length 3 cm is 15 cm.
Ronan and Kelsey each think of a number.
2 less than Ronan's number is equal to 4
lots of Kelsey's number.
3 lots of Ronan's number added to Kelsey's
number is 97.
Using the information above, write and
solve two simultaneous equations to work
out Ronan and Kelsey's numbers.
Answers
The 2 equations which can be used to solve the given situations of the numbers are:
x - 2 = 4x3x + x = 97What are equations?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. As in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.So, the equations that can be formed are:
Let, Ronan's number be 'x' and '4x' be Kelsey's number.
(1) x - 2 = 4xNow, solve as follows:
4x - x = -23x = -2x = -2/3Ronan's number be: -2/3
Kelsey's number be: 4 × 2/3 = -8/3
Let, let, Kelsey's number be 'x' and Ronan's number be '3x'.
(2) 3x + x = 97Now, solve as follows:
4x = 97x = 97/4x = 24.25Ronan's number be: 72.75
Kelsey's number be: 24.25
Therefore, the 2 equations which can be used to solve the given situations of the numbers are:
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A local polka band wants to make and sell CDs of its songs. Suppose it costs $ 1000 to record, $ 450 to edit, and $ 350 for album artwork, and suppose each CD that is manufactured will cost them $ 2.50
Answers
a) The total cost to produce 300 CD's is; $2550
b) The total cost C(n) in dollars of making n CDs is; C(n) = 1800 + 2.5n
How to find the total cost of production?We are given that;
Cost of recording an album = $1000
Cost to edit the album = $450
Cost for album art work = $350
Cost of each manufactured CD = $2.50
a) The fixed costs (no matter how many CDs are recorded) is;
Fixed costs = $1000 + $450 + $350 = $1800
The variable costs (depends on the number of CDs recorded) for 300 CD's is;
300 CDs * $2.50 = $750
Thus;
Total cost for 300 CD's = 1800 + 750 = $2550
b) We want to find the total cost function for making n number of CD's. From above, since Fixed cost is 1800 and variable cost is 2.5 per CD, then the function is;
C(n) = 1800 + 2.5n
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Complete question is;
A local polka band wants to make and sell CDs of its songs. Suppose it costs $ 1000 to record, $ 450 to edit, and $ 350 for album artwork, and suppose each CD that is manufactured will cost them $ 2.50
(a) How much will it cost to make 300 CDs?
(b) What is the total cost C(n) in dollars of making n CDs?
what is the approzimate surface area (including both side and base) of a 4m high right circular cone
Answers
The surface area is approximately 100.5m².
Surface Area = πrl + πr²
Where r is the radius of the base and l is the slant height.
Surface Area = π(2m)(4m) + π(4m)²
Surface Area = 100.5m²
The surface area of a right circular cone can be calculated by using the formula surface area = πrl + πr². In this particular case, the height of the cone is 4m and the radius of the base is 2m. Therefore the surface area of the cone is calculated as follows: π(2m)(4m) + π(4m)² = 100.5m². This surface area includes both the base and sides of the cone.
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The integers x and y are both n-bit integers. To check if X is prime, what is the value of the largest factor of x that is < x that we need to check? a. η b. n^2 c. 2^n-1 *n d. 2^n/2
Answers
Option (d) 2^n/2 is the correct answer.
To check if an n-bit integer x is prime, we need to check all the factors of x that are less than or equal to the square root of x. This is because if a number has a factor greater than its square root, then it also has a corresponding factor that is less than its square root, and vice versa.
So, to find the largest factor of x that is less than x, we need to check all the factors of x that are less than or equal to the square root of x. The square root of an n-bit integer x is a 2^(n/2)-bit integer, so we need to check all the factors of x that are less than or equal to 2^(n/2). Therefore, the value of the largest factor of x that is less than x that we need to check is 2^(n/2).
Option (d) 2^n/2 is the correct answer. We don't need to check all the factors of x that are less than x, but only the ones less than or equal to its square root.
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Susan has ribbon that is 4 feet long. She needs to cut the ribbon into 14 equal length pieces. How many feet long should each piece of ribbon be
Answers
Answer:
each ribbon should be 3.5(3 and a half or 3 1/2) feet long
Step-by-step explanation:
i divided 14 by 4
12y + 4 = 16y − 24 two step equations
Answers
Answer:
Attached is the problem solved
A bird with a reaction time (this is the time it takes the bird to react after seeing something) of 0.25 s is flying along at a speed of 13.0 m/s. The bird isn't paying attention, and suddenly sees an object 1.4 m in front of it. How far will the bird travel before it can begin to swerve away from the object? Give your answer in meters. Do not enter the units into the answer box. 40.5 points Will the bird in the previous question begin swerving before it hits the tree? Yes, the bird begins swerving before hitting the tree. (Hopefully it avoids a collision!) No, the bird sadly does not begin swerving before it hits the tree. (In this eventuality, please know that the bird was totally fine-so no worries.)
Answers
The bird will travel a distance of 3.25 meters before it can begin to swerve away from the object.
To calculate the distance the bird will travel before it can begin to swerve, we need to consider the bird's reaction time and its speed. The bird's reaction time is given as 0.25 seconds, and its speed is 13.0 m/s.
In 0.25 seconds, the bird will travel a distance equal to its speed multiplied by the reaction time:
Distance = Speed × Time
Distance = 13.0 m/s × 0.25 s
Distance = 3.25 meters
Therefore, the bird will travel 3.25 meters before it can start to swerve away from the object.
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A membership at Gym A costs $50 for 5 months. A membership at Gym B down the street costs $40 for 3 months. You write two equations in the form of y=kx to try and figure out which membership would be cheaper for a year. What is the value of k for the cheaper membership?
HELP PLS I NEED A ANSWER QUICKLY
Answers
The cost for a year is cheaper in Gym A.
The value of k for the cheaper membership is $10.
Which gym membership is cheaper?An equation in the form y = kx is known as a linear equation. A linear equation is an equation that increases at a constant rate.
In the equation : y = kx
y = dependent variable = total cost x = number of months k = constant of proportion / cost per monthk = y/x
Cost per month at Gym A = $50 / 5 = $10
Cost per month at Gym B = $40 / 3 = $13.33
Membership cost at Gym A for a year = $10 x 12 = $120
Membership cost at Gym B for a year = $13.33 x 12 = $160
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five couples were at a party. if each person shook hands exactly once with everyone else except his/her spouse, how many handshakes were exchanged? (note: one obviously doesn't shake hands with oneself.)
Answers
There were 75 handshakes exchanged at the party.
Each person at the party will shake hands with 8 other people (everyone except themselves and their spouse), so we can find the total number of handshakes by multiplying the number of people by 8 and then dividing by 2 (since each handshake involves two people).
However, we must be careful to avoid counting any handshakes between spouses, since the problem specifically states that each person does not shake hands with his/her spouse.
So, there are 5 couples, which means there are 10 people at the party. Each person will shake hands with 8 other people, but one of those 8 people is their spouse, so we need to subtract 5 (one handshake between each of the 5 couples). This gives us:
(number of people) x (number of handshakes per person) - (number of handshakes between spouses)
= 10 x 8 - 5
= 80 - 5
= 75
Therefore, there were 75 handshakes exchanged at the party.
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9. A snail moves at a speed of 8.5 meters per hour.
How long will it take a snail to travel 12 feet at this pace?
(Note: 1m = 3.28ft )
Answers
The snail will take approximately 0.43 hours or 25.8 minutes to travel 12 feet at the speed of 8.5 meters per hour.
Given, A snail moves at a speed of 8.5 meters per hour, 1m = 3.28ft. Let's convert meters per hour into feet per hour by multiplying it with 3.28ft/m. So, 8.5 meters per hour = 8.5 × 3.28 feet per hour ≈ 27.88 feet per hour.
Now, to calculate the time taken by a snail to travel 12 feet, we can use the formula: Time = Distance ÷ Speed
Time taken = 12 feet ÷ 27.88 feet per hour ≈ 0.43 hours (rounded to two decimal places)
Now, let's convert 0.43 hours to minutes by multiplying it with 60 minutes per hour: 0.43 hours × 60 minutes per hour ≈ 25.8 minutes (rounded to one decimal place). Therefore, it will take approximately 0.43 hours or 25.8 minutes for the snail to travel 12 feet at the speed of 8.5 meters per hour.
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O
umber of times a certain species
of cricket will chirp in one minute and the temperature outside. Her data is expressed
in the scatter plot and line of best fit below. Based on the line of best fit, what
temperature would it most likely be outside if this same species of cricket were
measured to chirp 120 times in one minute?
Temperature (Degrees Fahrenheit)
58
57
36
55
50
(60.47)
00
(75.51)
(90,55)
Answers
The expected change in temperature in degree Fahrenheit for each additional cricket chirp in one minute.
We have given the relationship between the number of times a certain species of cricket will chirp in one minute and the temperature outside.
Here, we see that the best fit is a linear regression.
On the y- axis temperature in degree Fahrenheit is labeled and on the x axis chirps per minute is labelled.
Since the slope = Rate of change of y/ Rate of change of x
Now after observing graph attached below,
So, the slope of line represent the expected change in temperature in degree Fahrenheit for each additional cricket chirp in one minute.
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Convert the fraction to a decimal: 5/8
Answers
5 ÷ 8 = 0.625
Therefore, 5/8 as a decimal is 0.625.
(0,0) and the point (-6,13)
Answers
Answer:
Slope? If so it is 13/-6
Step-by-step explanation:
Use y1-y2/x1-x2
I need help can anyone help please
Answers
Answer:
yuioolkknnhbcdaqwuuuuuu
Okay can you guys help me find which one is the variable. And like what it means for like example x could equal to distance in km
Answers
Answer:
a) 1000+0.05x ≥2200
b) x=24000
Step-by-step explanation:
a) So we know that Nadia for certain gets paid $1000 each month. That is a concrete amount that doesn't change, so the variable (x) would be placed on the 5% she earns from sales. We don't know how much she sells each month because it varies, so that will be represented by the X. Her goal is to raise NO LESS than $2200, which means the amount she earns from sales has to be greater than or equal to $2200.
b) From here just solve the equation for X:
The first side of a triangle of a triangle is 2 longer than the second side. The third side is 5 shorter than twice the second side. The perimeter is 49m. Find the length of each side.
Answers
Answer:
First side is 15 m.
Second side is 13 m.
Third side is 21 m.
Step-by-step explanation:
Let x be the second side of the triangle = x
The first side of a triangle is 2 longer than the second side = x + 2
The third side is 5 shorter than twice the second side. = 2x - 5
Perimeter = 49 m
The formula for finding the perimeter of triangle is:
P = a + b + c
Put the values in the formula
49 = x + x + 2 + 2x - 5
49 = 4x - 3
Use APE or Addition Property of Equality
49 + 3 = 4x
52 = 4x
Use DPE or Division Property of Equality to find the value of x
\(\frac{52}{4} = \frac{4x}{4}\)
13 = x
Now put the value of x in the equation
First side( x + 2) = 13 + 2 = 15
Second side( x ) = 13
Third side (2x - 5) =
2(13) - 5
26 - 5
= 21
PLS HELP.
7) Find RQ
Answers
Answer:
are we doing ur homework
Step-by-step explanation:
Your friend finds 24+58 by rewriting 58 as 6+52 and evaluating (24+6)+ 50 to another friend finds 24+58 by rewriting 24 as 22+2 and evaluating 22+(2+58) which friend is correct
Answers
Answer:
A
Step-by-step explanation:
Answer:
The answer is B: 22 + (2+58)
Step-by-step explanation:
I used the law of the associative property because that number will still add up to be at least 82.
y varies jointly as x and z. y = 36 when x= 3 and z=3. Find y when x=5 and z=2.y=
Answers
Where k is a constant
When y = 36 , x = 3 , z=3
\(\begin{gathered} k\text{ = }\frac{y}{xz} \\ k=\text{ }\frac{36}{3\times3}\text{ =}\frac{36}{9}\text{ = 4} \end{gathered}\)\(\begin{gathered} y\text{ = 4xz} \\ x=\text{ 5 , z = 2} \\ y\text{ = 4 }\times5\times2=40 \end{gathered}\)The value of y is 40
if a = 7 and b = 2 find the value of (a - 3) squared
Answers
Step-by-step explanation:
a = 7
(a - 3)² = (7 - 3)² = (4)² = 16
How would I graph this plz help me
Answers
Answer: [See attached immage]
The Answer: I really hope this helps!!!
Sanjay bought 4 packages of bottled water. A package contains 25 bottles of water that cost $1.20 each. Sanjay can use the
calculation below to find the total cost of the water.
4 x (25 x 1.2)
How can Sanjay simplify the calculation using only the associative property of multiplication?
Drag and drop the appropriate number or expression into each
Answers
According to the associative property of multiplication, the expression to find the cost will be (1.2 × 25) × 4 based on the property and the value is $120.
How to illustrate the information?It should be noted that the associative property of multiplication simply means that when multiplying three numbers, the answer will be the same regardless of how the numbers are grouped.
In this case, Sanjay bought 4 packages of bottled water and a package contains 25 bottles of water that cost $1.20 each.
From the information, the expression is illustrated as 4 x (25 x 1.2). It should be noted that this can also be written as (1.2 × 25) × 4 based on the property and the answer will be $120.
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describe how the graph of each function is related to the graph of f(x)=x^2
g(x)= -10 + x^2
Answers
Answer:
Translation down 5 units.
Step-by-step explanation:
The - 5 results in a shift of the whole graph down 5 units.
Each value of g(x) is 5 units less f(x).
Find the volume of the solid generated by revolving the region in the first quadrant bounded by the coordinate axes, the curve y = €* and the line * = 8 about the line x = 8.
Answers
The volume of the solid generated by revolving the region in the first quadrant bounded by the coordinate axes, the curve y = e^-x and the line x = 8 about the line x = 8 is approximately 1483.6 cubic units.
To find the volume of the solid generated by revolving the region in the first quadrant bounded by the coordinate axes, the curve y = e^-x and the line x = 8 about the line x = 8, we can use the method of cylindrical shells.
To find the volume of the solid, we need to integrate the area of each cylindrical shell over the height of the solid. Let r be the radius of a cylindrical shell at height y, and let h be the thickness of the shell. Then the volume of the shell is given by:
dV = 2πrh × h
where the factor of 2 comes from the fact that there are two cylindrical shells (one on either side of the line x = 8).
We can express r and h in terms of y:
r = 8 - y
h = e^8 - e^-x
Substituting these expressions into the formula for dV and integrating from y = 0 to y = 1, we get,
V = ∫(0 to 1) 2π(8 - y)(e^8 - e^-x) dy
= 2π ∫(0 to 1) (8e^8 - 8e^-x - ye^8 + ye^-x) dy
= 2π [8e^8 - 8e^-1 - (1/2)e^8 + (1/2)e^-1]
= 2π [15e^8 - 4e^-1]
≈ 1483.6 cubic units
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The given question is incomplete, the complete question is:
Find the volume of the solid generated by revolving the region in the first quadrant bounded by the coordinate axes, the curve y = e^-x and the line x = 8 about the line x = 8.