Find the derivative of the function F(x) = (x4 + 9x2 − 5)4
The required derivative of the function (x⁴ + 9x² − 5)⁴ is f'(x) = 4 (x⁴ + 9x² − 5)³(4x³ + 18x).
As per the question we have to determine the derivative of the f(x) = (x⁴ + 9x² − 5)⁴.
What is derivative?A derivative is defined as the rate of change of the function with respect to the respective variables.
Here,
According to the question,
f(x) = (x⁴ + 9x² − 5)⁴
Differentiate both sides with respect to x.
f'(x) = d[(x⁴ + 9x² − 5)⁴] / dx
f'(x) = 4 (x⁴ + 9x² − 5)³ × (4x³ + 9×2x)
f'(x) = 4 (x⁴ + 9x² − 5)³(4x³ + 18x)
Thus, the required derivative of the function (x⁴ + 9x² − 5)⁴ is f'(x) = 4 (x⁴ + 9x² − 5)³(4x³ + 18x).
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ally and barbara, and katherine will share the cost of a vacation rental for a week. aly agrees to pay 30% of the cost. barbara agrees to pay 0.45 of the coat. katherine will pay the remaining balance. if the total rental coast $960, how much will ally, barbara, and katherine each pay towards the week's rent?
which expression is represented by the model below?
5.6 times what equals to -19.04
The given equation can be rearranged as a division problem: -19.04 divided by 5.6. The solution to this is -3.4. Thus, 5.6 times -3.4 equals -19.04.
Explanation:To answer the question, we must find the unknown variable in your given equation, where you are multiplying a number (5.6) by some unknown figure to get -19.04. This type of math problem is a division problem arranged differently. Instead of saying '5.6 times what equals to -19.04', we can rearrange it to say '-19.04 divided by 5.6 equals what'.
To get the answer, simply divide -19.04 by 5.6, which equals -3.4. So 5.6 times -3.4 equals -19.04.
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A family pass to amusement park cost $54 using the distributive property write an expression that can be used to find the cost in dollars of 8 family
Which linear function has the same y-intercept as the one that is represented by the graph?
A rectangular field is to be bounded by a fence on 3 sides and a straight stream on the 4th side. Find the dimensions of the field with maximum area that can be enclosed using 1000 ft of rope. This is in the applied maximum and minimum chapter btw.
To maximize the area of the rectangular field, express the area in terms of one variable, derive the area function, and set it to zero for solving. The sides of the field yielding the maximum area are obtained using these calculations.
Explanation:This question involves optimization in calculus, specifically related to finding the maximum area of a rectangle. In such a problem, the first step is to express the area (A) of the rectangle in terms of one variable. Given a fence that is 1000 ft in length, if we name the side perpendicular to the stream as 'x', and the side parallel to it (bounded by the fence) as 'y', the perimeter of the field is 2x + y = 1000.
We can express y in terms of x: y = 1000 - 2x. The area of the rectangle, A = x*y = x*(1000 - 2x).
To find the maximum area, we find the first derivative of A with respect to x, set it to zero and solve for x. The second derivative test will confirm if it's a maximum. Based on the solutions, the maximum area is achieved with the dimensions of the rectangular field being specific values of x and y that you compute.
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What is the sales tax on a jacket priced at $350 if the sales tax rate is 7%
Which equation represents a line that passes through (–9, –3) and has a slope of –6?
What kind of graph is this?
Most evenings after dinner Duarte spends 30 minutes playing chess with his dad. Write an equation for the number of minutes, m, that Duarte spent playing chess with his dad if they played chess together e evenings.
dr. lee went to a bank to get a loan for some new furniture for the waiting area at her clinic. she wanted to borrow $5,000 to be paid back over 3 years. last week the interest rate was 4.25%. but this week theinterest rate went up to 4.50%. how much additional interest will Dr. lee pay because she waited the extra week
Find the equation of the ellipsoid passing through the points (±7,0,0),(0,±1,0)(±7,0,0),(0,±1,0) and (0,0,±4)
Colin drove 45 minutes to the airport. He arrived 90 minutes before his flight departed, and then he spent 70 minutes in the air. Once he landed, Colin spent 20 minutes gathering his luggage, and then he drove 35 minutes to his hotel. What must be true of any expression that represents the total time that Colin spent traveling from his house to the hotel? The numbers can be added in any order. The number 45 must be the first addend, and 35 must be the last addend. The numbers must be added in the order 45, 90, 70, 20, and 35. The numbers must be added in either the order 45, 90, 70, 20, and 35 or the order 35, 20, 70, 90, and 45.
Answer:
The numbers must be added in the order 45, 90, 70, 20, and 35.
Step-by-step explanation:
Answer:
The numbers must be added in the order 45, 90, 70, 20, and 35
Step-by-step explanation:
:3
What is 600000-347201
Match the pairs of equations that represent concentric circles. Tiles
Andreus made $625 mowing yards. He worked for 5 consecutive days and earned the same amount of money each day. How much money did Andreus earn per day
Amanda used 3/4 cup of sugar to make 2 dozen cookies. How much sugar is in each cookie? (Dozen=12)
Write the value of 1710 in standard form
The airport garage charges $5 to park for the first hour and then $3.50 an hour for any additional hours. Ben paid $57.50 to park there one day when he flew to another city. How many hours was he parked at the airport?
Final answer:
Ben was parked at the airport for a total of 16 hours, after calculating the initial cost for the first hour and then dividing the remainder by the hourly rate for additional hours.
Explanation:
The student's question asks how many hours Ben was parked at the airport, given that the parking cost is $5 for the first hour and $3.50 for each additional hour, with a total fee of $57.50.
First, we subtract the initial $5 from the total cost to determine the cost of additional hours:
$57.50 - $5 = $52.50 for additional hours
Next, we divide the remaining cost by the hourly rate for additional hours to find the number of additional hours Ben parked:
$52.50 ÷ $3.50/hour = 15 hours
Finally, we add the first hour to the additional hours to calculate the total hours parked:
15 hours + 1 hour = 16 hours
Thus, Ben was parked at the airport for a total of 16 hours.
write 129.04 in words
During a catered lunch, an average of 4 cups of tea are poured per minute. The lunch will last 2 hours. How many gallons of tea should the caterer bring if there are 16 cups in one gallon?
Your hair is 6 inches long and grows at a rate of 144 millimeters per year. a. Convert 144 millimeters per year to inches per year. Round your answer to the nearest tenth. b. Write an equation that represents the length y (in inches) of your hair after x years. c. How long is your hair after 4 years?
The rate of hair growth in inches is 5.67 inches per year and in 4 years hair will be 28.68 inches long.
As mentioned in the question,
Your hair is 6 inches long and grows at a rate of 144 millimeters per year. a. Convert 144 millimeters per year to inches per year.
The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
1 inch = 25.4 millimeters,
For, also 1 millimeters = 1 / 25.4 inches,
So,
144 millimeters per year = 144 / 25.4 inches per year
= 5.67 inches per year
Now,
Growth after 4 years,
= 4 × 5.67 + 6
= 28.68
Thus, the rate of hair growth in inches is 5.67 inches per year and in 4 years hair will be 28.68 inches long.
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Write these decimal fractions in words 0.17
Which of the following is the best example of a characteristic of an experiment?
a.Participants should be selected into the treatment group randomly.
b.Participants are rarely aware that they are part of an experiment.
c.Participants are observed without researchers making changes to their behaviors.
d.The results of an experiment are based on a questionnaire given to a random sample of the population.
Answer with sometimes, always, or never true. Give an example/counterexample.
When a point is reflected across the y-axis, the new point has a negative x-coordinate.
Final answer:
The statement that a point reflected across the y-axis results in a point with a negative x-coordinate is sometimes true, depending on the original point's location relative to the y-axis.
Explanation:
When a point is reflected across the y-axis, the result depends on the initial position of the point relative to the y-axis. The statement that the new point has a negative x-coordinate is sometimes true. If a point lies to the right of the y-axis (positive x-coordinate), reflecting it across the y-axis will indeed result in a point with a negative x-coordinate. However, if the original point is to the left of the y-axis (already has a negative x-coordinate), reflecting it across the y-axis will give it a positive x-coordinate.
Example
If the original point is (3, 2), reflecting it across the y-axis results in (-3, 2), which supports the statement.
If the original point is (-4, 5), reflecting it across the y-axis yields (4, 5), which contradicts the statement.
Therefore, the correct answer is sometimes true, demonstrating the importance of considering the position of the original point in relation to the y-axis.
Which linear inequality is represented by the graph?
a.y >2/3 x – 2
b.y < 2/3x + 2
c.y2/3 > 2/.+ 1
d.y<2/3 x – 1
Find all the real fourth roots of 256.
4
-8 and 8
8
-4 and 4
Fred Johnson's total insurance premium is $1,200. His employer pays 60% of the total premium. How much does Fred pay? $480 $720 $2,000 $3,000
Answer: First option is correct.
Step-by-step explanation:
Since we have given that
Amount of Fred Johnson's total insurance premium = $1200
Percentage of total premium his employer pays = 60%
Remaining percentage of total premium he pays is given by
[tex]100\%-60\%=40\%[/tex]
So, amount of insurance premium Fred Johnson pay is given by
[tex]\frac{40}{100}\times 1200\\\\=40\times 12\\\\=\$480[/tex]
Hence, First option is correct.
Enter the degree of the polynomial
5x5 + 8x2 + 2x – 3x9 – 8x4 – 4x5
Answer:
9
Step-by-step explanation:
I got it right on ape-x