By applying concepts from vectorial calculus, we conclude that the gradient of the one variable function y = 2 · x³ - 7 · x + 4 when x = -2 is equal to 17.
How to find the gradient of a functionA gradient is a generalization of the tangent curve used for multivariate function, that is, a function with more than one variable. In this case we have a function with one variable, which means that the gradient is equal to the slope:
[tex]\nabla f = \frac{df}{dx}[/tex] (1)
Now we proceed to calculate the gradient of the curve:
[tex]\nabla f = 6\cdot x^{2}-7[/tex]
[tex]\nabla f = 6\cdot (-2)^{2}-7[/tex]
[tex]\nabla f = 17[/tex]
By applying concepts from vectorial calculus, we conclude that the gradient of the one variable function y = 2 · x³ - 7 · x + 4 when x = -2 is equal to 17.
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Select the correct word to describe the function. the equation y = startfraction 5 x cubed over 8 endfraction represents function. the equation y = 6 + 0.25 ln x represents function. the equation y = startfraction 18 over 1 + 6 e superscript negative 0.25 x baseline endfraction represents function. the equation y = 5x3 + 8 represents function.
The functions and their descriptions are:
Polynomial: [tex]y = \frac{5x^3}{8}[/tex] and [tex]y = 5x^3 + 8[/tex]Logarithm: [tex]y = 6 + 0.25\ln(x)[/tex]Exponential [tex]y = \frac{18}{1 + 6e^{-0.25x}}[/tex]How to describe the functions?The functions are given as:
[tex]y = \frac{5x^3}{8}[/tex]
[tex]y = 6 + 0.25\ln(x)[/tex]
[tex]y = \frac{18}{1 + 6e^{-0.25x}}[/tex]
[tex]y = 5x^3 + 8[/tex]
The functions would be described based on the type of function they represent.
Functions that use the "ln" keyword are logarithmic functions, while functions that use the "e" keyword are exponential functions.
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Answer:
Select the correct word to describe the function.The equation represents ✔ a powera logistica logarithmican exponential function.The equation y = 6 + 0.25 ln x represents X a logistica polynomial✔ a logarithmican exponential function.The equation represents a power✔ a logistica polynomiala logarithmic function.The equation y = 5x3 + 8 represents a powera logistic✔ a polynomialan exponential function.
Step-by-step explanation:
you are so welcome
what would i put in, in the blanks? please help, i don’t get this
Answer:
Parent function
[tex]f(x)=\log_2(x)[/tex]
Since we cannot take logs of zero or negative numbers, the domain is [tex](0, \infty)[/tex] and there is a vertical asymptote at [tex]x=0[/tex].
There are no horizontal asymptotes and the range is [tex](- \infty,\infty)[/tex].
The end behaviors of the parent function are:
[tex]\textsf{As } x \rightarrow 0^+, f(x) \rightarrow - \infty[/tex]
[tex]\textsf{As } x \rightarrow \infty, f(x) \rightarrow \infty[/tex]
To determine the attributes of the given function, compare the given function with the parent function.
Given function
[tex]f(x)=- \log_2(x)+5[/tex]
The given function is reflected in the x-axis. Therefore, the end behaviors are a reflection of those of the parent function:
[tex]\textsf{As } x \rightarrow 0^+, f(x) \rightarrow \infty[/tex]
[tex]\textsf{As } x \rightarrow \infty, f(x) \rightarrow - \infty[/tex]
As the given function is translated vertically (5 units up) only, the domain, range and asymptote will not change, since the function has not been translated horizontally.
[tex]\textsf{Domain}: \quad (0, \infty)[/tex]
[tex]\textsf{Range}: \quad (- \infty, \infty)[/tex]
[tex]\textsf{Asymptote}: \quad x=0[/tex]
Conclusion
The function f(x) is a [tex]\boxed{\sf logarithmic}}[/tex] function with a [tex]\boxed{\sf vertical}}[/tex] asymptote of [tex]\boxed{x = 0}[/tex].
The range of the function is [tex]\boxed{(- \infty, \infty)}[/tex], and it is [tex]\boxed{\sf decreasing}[/tex] on its domain of [tex]\boxed{(0, \infty)}[/tex].
The end behavior on the LEFT side is as [tex]\boxed{x \rightarrow 0^+}[/tex], [tex]\boxed{f(x) \rightarrow \infty}[/tex], and the end behavior of the RIGHT side is [tex]\boxed{x \rightarrow \infty}[/tex], [tex]\boxed{f(x) \rightarrow -\infty}[/tex].
Ok help me I don’t understand stand this
Answer:
Step-by-step explanation:
Comment
It is not possible to figure out what choices are are given for the first blank. I will say that the probable choice has the word product in it.
The second blank is the actual number of choices. It is 3 page count times color or 3*4 = 12 different choices.
Answer
product
12
HELP PLEASE ‼️‼️‼️‼️ I WILL MARK BRAINLIEST
Answer:
102
Step-by-step explanation:
HELP!!! 100 PNTS+BRANLIEST TO QUICK AND CORRECT ANSWER!!!!!!!!
In the small town of Middleton, there are only two restaurants that serve pizza- a small family owned Italian restaurant and a new franchise pizza restaurant. In a recent review of the franchise, a food critic reported that the pizza was delicious as promised. The only negative review that the franchise received from the critic was in reference to the inaccurate delivery time quoted during the online order process. In response to the article, the franchise owner used a program to analyze the online pizza orders that took place during the week before the review. He chose to track the orders at 6pm each day. He recorded his results in the frequency table below. Use the frequency table to create a box and whisker plot of the On Time data values. In your final answer, include all calculations necessary to create the box and whisker plot. Use the frequency table to create a box and whisker plot of the Late data values. In your final answer, include all calculations necessary to create the box and whisker plot.
Answer:
Yes
Step-by-step explanation:
1. Yes , the data franchise owner is collecting, will be helpful in order to counter the criticism from the critic. As he has a record for every delivery they are making on daily basis.
2. The scenario is that for every fifth customer , the owner cross the four lines he makes. Thus a pack of five and easy to remember. As the data on regular week days is less, As can do the same for the third customer. Crossing the 2 lines for 3rd customer.
3. With this provision of crossing the third customer, the owner can have a better check on the late delivery. As it will bring in his notice earlier as compared to fifth crossing.
4. With the data as provided in the table, we can come to the conclusion that on weekends , i.e. both on time delivery and late deliveries are high in numbers. It must be because of high demand on that days. So owner must make some provision like hiring some more delivery boys for weekend in order to reduce the late deliveries.
How do i add and subtract
Answer:
take the dots and either put them together or rake them away
Step-by-step explanation:
Example: .....+..=....... five dots plus two dots equals seven dots.
......-...=... six dots minus three dots equals three since you are taking away three
i hope u found this helpful.
A six-sided number cube is rolled and the proportion of 3s is calculated. The graph shows the long-run relative frequency of 100 rolls of this die. A graph titled proportion of threes has frequency on the x-axis, and probability on the y-axis. The graph increases, and then stays steady around y = 0.17. Which conclusion can be drawn from this graph? There is a 20% chance of rolling a 3 with this die. The long-run frequency of rolling a 3 appears to be about 0.17. Because the probabilities on the left part of the graph fluctuate so much, we cannot conclude that this is a fair number cube. This number cube must be fair because each outcome of rolling a 1, 2, 3, 4, 5, or 6 has the same probability of occurring.
The conclusion that can be drawn from this graph on the long-run frequency of 100 rolls is The long-run frequency of rolling a 3 appears to be about 0.17.
What does the graph show?At the 0.17 probability, the proportion of 3s calculated levels off from around the 40th roll to the 100th roll.
This means that the long-run frequency of rolling a 3 is around 0.17 because this was the probability seen for most of the rolls over time.
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36. During rehearsal for the Founders' Day choir
program, the director, Mrs. Mazurek, tried 3 different
configurations, each using all the choir members at the
rehearsal. One configuration was to have only rows of
12, one was to have only rows of 15, and one was to
have only rows of 20. None of these configurations
worked because for each, the last row had 1 person
less than the other rows. What was the least of the
possible numbers of choir members at the rehearsal?
The LCM stands for the least common multiple. The least of the possible number of choir members at the rehearsal is 59.
What is LCM?The least common multiple that is divisible by both a and b is the smallest positive integer, lowest common multiple, or smallest common multiple of two numbers a and b, generally indicated by LCM.
Given the configurations of choir members at the rehearsal, which are,
One configuration was to have only rows of 12, One was to have only rows of 15, And one was to have only rows of 20.Now, it takes the LCM of 12, 15, and 20, then the LCM will be 60, But since None of these configurations worked because for each, the last row had 1 person less than the other rows. The number of members was 1 less than the LCM.
Hence, the least of the possible number of choir members at the rehearsal is 59.
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how many minutes does the white vacuum need to clean 86.25 square feet?
black vacuum cleans 8 square feet per min
white vacuum cleans 60 square feet for 8 min
red vacuum cleans 150 square feet for 25 min
Answer:
1.5 hours
As a general rule, 1,000 square feet of the house should take 1.5 hours to clean, according to Cleaning 4 Profit. So a 3,000 square feet home should take 3 hours to clean, and so on.
19. What are equivalent statements to a + 3 = 18 and 4 b = 32?
a = 18-3 and b = 32/4
a=18/3 and b = 32/4
a = 18/3 and b = 32-4
a = 18-3 and b = 32 - 4
Answer:
The choice second . a=18/3 and b = 32/4
Step-by-step explanation:
[tex]a + 3 = 18 \\ a = 18 - 3[/tex]
[tex]4b = 32 \\ \\ b = \frac{32}{4} [/tex]
Question 18
A wholesale grocery supplier shipped x2-pound blocks of cheese and y3-pound blocks of cheese to a caterer. The total weight of the cheese in the shipment was 44 pounds, and
the shipment consisted of 18 blocks of cheese. Which of the following systems of linear equations best represents this situation?
z+y=18
A
3z +2y=44
z+y=18
2x + 3y = 44
z+y=44
3z + 2y = 18
z+y=44
2z+3y=18
B
C
D
Imported (1)
The G
The system of linear equations that best represents the situation are:
z+y=18
3z +2y=44
What are the linear equations?In order to determine the values of the two types of cheese, two set of linear equations can be formed from the question. The equations have to be solved together using either the elimination , substitution or graphical methods.
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Eric plays basketball and volleyball for a total of 95 minutes every day. he plays basketball for 25 minutes longer than he plays volleyball. part a: write a pair of linear equations to show the relationship between the number of minutes eric plays basketball (x) and the number of minutes he plays volleyball (y) every day. (5 points) part b: how much time does eric spend playing volleyball every day? show your work. (3 points) part c: is it possible for eric to have spent 35 minutes playing basketball if he plays for a total of exactly 95 minutes and plays basketball for 25 minutes longer than he plays volleyball? explain your reasoning. (2 points)
Answer:
a-x=y+25
b-35 minutes
c-nort possible
Step-by-step explanation:
can't explain due to the fact it will take 30m to type up
A hiker walks x metres up a hill at 6/5 m/s and walks back down the same path to where they started at 2 m/s.
Give a simplified expression for the total time in seconds of the walk in terms of x (showing working out).
The total time in seconds of the walk-in terms of x is given as (4/3)x
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the distance walked, hence:
Total time = [x / (6/5)] + x/2 = (4/3)x
The total time in seconds of the walk-in terms of x is given as (4/3)x
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please help with this thank you!
Answer:
3
Step-by-step explanation:
18-15=3
Answer:
first option, 3
Step-by-step explanation:
The interquartile range is the difference between Q3 and Q1.
Q1 is the lower bound of the box = 15
Q3 is the upper bound of the box = 18
Q3 - Q1
= 18 - 15
= 3
Which of the following choices lists the values of the side lengths of a triangle with 45-45-90 degree angles and a leg = 5?
5, 5, 5
5, 1, 5
1, 5, 5
1, 1, 5
A triangle is a three-edged polygon with three vertices. The length of the sides of the triangle is 5, 5, and 5√2.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.
Since the two angles are equal, therefore, the length of the two legs of the isosceles right triangle will be equal and will be less than the hypothenuse.
Hence, the length of the sides of the triangle is 5, 5, and 5√2.
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Find the volume of the rectangular prism below
V = L * W * H
Answer:
40[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
V = L × W × H
V = 1.5 × 6 × 4.5
V = 40.5 or 40[tex]\frac{1}{2}[/tex]
Answer:
40 1/2ft
Step-by-step explanation:
H(4 1/2 )x W(1 1/2) = 6.75
HW(6.75)x L(6) = 40.5
0.75x + 0.8(x + 10) = 101
what is x
Step-by-step explanation:
0.75x + 0.8(x + 10) = 101
0.75x + 0.8x + 8 = 101
1.55x = 101 - 8
1.55x = 93
x = 93 ÷ 1.55
x = 60
Represent -5 / 4 and 5 / 4 on number line
Answer:
Image included:
Step-by-step explanation:
Select the correct answer from the drop-down menu. Simplify the expression. (1-cot(r))^2/cot(r)
The simplified form of the given expression is tan(r) + cot(r) - 2
Simplifying trigonometric functionsFrom the question, we are to simplify the given trigonometric function
The given trigonometric function is
[tex]\frac{(1-cot(r))^{2} }{cot(r)}[/tex]
Expanding, we get
[tex]\frac{(1-cot(r))(1-cot(r)) }{cot(r)}[/tex]
Simplifying
[tex]\frac{1 - 2cot(r) +cot^{2}(r) }{cot(r)}[/tex]
[tex]\frac{1}{cot(r)} -\frac{2cot(r)}{cot(r)}+\frac{cot^{2}(r) }{cot(r)}[/tex]
[tex]\frac{1}{cot(r)} -2+cot(r)[/tex]
Recall: [tex]tan(x) = \frac{1}{cot(x)}[/tex]
Therefore, we get
[tex]tan(r) -2 + cot(r)[/tex]
[tex]tan(r) + cot(r)-2[/tex]
Hence, the simplified form of the given expression is tan(r) + cot(r) - 2.
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Please help me!
Explain how to use the graphs of systems of equations to state when the system has one solution, no solution, or infinite solutions. Be specific.
Explanation:
The solution set for a system of equation is the set of points where the graphs of the equations intersect.
__
general caseA system will have one solution if there is a single point of intersection of the graphs of the equations.
A system will have no solutions if the graphs have no points of intersection.
A system will have an infinite number of solutions if the graphs intersect at an infinite number of points.
_____
linear equationsWhen the equations are linear equations, their graphs are straight lines. If the lines have different slopes, they must intersect at exactly one point: there will be one solution.
If the lines have the same slope, there are two possibilities:
the lines are parallel -- no solutionsthe lines are coincident -- infinite solutionsThe attached graph illustrates these cases.
the red and blue lines are the graphs of a system of equations with one solution. Those lines have different slopesthe blue and green lines are the graphs of a system of equations with no solution. Those lines are parallel.The red and (dotted) purple lines are the graphs of a system of equations with infinite solutions. Those lines are coincident.I WILL GIVE BRAINLIEST here is a square
Answer:
135 degrees
Step-by-step explanation:
180-90=90/2=45
180-45=135
Hope this helped:)
Write your answer in simple solution (4x^3+2x+6)+(2x^3-x^2+2)
Make a table to help solve this problem. Cory, Srey, Molly, and Mao each visited a different city: Santa Clara, Seattle, Des Moines, and Pittsburgh. Cory and Molly visited cities with two words in their names. Mao and Cory visited cities whose names start with an S. Who visited Pittsburgh?
From the table we can say Srey visited Pittsburgh if the Cory, Srey, Molly, and Mao each visited a different city: Santa Clara, Seattle, Des Moines, and Pittsburgh.
What is reasoning?When making a choice or addressing an issue, reasoning is the ability to appraise things rationally by using logic based on new or existing information.
We have:
Cory, Srey, Molly, and Mao each visited a different city: Santa Clara, Seattle, Des Moines, and Pittsburgh. Cory and Molly visited cities with two words in their names.
Mao and Cory visited cities whose names start with an S.
The table can be make to show the information provided:
Cory - city with 2 words
Molly - city with 2 words
Mao - starting with an s
Cory - starting with an s
cities are : Seattle, Santa Clara,Pittsburgh,Des Moines
The table is:
Name City name
Cory Santa Clare
Molly Des Moines
Mao Seattle
Srey Pittsburgh
Thus, from the table we can say Srey visited Pittsburgh if the Cory, Srey, Molly, and Mao each visited a different city: Santa Clara, Seattle, Des Moines, and Pittsburgh.
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help me I need the answer on paper help me now
Answer:
x = 144
Step-by-step explanation:
Angle sum of heptagon = 900
5x + 90 + 90 = 900
5x + 180 = 900
5x + 180 - 180= 900 - 180
5x = 720
Divide both sides by 5
x = 144
Work out the value of 2⁰
Answer:
1
Key:
[tex]a^0=1,\:\quad \:a\ne \:0[/tex]Step-by-step explanation:
[tex]2^0=1[/tex]
1. Marc and Julian are considering the following investments for their portfolio. Help
them evaluate each one by weighing the risk versus return. Rank each as low,
moderate, or high in each category. (12 points)
The risk versus return of the investments that Marc and Julian are considering are:
Money Market savings account - Low.IRA - Moderate. Stock in new high tech company - High. Mutual Fund - Moderate. Five year CD (2% interest) - Low.High-yield five-year bond - High. How risky are these investments?Money Market savings accounts are offered by commercial banks and are quite safe which is why they have low returns. The same is true of a Five year CD.
IRAs and Mutual funds are considered moderate because they offer higher rates than CDs but with higher risk as well.
Stock and high-yield bonds are quite risky but they have a chance of a high return as well.
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Suppose a bag contains 5 blocks. 3 red, 1 yellow and 1 green. what is the probability of selecting a red block?
answer is 3/5
since there are 3 red, there is a 3 blocks out of 5 blocks chance that a red block will chosen
Liliana wants to write an equivalent expression for n + 3 minus 5 n + 6. Which of her attempts uses the algebraic properties correctly?
Answer:
n+3-(5n+6)=0
n+3-5n-6=0
5n-n=6-3
4n=3
4n/4=3/4
n=3/4
1 tablespoon is equivalent to _____ ml.
Answer:
14.7868 ml are equal to 1 tablespoon
Step-by-step explanation:
1 tablespoon is equivalent to __14.7868___ ml.
Hope This Helped
Answer:
14.7868ml or 15 ml
Step-by-step explanation:
it can be either one since 14.7686 is close to 15
Georgia drove 156 miles in 4 hours. If this rate continue, how many miles can he drive in 7 hours
Answer: he drives 273 miles for 7 hours
Step-by-step explanation: