The point c satisfying the conclusion of the Mean Value Theorem for the function f(x) = x^-8 on the interval [1, 5] is: c = 1.4697
How to solve mean value theorem?The conclusion of the Mean Value Theorem says that there is a number
c in the interval (1, 5) such that:
f'(c) = (f(5) - f(1))/(5 - 1)
We are given the function f(x) = x⁻⁸
Thus:
f(1) = 1⁻⁸ = 1
f(5) = 5⁻⁸ = 0.00000256
Thus:
f'(c) = (0.00000256 - 1)/4
= -0.25
f'(c) = -8x⁻⁹
Thus:
-8c⁻⁹ = -0.25
c⁻⁹ = 0.25/8
c⁻⁹ = 0.03125
c = 0.03125^(-1/9)
c = 1.4697
Read more about Mean Value Theorem at: https://brainly.com/question/19052862
#SPJ1
The mapping diagram represents a relation where x represents the independent variable and y represents the dependent variable. Is the relation a function? Explain. Yes, because for each input there is exactly one output Yes, because for each output there is exactly one input No, because for each input there is not exactly one output No, because for each output there is not exactly one input
Answer:No
Step-by-step explanation:
Because each X is an input, this means that Y is obviously the output.
In order for a set of data, there must ALWAYS be one output for every input, no more, no less. Because this particular set of data has multiple Y values with respect to different X values, this is not a function. Your correct answer is "No, because for each input there is not exactly one output."
50 Points
Janey paints a block of wood with gold glitter for an art project. The block measures
8 inches by 10 inches by 20 inches.
After she's done, she decides to make two blocks by cutting through the block on the
red line. She still wants each block to be covered with gold glitter.
What is the total area of the cut surfaces she still needs to paint?
Answer the questions to find out.
1. What is the shape of each cut surface? what are its dimensions?
2. What is the area of each cut surface?
3. What is the total area Jenny needs to paint? Explain how you found your answer.
Answer:
The shape of each cut surface is a rectangle. The dimensions of the first cut surface are 8 inches by 10 inches, and the dimensions of the second cut surface are 10 inches by 20 inches.
The area of the first cut surface is 8 inches x 10 inches = 80 square inches. The area of the second cut surface is 10 inches x 20 inches = 200 square inches.
To find the total area Jenny needs to paint, we need to add the area of the first cut surface to the area of the second cut surface.
Total area = Area of first cut surface + Area of second cut surface
Total area = 80 square inches + 200 square inches
Total area = 280 square inches
Therefore, Jenny needs to paint a total area of 280 square inches.
factor the expression 6x^3 + 5x
Answer:
x(6x^2 + 5)
Step-by-step explanation:
To factor the expression 6x^3 + 5x, we can first factor out the greatest common factor of the two terms, which is x. This gives:
x(6x^2 + 5)
We can see that 6x^2 + 5 cannot be factored any further using integer coefficients, so the final factored form of the expression is:
x(6x^2 + 5)
A candy store uses 10. 3 grams of sugar each hour. How many grams of sugar will the store use in 10 hours?
The candy store will use 103 grams of sugar in 10 hours.
To find out how many grams of sugar the store will use in 10 hours, we can simply multiply the amount of sugar used in one hour (10.3 grams) by the number of hours (10).
To solve the problem, we use a simple multiplication formula: the amount used per hour (10.3 grams) multiplied by the number of hours (10) to find the total amount of sugar used in 10 hours.
We can interpret this problem using a rate equation: the rate of sugar usage is 10.3 grams/hour, and the time period is 10 hours. Multiplying the rate by the time gives the total amount of sugar used.
So the calculation would be:
10.3 grams/hour x 10 hours = 103 grams
Therefore, the candy store will use 103 grams of sugar in 10 hours.
Learn more about Basic Maths:
https://brainly.com/question/17083065
#SPJ4
There is exactly 111 pair of parallel sides in the following shape.what is the area of the shape? \text{ units}^2 units 2 start text, space, u, n, i, t, s, end text, squared
Therefore, the answer is not possible to determine without additional information.
There are exactly 111 pair of parallel sides in the shapeTo find:
Area of the shape Formula used:Area of the parallelogram= base × height Explanation: We know that the parallelogram has two pairs of parallel sides. Since we are given that there are 111 pairs of parallel sides in the shape, we can infer that there are 55.5 parallelograms.
But the problem does not specify whether these parallelograms are of the same size or not. Hence we do not know if they will form a single shape or multiple shapes.In the absence of the above information, we cannot determine the area of the shape.
for such more questions on parallelogram
https://brainly.com/question/970600
#SPJ11
Is 4, 5, and 6 a right triangle??..
Step-by-step explanation:
If they are RIGHT triangles then the Pythagorean theorem would apply
c^2 = a^2 + b^2 where c is the long side ( hypotenuse)
4) does 10^2 = 6^2 + 8^2 ?
100 = 36 + 64 Yes....it is a right triangle
5) does 8^2 = ( sqrt26)^2 + sqrt(28^2) ?
64 = 26 + 28 NO....it is NOT a right triangle
6) you should try this one yourself .....
Grace wants to buy carpet to cover her whole living room, except for the tiled floor. The tiled
floor is 6ft by 3-ft. Find the area the carpet needs to cover.
Therefore, the area that the carpet needs to cover is: LW - 18 square feet.
What is area?Area is a mathematical term that refers to the amount of space occupied by a two-dimensional object or shape. It is typically measured in square units such as square feet, square meters, or square inches.
Here,
If the tiled floor is excluded from the area that needs to be covered by the carpet, then we need to find the area of the living room without the tiled floor and add the tiled floor's area to it.
Let's assume that the living room is a rectangular shape with length L and width W.
The area of the living room without the tiled floor is:
Area = L x W - (6 x 3) (since the tiled floor has an area of 6 ft x 3 ft)
Area = LW - 18 square feet
To know more about area of rectangle,
https://brainly.com/question/29294714
#SPJ1
John and his family are going on vacation. They travel 137.5 miles in 2.5 hours. What is the average miles per hour that they travel?
The average miles per hour that John and his family travel is 55 mph.
What is the average annual mileage?American drivers now log a total of 14,263 miles in a single year on average. Around 1,200 miles are driven per month on average, according to this information.
We must divide the whole distance travelled by the total time taken by John and his family in order to determine their average miles per hour:
Total distance x Total time equals average speed.
In this instance, their total journey distance was 137.5 miles, and their total travel duration was 2.5 hours. Hence, we can enter the following values into the formula:
Average speed = 137.5 miles / 2.5 hours
137.5 divided by 2.5 results in:
Average speed is 55 miles per hour.
John and his family therefore travel at an average speed of 55 mph.
To know more about average miles visit:
https://brainly.com/question/27274794
#SPJ1
57% of people in state prisons for drug offenses in the us are african american. what percentage of illicit drug users in the us are african american?
The percentage of illicit drug users in the US are African American is a. 14%
According to data from the National Survey on Drug Use and Health, in 2019, 14.5% of African Americans reported using illicit drugs in the past month, compared to 12.4% of the overall population. While African Americans are overrepresented in state prisons for drug offenses, they do not use drugs at a significantly higher rate than other racial and ethnic groups.
It's important to note that drug use is a complex issue with many social and economic factors at play. It's crucial to approach drug use and addiction with a public health perspective that prioritizes prevention, treatment, and harm reduction over punitive criminal justice approaches.
Learn more about criminal justice and racial disparities in the United States:https://brainly.com/question/30492838
#SPJ11
Your question is incomplete, but probably the complete question is :
57% of people in state prisons for drug offenses in the US are African American. What percentage of illicit drug users in the US are African American?
a. 14%
b. 28%
c. 42%
d. 56%
I need help with this please
Valerie is a member of a movie club. She pays a fixed fee of $40 annually. She must pay $6 for every movie she rents. She rented 14 movies this year. What is the total amount that she paid this year
Valerie paid a total amount of $124 this year for her movie club membership and the 14 movies she rented.
What is total amount?In math, the total amount typically refers to the final sum or result of a calculation involving multiple numbers or quantities.
Valerie pays a fixed fee of $40 annually, and she rented 14 movies at a cost of $6 each. Thus, the total amount she paid this year can be calculated as follows:
Total cost of movie rentals = 14 x $6 = $84
Adding the fixed annual fee to the rental costs:
Total amount paid by Valerie this year = $40 + $84 = $124
Therefore, Valerie paid a total of $124 this year for her movie club membership and the 14 movies she rented.
To learn more about total amount visit:
https://brainly.com/question/26959824
#SPJ9
ΔQRS is an isosceles triangle. What is the length of RT¯¯¯¯¯
? Round to the nearest hundredth. Enter your answer in the box.
Answer:9.22
Step-by-step explanation:
You dont need the left side of this triangle to figure out the answer. You can use the fact that the remaining side to find is of a right triangle and use pythagorean theorem to solve.
Since 11 is the hypotenuse, and the pythagorean theorem states that a^2 +b^2 = c^2, the hypotenuse being c, you can reverse the equation like this:
11^2-6^2=rt^2
if you plug this in, you get that rt is exactly equal to 9.21954445729
Since you asked for it rounded to the nearest hundredth, you can round it to 9.22
use half angle identity. help
pls
Required value of the given expression is (1+√2)
Given expression is [tex]tan \frac{11\pi}{8} [/tex]
We want to solve it.
Now,
[tex] \tan( \frac{11\pi}{8} ) = \tan( \frac{3\pi}{8} + \frac{8\pi}{8} ) \\ = \tan( \frac{3\pi}{8} + \pi ) \\ = \tan( \frac{3\pi}{8} ) [/tex]
Finding [tex] \tan( \frac{3\pi}{4} ) [/tex]
Let,
[tex] \tan(2t) = \tan( \frac{3\pi}{4} ) = - 1[/tex]
Use half angle identity,
[tex] \tan(2t) = \frac{ 2\tan(t) }{1 - {tan}^{2} t} \\ - 1 = \frac{ 2\tan(t) }{1 - {tan}^{2} t} \\ {tan}^{2} t - 2tant - 1 = 0[/tex]
Let,[tex]x = tant[/tex]
So,[tex] {x}^{2} - 2x - 1 = 0[/tex]
Now, [tex]x = 1 \pm \sqrt{2} [/tex]
So,
[tex]tant = tan \frac{3\pi}{8} = 1 \pm \sqrt{2} [/tex]
[tex]tan \frac{3\pi}{8} [/tex] is positive,then required value is 1+√2.
So, option D is the correct answer.
Learn more about angles:
https://brainly.com/question/30147425
#SPJ1
4. George sails his boat 3.7 miles from the dock at the mainland to Paradise Island. From Paradise Island, a 72 degree angle is formed between the dock at the mainland and shipwreck rock. If the distance between Shipwreck rock and the dock is 5.6 miles, approximately how far does George need to sail from paradise island to reach shipwreck rock?
George needs to sail close to 3.7 miles from Paradise Island to reach Shipwreck Rock.
How do we calculate?Applying the law of cosines:
c^2 = a^2 + b^2 - 2ab cos(C)
where:
c = the unknown distance
a = 3.7 miles (distance from the dock at the mainland to Paradise Island)
b = 5.6 miles (distance from the dock at the mainland to Shipwreck Rock)
C = 72 degrees (angle formed between the dock at the mainland and Shipwreck Rock)
The we convert the angle from degrees to radians:
72 degrees = (72/360) * 2π radians = 1.2566 radians (approx.)
Substituting the values into the formula and solving for c:
c^2 = 3.7^2 + 5.6^2 - 2(3.7)(5.6)cos(1.2566)
c^2 = 13.69
c ≈ 3.7 miles
learn more about law of cosines at: https://brainly.com/question/30249060
#SPJ1
By the 46th day, there are 400 water lilies in the pond. the estimate you made:____.a. close to 46 (or exactly right) because it was estimated well.b. too low because the quick exponential growth was not accounted for. c. too high because the exponential growth was overestimated.
By the 46th day, there are 400 water lilies in the pond. the estimate you made: a). close to 46 (or exactly right) because it was estimated well.
We know that the regression equation is: y = 3.915(1.106)ˣ and that the pond can hold 400 water lilies.
y = 3.915(1.106)ˣ
Here, y is equal to the number of water lilies the pond can hold.
So, y = 400
And, x is the required time taken.
So,
400 = 3.915(1.106)ˣ
⇒ (1.106)ˣ = 400/3.915
⇒ (1.106)ˣ = 102.17
Taking logarithm on both sides, we get
log (1.106)ˣ = log (102.17)
⇒ x log (1.106) = log (102.17) .............. [log aˣ = x loga]
⇒ x = [log (102.17)/log (1.106)]
⇒ x = 45.92
x ≅ 46
So, the pond will take 46 days to become full.
To learn more about regression equation, click here:
brainly.com/question/30738733
#SPJ4
Complete question:
Regression equation: y = 3.915(1.106)ˣ . The pond can hold 400 water lilies. by what day will the pond be full? write and solve an equation. the pond will be full by the end of day.
Answer:
b
Step-by-step explanation:
just did it
Consider the expression (x2−9)(x+4). Select all the values of x for which (x2−9)(x+4)=0
Answer:
X= 567890
Step-by-step explanation:
Answer:
See below, please.
Step-by-step explanation:
Using the zero product property, we can set each factor equal to zero and solve for x:
(x² - 9)(x + 4) = 0
(x² - 9) = 0 or (x + 4) = 0
For the first factor, we can factor it further as the difference of squares:
(x + 3)(x - 3) = 0
So, either (x + 3) = 0 or (x - 3) = 0, giving us:
x = -3, x = 3, or x = -4
Therefore, the values of x for which (x² - 9)(x + 4) = 0 are -3, 3, and -4.
help please i’ll give brainliest!!!
Answer:
Apparently it's 4800 according to desmos.
Step-by-step explanation:
Step-by-step explanation:
x y
-3 150
-2 300
-1 600
0 4800
As you can see, for negative values of x, the area burned becomes smaller and smaller as x becomes more negative. This is because the equation y = 4800(2)^x has a base of 2, which means that as x becomes more negative, 2^x becomes smaller and smaller, causing y to become smaller and smaller as well.
Please answer my question by the way the number 4 and 5 is FOIL.
Using FOIL method for the multiplication, we have:
1: 3x (5x - 4) = 15x² - 12x
2: x²(5x² + 3y + 1) = 5x⁴ + 3x²y + x²
3: (4x + 3)(4x -5) = 16x² - 8x - 15
4: (7x - 3)(4x - 5) = 28x² - 47x + 15
How to carry out multiplication using FOIL?
FOIL is an acronym that stands for "First, Outer, Inner, Last". It is a mnemonic device that is commonly used to remember the process of multiplying two binomials.
No. 1
3x (5x - 4) = 3x*5x + 3x*(-4)
= 15x² - 12x
No. 2
x²(5x² + 3y + 1) = x²*5x² + x²*3y + x²*1
= 5x⁴ + 3x²y + x²
No. 3
(4x + 3)(4x -5) = 4x(4x-5) + 3(4x-5)
= 4x*4x + 4x*(-5) + 3*4x + 3*(-5)
= 16x² - 20x + 12x - 15
= 16x² - 8x - 15
No. 4
(7x - 3)(4x - 5) = 7x(4x - 5) - 3(4x - 5)
= 7x*4x + 7x*(-5) - 3*4x - 3*(-5)
= 28x² - 35x -12x + 15
= 28x² - 47x + 15
Learn more about FOIL method on:
https://brainly.com/question/27980306
#SPJ1
use laplace transforms to solve the initial value problem where primes indicate derivatives with respect to t.
To use Laplace transforms to solve the initial value problem where primes indicate derivatives with respect to t, follow these steps.
Write down the given differential equation and initial conditions. Apply the Laplace transform to both sides of the differential equation, using the properties of Laplace transforms for derivatives. Substitute the initial conditions into the transformed equation to get a new equation with no derivatives.Solve this new equation for the Laplace transform of the desired solution function. Apply the inverse Laplace transform to find the solution function in the time domain.Remember to be accurate and concise while solving the problem.
More On Laplace Transforms: https://brainly.com/question/29583725
#SPJ11
does this table represent a proportional relationship
Yes its i Think If its not sorry
Jessica went deep sea diving. She make the first stop on her descent at 25 meters below the surface of the water. From that point she dives down further, stopping every 5 meters. If she makes 4 additional stops, which number represents her position, relative to the surface of the water?
*
A 45
B 20
C -20
D -45
Jessica's position relative to the surface of the water after making 4 additional stops is 45 meters below the surface.Option(A) is correct.
What is sea diving?Divers who engage in scuba diving use breathing apparatus that is entirely independent of a surface air source. Christian J. Lambert-sen came up with the moniker "scuba," which stands for "Self-Contained Underwater Breathing Apparatus," in a 1952 trademark application.
According to question:Jessica's position relative to the surface of the water can be represented by the following arithmetic sequence:
[tex]$$25, 30, 35, 40, 45$$[/tex]
where the first term is 25 and the common difference is 5 (the distance between each stop).
To find the fifth term (her position after making 4 additional stops), we can use the formula for the nth term of an arithmetic sequence:
[tex]$$a_n = a_1 + (n-1)d$$[/tex]
where [tex]$a_1$[/tex] is the first term, d is the common difference, and n is the term number.
Plugging in the values we know, we get:
[tex]$$a_5 = 25 + (5-1)5 = 45$$[/tex]
Therefore, Jessica's position relative to the surface of the water after making 4 additional stops is 45 meters below the surface.
To know more about Meter visit:
brainly.com/question/22552981
#SPJ1
An object's _____ are the tasks or functions that the object performs when it receives a command to do so.
a. roles
b. utilities
c. methods
d. instances
An object's methods are the tasks or functions that the object performs when it receives a command to do so.
What are the methods?The methods of an object describe what the object can perform. In object-oriented programming (OOP), objects are a key element of the language. Each object has a collection of methods that it can perform.
Methods are similar to functions or procedures in traditional programming. They're the code that the object executes in response to a command. Because objects have methods, programming in object-oriented programming (OOP) languages involves defining the object classes, which specify the methods and properties that each object in that class will have.
Roles:- Roles specify the various abilities that an object can perform. In object-oriented programming (OOP), these roles are often defined through interfaces, which specify the set of methods that an object must implement in order to fulfill the role. The role of an object is determined by the methods that it implements.
Utilities:- Utilities are typically unrelated to an object's role, but rather are commonly used functions that are available throughout a system or application. They often provide functionality that is required by many different objects in the system.
c. methods is the correct option.
To know more about the "object-oriented programming (OOP)": https://brainly.com/question/4560494
#SPJ11
(8x - 12) = (3x + 5)
Answer:
x = [tex]\frac{17}{5}[/tex]
Step-by-step explanation:
(8x - 12) = (3x + 5) ← remove parenthesis
8x - 12 = 3x + 5 ( subtract 3x from both sides )
5x - 12 = 5 ( add 12 to both sides )
5x = 17 ( divide both sides by 5 )
x = [tex]\frac{17}{5}[/tex]
or x = 3.4 ( in decimal form )
if y varies directly as x, and y=7 when x=3, find when x=7
By definition, direct variation takes the following form:
y=kx
Where k is the proportionality constant.
You can find k given the information in the problem:
7=3k
k=3/7
You can now find y when x=7 as follows:
y=(7*3)
Values can be substituted. Then:
y=(7*7)/3
y=49/3
If y varies directly from x, then the value of y = 49/3 when x = 7.
If y varies directly from x, we can write its relationship in the form of the equation below :
y = m*x
Where m is the slope of the line on the graph.
From the given data:
y=7
x=3,
We can substitute these values in the above equation and find m :
7 = m*3
m = 7/3
So, the equation can also be written as follow:
y = 7/3 x
Finding y when x=7, then substituting the x value in the above equation we get:
y = (7/3)*(7)
y = 49/3
Therefore the value of the y = 49/3.
to learn more about the slope:
https://brainly.com/question/28645794
Kelly is flying a kite to which the angle of elevation is 70 degrees. The string on the kite is 65 meters long. How far is the kite above the ground?
If Kelly is flying a kite to which the angle of elevation is 70 degrees. The string on the kite is 65 meters long. The kite is about 61 meters above the ground.
How to find the height?We can use trigonometry to solve the problem. Let's call the height of the kite above the ground "h".
Using trigonometry, we can write:
sin (70) = h / 65
Solving for h, we get:
h = 65 * sin(70)
h= 65 * 0.9397
h ≈ 61 meters
Therefore, the kite is about 61 meters above the ground.
Learn more about height here: https://brainly.com/question/73194
#SPJ1
Q5. For all values of x, b) Solve fg(x) = gf(x)
g(x)=x-5
f(x)=x²+1
Answer:
To solve fg(x) = gf(x), we need to find the values of x that satisfy this equation. First, let's calculate fg(x):fg(x) = f(g(x)) = f(x-5) = (x-5)² + 1 Now, let's calculate gf(x):gf(x) = g(f(x)) = g(x² + 1) = (x² + 1) - 5 = x² - 4So, we have the equation:(x-5)² + 1 = x² - 4 Expanding (x-5)², we get:x² - 10x + 26 = x² - 4 Simplifying, we get:-10x + 26 = -4-10x = -30x = 3 Therefore, the solution to fg(x) = gf(x) for all values of x is x = 3.
equivalent fractions for 7/12 and 5/6
Answer:
14/24, 21/36, 28/48, 35/60, 42/72, 49/84, 56/96 are equivalent fractions of 7/12.
10/12, 15/18, 20/24, 25/30. are equivalent fractions of 5/6
Step-by-step explanation:
No idea how to use this app tbh
Answer:
-10
Step-by-step explanation:
I added a photo of my solution
Answer:
Answer is -10
Step-by-step explanation:
Terrell is a dog trainer. He charges $75 for each training session plus $1.45 per mile that he must drive to and from the session. Write an expression to represent this situation. Explain your answer.
(in the expression let x represent the number of miles.)
The expression 75 + 1.45x represents the total cost of a training session with Terrell
The expression to represent this situationLet x be the distance (in miles) that Terrell must drive to and from the training session.
Then the total cost C of the training session, in dollars, can be expressed as:
C = 75 + 1.45x
The first term, 75, represents the base fee that Terrell charges for each training session. The second term, 1.45x, represents the additional cost that Terrell incurs due to the distance he has to drive. This second term is calculated by multiplying the distance x by the rate of $1.45 per mile.Therefore, the expression 75 + 1.45x represents the total cost of a training session with Terrell, including both the base fee and the additional cost for driving.
Read more about linear relation at
https://brainly.com/question/30318449
#SPJ1
daisy has the following production possibilities frontier per week. her resource is 5 lbs of flour. note: you will use this ppf to answer the next several questions. given daisy's ppf, the following production combo, 9 pies and 8 tarts is
The following question is incomplete.
Please complete the question so it can be answered.
Without the actual Production possibility frontier table or chart we cannot determine the exact quantities.
However, based on the information provided, we can determine that the production combo of 9 pies and 8 tarts is a point on Daisy's PPF.
This means that Daisy can produce 9 pies and 8 tarts per week using her available resources of 5 lbs of flour.
To fully analyze production possibilities of Daisy, we would need to see her complete PPF, which would show all possible combinations of pies and tarts that she could produce with her resources.
For more about Production Possibility Frontier please refer to:
https://brainly.com/question/17581360