27. If f is the function given by f(x) = int[4,2x] (sqrt(t^2-t))dt, then f'(2) =
Answers
F is the function given by f(x) =\(int[4,2x] (\sqrt{(t^2-t))dt,\)
then \(f'(2)= 2\sqrt{(28)-8.\)
To find f'(2), we need to differentiate the Function f(x) with respect to x and then evaluate it at x = 2.
Using the Second Fundamental Theorem of Calculus, we know that:
\(f(x) = int[4,2x] (\sqrt{(t^2-t))dt\)
So, to differentiate f(x), we need to use the Chain Rule and the Fundamental Theorem of Calculus:
\(f'(x) = d/dx \ int[4,2x] (\sqrt{(t^2-t))dt\\= (\sqrt{((2x)^2-2x)}-\sqrt{(4^2-4))} \times d/dx (2x)\\= (\sqrt{(4x^2-2x)-4)} * 2\\= 2\sqrt{(4x^2-2x)-8\)
Now, we can evaluate f'(2) by substituting x = 2 into the above expression
\(f'(2) = 2\sqrt{(4(2)^2-2(2))-8\\= 2\sqrt{(28)-8\)
Therefore, \(f'(2) = 2\sqrt{(28)-8.\)
To Learn More About Function
https://brainly.com/question/11624077
#SPJ11
Related Questions
find all of the zeros of the polynomial ()=5 34 143 422 −32−96, given that −3 and 4 are zeros
Answers
The zeroes of the given polynomial x⁴ + x³ - 34x² - 4x + 120 are: 2, -2, -6, and 5.
In mathematics, polynomials are expressions consisting of variables and coefficients, combined using addition, subtraction, and multiplication. The zeroes of a polynomial are the values of the variable for which the polynomial evaluates to zero.
The given polynomial is x⁴ + x³ - 34x² - 4x + 120. We are told that two of its zeroes are 2 and -2. Let's call the remaining zeroes (if any) as 'a' and 'b'. To find the remaining zeroes, we can use polynomial division or synthetic division to reduce the polynomial.
We now have a quadratic equation: x² + x - 30 = 0. To find the remaining zeroes, we can factorize this quadratic equation or use the quadratic formula.
Factoring:
x² + x - 30 = 0
(x + 6)(x - 5) = 0
From the factorization, we find two additional zeroes: x = -6 and x = 5.
To know more about polynomial here
https://brainly.com/question/11536910
#SPJ4
Complete Question:
Find all the zeroes of the polynomial given below having given numbers as its zeroes.
x⁴ +x³ −34x² −4x+120;2,−2.
What are the minimum number of nodes and arcs that need to be deleted to reduce a full binary tree of height > 2 to be a forest of 4 binary trees.
Answers
To reduce a full binary tree of height > 2 to a forest of 4 binary trees, delete 3 nodes (2 leaves, 1 internal) and their associated arcs.
To reduce a full binary tree of height greater than 2 to a forest of four binary trees, we need to delete a minimum of 3 nodes and 3 arcs. Here's a brief solution:
1. Start with the full binary tree of height greater than 2.2. Delete any one leaf node and its associated arc. This creates the first binary tree in the forest.3. Delete another leaf node and its associated arc. This creates the second binary tree in the forest.4. Delete a non-leaf node (internal node) and both its associated arcs. This splits the remaining portion of the original tree into two binary trees.5. Delete the remaining nodes and arcs to create the third and fourth binary trees in the forest.
By following these steps, we have reduced the full binary tree to a forest of four binary trees by deleting a minimum of 3 nodes and 3 arcs.
To learn more about binary click here
brainly.com/question/31413821
#SPJ11
alex is going on a 540 mile journey so far he has travelled 1 percent of his journey how many miles has he travelled
Answers
Answer:
5.4
Step-by-step explanation:
he has traveled 5.4 miles
Answer:
5.4 miles
Step-by-step explanation:
The distance which Alex is going to cover= 540 miles
The Percentage of distance which he had travelled= 1%
The actual distance he had travelled= 1% of 540
= \(\frac{1}{100}\) x 540
= 5.4 miles
∴ Alex covered 5.4 miles as he travelled by 1 percent of his journey
what is the slope of the line?? PLZ help
Answers
The line starts at 0 and goes up by 2 from there.
Airline companies are interested in the consistency of the number of babies on each flight, so that they have adequate safety equipment. Suppose an airline conducts a survey. Over Thanksgiving weekend, it surveys 6 flights from Boston to Salt Lake City to determine the number of babies on the flights. R determines the amount of safety equipment reeded by the result of that study.
Select the ways that you would improve the survey if it were to be repeated.
i. Ask travelers to fill out a questionnaire
ii. Conduct the survey at the entrance to the airport.
iii. Conduct the survey during different times of the year.
iv. Conduct the survey on different days of the week.
v. Conduct the survey using flights to and from various locations
Answers
To improve the survey on the consistency of the number of babies on each flight, it would be beneficial to ask travelers to fill out a questionnaire, conduct the survey during different times of the year, on different days of the week, and using flights to and from various locations.
To improve the survey on the consistency of the number of babies on each flight, the following options can be considered:
i. Ask travelers to fill out a questionnaire: By asking travelers to fill out a questionnaire, the airline can collect data on the number of babies on each flight more accurately. This method allows for systematic data collection and reduces reliance on memory or estimation.
iii. Conduct the survey during different times of the year: Conducting the survey during different times of the year helps to capture seasonal variations in the number of babies on flights. It provides a broader perspective on the consistency of the number of babies across different travel periods.
iv. Conduct the survey on different days of the week: Surveying flights on different days of the week allows for an examination of any day-specific patterns or variations in the number of babies on flights. This helps in understanding if there are specific days that have higher or lower numbers of babies.
v. Conduct the survey using flights to and from various locations: Extending the survey to flights to and from various locations helps in capturing the variability of the number of babies across different routes. It provides a more comprehensive understanding of the consistency of the number of babies on flights, taking into account different origins and destinations.
ii. Conduct the survey at the entrance to the airport: Conducting the survey at the entrance to the airport may not be an effective method to gather accurate data on the number of babies on flights. This approach may be prone to biases, as not all travelers entering the airport would necessarily be taking a flight. It is better to survey passengers specifically on the flights being studied.
To know more about consistency,
https://brainly.com/question/30501318
#SPJ11
What is the value of x in the equation below?
6(x-3) = 72
12
15
20
24
Answers
Answer:B
Step-by-step explanation:
Please help 10 points
Answers
The question gives away that she had earned more last week than this week. So the result has to be greater than £80.
If we solve for a,
a - 10 = 80
Add 10 to both sides, we get a = 90
The answer is a - 10 = 80
use elementary row or column operations to find the determinant. 3 −3 −2 3 1 2 −6 6 4
Answers
To find the determinant using elementary row or column operations, we can use the following steps:
1. Rewrite the matrix in an augmented form with the identity matrix on the right:
3 -3 -2 | 1 0 0
3 1 2 | 0 1 0
-6 6 4 | 0 0 1
2. Use elementary row operations to transform the matrix into an upper triangular form:
R2 = R2 - R1
R3 = R3 + 2R1
R3 = R3 + 2R2
3 -3 -2 | 1 0 0
0 4 4 | -1 1 0
0 0 0 | -2 2 1
3. The determinant of an upper triangular matrix is the product of its diagonal elements:
det(A) = 3 x 4 x 0 = 0
Therefore, the determinant of the original matrix is 0.
https://brainly.com/question/31485592
#SPJ11
The United States Postal Service (USPS) now offers a service that allows customers to ship packages at a flat rate based on box size (small, medium, large) rather than by weight. The USPS records the weight of all small packages shipped using this new service and finds a normally distributed variable with a mean of 6.9 pounds and a standard deviation of 10 ounces (.63 pounds).
Required:
What is the probability that a package shipped in a small size box will weigh more than 6 pounds?
Answers
The probability that a package shipped in a small size box will weigh more than 6 pounds is 0.9236, or 92.36%.
To find the probability that a package shipped in a small size box will weigh more than 6 pounds, we need to convert the weight of 6 pounds to the same unit as the mean and standard deviation given in the problem, which is pounds.
Since 1 pound is equal to 16 ounces, 6 pounds can be expressed as 6 * 16 = 96 ounces. Converting 96 ounces to pounds gives us 96 / 16 = 6 pounds.
Now that we have the weight in pounds, we can use the normal distribution to calculate the probability.
The mean weight of small packages is given as 6.9 pounds, and the standard deviation is 10 ounces, which is equivalent to 0.63 pounds. To find the probability that a package weighs more than 6 pounds, we need to calculate the area under the curve to the right of 6 pounds.
To do this, we can use a standard normal distribution table or a statistical calculator. Using the standard normal distribution table, we can find the corresponding z-score for 6 pounds by subtracting the mean from 6 pounds and dividing by the standard deviation:
z = (6 - 6.9) / 0.63 = -1.429
Looking up the z-score of -1.429 in the standard normal distribution table, we find that the corresponding area to the right of -1.429 is 0.9236.
Therefore, the probability that a package shipped in a small size box will weigh more than 6 pounds is 0.9236, or 92.36%.
For more question on probability visit:
https://brainly.com/question/25839839
#SPJ8
Select the expression that can be used to find the volume of this rectangular prism. A. ( 6 × 3 ) + 15 = 33 i n . 3 (6×3)+15=33 in.3 B. ( 3 × 15 ) + 6 = 51 i n . 3 (3×15)+6=51 in.3 C. ( 3 × 6 ) + ( 3 × 15 ) = 810 i n . 3 (3×6)+(3×15)=810 in.3 D. ( 3 × 6 ) × 15 = 270 i n . 3
Answers
Answer:
D
Step-by-step explanation:
(3x6)x15=270 in
the volume formula is base times width times height.
Answer:
D
Step-by-step explanation:
i took the quiz
X+2 - x+3;x2+x-2 - x2-1
Answers
Answer:
x+2-x+3
x-x+2+3
2+3
5
2x+x-2-2x-1
2x-2x+x-2-1
x-2-1
x-3
I need help with this question please
Answers
Answer:
y = - |x| - 4
Step-by-step explanation:
this is an absolute value graph
Gayle installed a rectangular section of hardwood flooring measuring 12 ft by 12 ft in her family room. She plans on increasing the area of the flooring to 256 ft2 by increasing the width and length by the same amount, x. Which equation can be used to find x?
A. 256=(12+x)(12+x)
B. 256=(12−x)(12−x)
C. 256=12(12+x)
D. 256=12(12−x)
Answers
Given information:Gayle installed a rectangular section of hardwood flooring measuring 12 ft by 12 ft in her family room. She plans on increasing the area of the flooring to 256 ft2 by increasing the width and length by the same amount, x.
Formula for the area of a rectangular is given as follows:Area of a rectangular = Length × WidthLet, the width and length of the rectangular be x.So, the area of the rectangular after increasing the width and length by the same amount will be:(12 + x) × (12 + x)According to the question, the area of the rectangular after increasing the width and length by the same amount is 256.So, the equation that represents the given situation is:256 = (12 + x) × (12 + x)256 = (12 + x)²Answer:Option A: 256 = (12 + x) × (12 + x) is the correct equation to find x.
To know more about width and length,visit:
https://brainly.com/question/30619640
#SPJ11
Find the HCF of
\( 4x {}^{2} y \: and \: 12xy {}^{3} \)
Answers
Answer:
I hope the pic i gave is helpful!!!
![Find the HCF of[tex] 4x {}^{2} y \: and \: 12xy {}^{3} [/tex]](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/cYdbFjwAreErXb5YD0lAAQbXjoPGnhcD.jpeg)
pls help asap if you can!!!
Answers
The statement that best proves that <XWY ≅ <ZYW is that two parallel lines are cut by a transversal, then the alternate interior angles are congruent
How to determine the statementTo determine the correct statement, we need to know the properties of a parallelogram.
These properties includes;
Opposite sides are parallel. Opposite sides are congruent. Opposite angles are congruent. Same-Side interior angles (consecutive angles) are supplementary. Each diagonal of a parallelogram separates it into two congruent triangles.The diagonals of a parallelogram bisect each other.Learn more about parallelogram at: https://brainly.com/question/10744696
#SPJ1
1004.8 into 3 significant figures
Answers
Rounding off the 1004.8 into 3 significant figures will give 1000.
Significant Figures:Since significant figures are established as digits, they are also known as significant digits. By counting all of the values beginning with the first non-zero digit on the left, it is possible to determine the number of significant digits.
For example, the number of significant figures in 567 is 3.
The number of significant figures in 2.671 is 4.
Here we have a number
1004.8 need to be rounded off for 3 significant figures
Since 4 is less than 5 then the resultant number = 1000
[ 4 and 8 neglected since 4 < 5]
Therefore,
Rounding off the 1004.8 into 3 significant figures will give 1000.
Learn more about Significant Figures at
https://brainly.com/question/29153641
#SPJ1
a dataset on 91 roller coasters lists the duration of the ride in seconds in addition to the drop height in feet for some of the coasters. one coaster, the tower of terror, is unusual for having a large drop but a short ride. after setting it aside, a regression to predict duration from drop for the remaining 90 coasters has r29.4%. complete parts a through c.a) What are the variable and units in this regression? The predictor variable is ___ in units of ___ and the response variable is ___ in units of ___ b) What units does the slope have? Feet, Seconds per foot, Seconds, Feet per second. c) Is the slope probably positive or probably negative? Explain. The slope is probably ____ because ___
Answers
(a) The predictor variable is Fall in feet and the response variable is Duration in seconds.
(b) The slope is in seconds per foot.
(c) The slope may be negative, as greater drop heights generally result in longer travel times.
(a) The predictor variable in this regression is Drop, which represents the drop height of the roller coaster, in feet, in feet. The response variable is Duration, which represents the duration of the trip, in seconds, in seconds.
(b) The units of slope in this regression are seconds per foot. This means that for each unit of increase in descent height in feet, the travel time will increase or decrease the value of the slope, measured in seconds per foot.
(c) The slope can be negative, as greater drop heights generally result in longer ride times, and the Tower of Terror roller coaster, which was exceptionally short despite its large drop height, has were removed from the analysis.
Therefore, the remaining 90 roller coasters in the dataset likely exhibit a negative relationship between drop height and time, meaning that as drop height increases, ride time decreases .
The Low R-value squared 29.4% means that the relationship between roller coaster drop and ride time in the data set is highly variable, but the negative slope indicates a general downward trend.
Learn more about Slope:
https://brainly.com/question/3605446
#SPJ4
another name for the Sacrament of Holy Orders
Answers
Answer:
I believe its Ordination
Step-by-step explanation:
Answer:
Another name for the Sacrament of Holy Orders is "Ordination". This sacrament confers the power and authority to perform sacred duties and functions within the Church hierarchy. It is administered to individuals who have been called to serve as deacons, priests, or bishops in the Catholic Church.
Step-by-step explanation:
I need help, my teacher didnt teach up this
Answers
Answer:
The volume is 1539.38
Step-by-step explanation:
Answer:
384.7 cubic inches
Step-by-step explanation:
formula to find Volume of a Cylinder:
V = π · r² · h
7 is the diameter, so r = 3.5
V = π (3.5)² · 10
V = π (12.25)(10)
V = π · 122.5
V ≈ 384.7 in³
What is the smallest sum of money that can be made up of an exact number of 10cent pieces or 25 cent pieces
Answers
Answer:
zerooooooooooooooooooooooooooooooo
If the original quantity is 8 and the new quantity
is 2, what is the percent decrease?
Answers
If the original quantity is 8 and the new quantity is 2, then the correct answer is 75%.
How did we figure this out?
For this question we need to subtract and multiply the numbers. We know that 2 = 25% of 8 so:
\(\boxed{8-2=6}\\\boxed{6/2=3}\)
We are going to take that 25% and multiply it with 3 to get are final answer.
What is the missing number of 25 and 3?\(\boxed{25*3=75}\\\boxed{So,2=75}\)
Therefore, If the original quantity is 8 and the new quantity is 2, then the correct answer is 75%.
what were descartes’ chief contributions to mathematics?
Answers
Answer:Descartes’s chief contributions to mathematics were his analytical geometry and his theory of vortices, and it is on his researches in connection with the former of these subjects that his mathematical reputation rests. Who is Rene Descartes is he known for? Descartes has been heralded as the first modern philosopher.
Step-by-step explanation:
What is the perimeter of a right triangle with legs measuring 9 ft. and 12 ft.
O
Answers
pls help 11111111111111
Answers
Answer:
g(x) = \(2^{x}\) + 4
Step-by-step explanation:
Given f(x) then f(x) + c is a vertical translation of f(x)
• If c > 0 then a shift up of c units
• If c < 0 then a shift down of c units
Here the shift is 4 units up , then
g(x) = \(2^{x}\) + 4
Answer:
the answer is B g(x)=2^x+4
Step-by-step explanation:
Can someone heeeeelp???
Answers
23+44=67
23+35=58
67+58+55=180
Which triangles are congruent? 30° 110° A 30° 45° B 110° 40 C С
Answers
Answer:
It would be triangles A & C
Step-by-step explanation:
This is because all of the angles within triangle add up to 180, with this, you can do the following to find the missing sides:
Tri A:
180-110-30 = 40
Tri B:
180-45-30 = 105
Tri C:
180-110-40 = 30
When you do this, look at the angles of the triangles. You see that Triangle A with the angles 110, 30, and 40 all match with those seen in Triangle C.
Therefore, the two triangles are congruent.
anybody know the answer? please help
Answers
Answer:
the first one. slope is 1/2 and y intercebt (b value) is positive 2.
Step-by-step explanation:
Answer:
y=1/2x+2
Step-by-step explanation:
This equation is linear because the graph is a straight line. Therefore, use the slope-intercept form y=mx+b to create the equation.
To find m (the slope), pick two points like (0,2) and (2,3). Find the change in y over the change in x: (y2-y1)/(x2-x1).
y2=3, y1=2, x2=2, x1=0
(3-2)/(2-0)= 1/2
This is the slope which means the equation is one of the first 2 options.
Next find b (the y-intercept) by finding the y value on the graph when x=0. When x=0, y=2. Therefore, b=2 and the final equation is y=1/2x+2
Write a possible equation for a cosine function that has a maximum point at (1, 11) and a minimum point at (8, 3).
Answers
M = A + |B| is the function's highest possible value. When sin or cos x equals 1, this maximum value is reached. m = A |B| is the function's lowest possible value. If either cos x or sin x is equal to 1, this minimum will be reached.
How do you find the maximum and minimum of a cosine function?The sine and cosine functions are graphed; to find the values of the sine and cosine functions for a variety of various degrees of angles, use a calculator, computer, or a collection of trigonometry tables (or radian).Because the sine and cosine functions have periods of 2, the patterns are continually repeated to the left and right.The sine and cosine functions can have a number of additional terms and factors added to them, changing how they look.The graph of the sine functions can be vertically shifted by adding the extra term A to the equation y = A + sin x. The sine function can have different amplitudes because to the additional element B in the equation y = B sin x. The graph's highest and minimum values, or one half of those values, make up the amplitude, or | B |, which is the maximum deviation from the x-axis. Both y = A + B sin x and y = A + B cos x are produced by combining these values. The minimum and maximum values for these two functions are specified by the following formulas. M = A + |B| is the function's highest possible value. When sin or cos x equals 1, this maximum value is reached. m = A |B| is the function's lowest possible value.If either cos x or sin x is equal to 1, this minimum will be reached.Example :
Draw the y = 1 + 2 sin x function on a graph. Which values represent the function's maximum and minimum?1 + 2 = 3 is the highest possible value. 1 + 2 = 1 is the minimum value.To Learn more About sin or cos refer To:
https://brainly.com/question/28160425
#SPJ1
Find the area of the trapezoid. Leave your answer
in simplest radical form.
18 ft
8 ft
60°
Not drawn to scale
56-√√3 f²
® 64-√√3 1²
22031
32-√√3 ft²
Answers
Area of trapezoid in simplest radical form is 64√3 ft² .
Given,
The short leg of the triangle has length (8 ft)(cos 60°), or (8 ft)(1/2), or 4 ft.
The long leg (represented by the dashed line) is (8 ft)(sin 60°), or
(8 ft)(√3/2), or 4√3. This is also the width of the horizontal trapezoid.
Now,
The area of this horizontal trapezoid is:
A = sum of horizontal sides/2 × width
Here, the area is:
=(18 ft + (18 ft - 4 ft) /2 × 4√3
= 64√3 ft² .
Learn more about trapezoid,
https://brainly.com/question/31380175
#SPJ1
evaluate 2a(b + 8) if a = 3 and b = 5. A. 33 B. 38 C. 65 D. 78
Answers
Answer: 78
Explanation: Whenever we deal with an evaluation problem, make sure to always use parenthses when substituting numbers in for variables.
Notice that we have a set of parenthses in our original problem.
To avoid the confusion of having too many sets
of parenthses, let's change the parenthses to brackets.
So we have 2(3) [(5) + 8].
Simplifying from here, we have (6) [(13].
Multiplying, we get 78.
Answer:
D.
Step-by-step explanation:
6*13=78