Let f'(x) = xIn(2x). Determine a simplified expression for the rate of change of f'(x)
The simplified expression for the rate of change of f'(x) is x²(2 ln(2x) - 1)/4 + c.
What is integration?It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.
It is given that:
f'(x) = xIn(2x)
To find the simplified expression for the rate of change of f'(x) integrate the function:
∫f'(x) dx = ∫xIn(2x) dx
Using integration by parts:
∫uv dx = uv - ∫u'v
After solving:
∫xIn(2x) dx = x²(2 ln(2x) - 1)/4 + c
Thus, the simplified expression for the rate of change of f'(x) is x²(2 ln(2x) - 1)/4 + c.
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1. the sum of three and seven divided
by two
2.the sum of four and nine times three
3.ten divided by the product of four
and five
4.the sum of one and two divided
by twenty
Answer:
1. (3 + 7) ÷ 2 = 5
2. (4 + 9) x 3 = 39
3. 10 ÷ (4 x 5) = 1/2
4.(1 + 2) ÷ 20 = 3/20
question content area top part 1 a farmer has 240 bushels of to sell at roadside stand. sells an average of 15 3/5 each day. represent the total change in the number of bushels has for sale after 6 days
Given,
Total no. of bushels = 240
On average, no. of bushels sold by the farmer each day = [tex]15\frac{3}{5}[/tex] =[tex]\frac{78}{5}[/tex]
Therefore,
total no. of bushels sold by the farmer at the end of 6th day
= [tex]15\frac{3}{5}[/tex] x 6 = [tex]\frac{78}{5}[/tex] x 6 = 78 x 1.2 = 93.6
So, no. of bushels left = 240 - 93.6 = 146.4
Hence, the change in bushels is of 93.6 after 6 days of sale.
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3*19*14+18/2 whats the awnser
Answer:
807
Step-by-step explanation:
because u multipy 3x19x14+18/2 and u get 807
Answer:
807
Step-by-step explanation:
3*19*12=798
18/2 = 9
798 + 9 = 807
at what rate percent compound interest wil Rs2000 amount to Rs2420 in 2 years.
The Compound Interest of Principle 2000 will become 2420 within 2 years when the rate of interest is 21%
Compound interest = P(1 + R ÷ 100) to the power of n,
where P = Principle
R = Rate of Interest
n = no. of years
According to the given question,
Principle(P) =Rs2000
Rate of interest (R) =?
no. of years(n) = 2 years
given CI (Compound Interest) = Rs2420
CI = 2000(1 + R ÷ 100)² = 2420
= 20(100 +R) = 2420
= 100 + R = 2420 ÷ 20
= 100 + R = 121
= R = 121 - 100
= R = 21%
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45 percent of what number is 99
actually the number is "x", which oddly enough is the 100%, so we know that 45% of "x" is 99, what is "x" anyway?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 99& 45 \end{array} \implies \cfrac{x}{99}~~=~~\cfrac{100}{45} \\\\\\ \cfrac{x}{99}=\cfrac{20}{9}\implies 9x=1980\implies x=\cfrac{1980}{9}\implies x=220[/tex]
Tom sold t-shirts and hats at a festival. He made a $5 profit for each t-shirt he sold. He also made a profit of $40 from selling hats. If he made a total profit of $125, how many t-shirts did he sell?
The total number of t-shirts sold by Tom equals to 17 t-shirt.
What is a profit?Basically, a profit refers to the difference between the revenue that an entity has received from its outputs and the opportunity costs of its inputs.
We need to note that he made a total profit of $125. From here, we will proceed to use that data to solve other sections.
From the total profit of $125, he also made a profit of $40 from selling hats. That means that the T-shirt sales alone gives him a profit of $85 ($125 - $40).
Total quantity of t-shirt sold is computed as follows:
= Total profit from t-shirt / Profit per shirt
= $85 / $5
= 17 t-shirt
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Normally a chef uses 13 ounces of chocolate to make chocolate chip cookies. But he started using 16.12 ounces instead. He should advertise the cookies as having _____ percent more chocolate
Group of answer choices
Answer:
24%
Step-by-step explanation:
[tex]16.12 - 13 = 3.12\\3.12 * 100 = 312 \\312 / 13 = 24[/tex]
24% more chocolate
1.00 + 0.24 = 1.24
13 * 1.24 = 16.12
Which equation is the inverse of y = 16x2 + 1?
y = plus-or-minus StartRoot StartFraction x Over 16 EndFraction minus 1 EndRoot
y = StartFraction plus-or-minus StartRoot x minus 1 EndRoot Over 16 EndFraction
y = StartFraction plus-or-minus StartRoot x EndRoot Over 4 EndFraction minus one-fourth
The inverse of the given function, y = 16x² + 1 is: B. y = ±√(x - 1)/16
What is an inverse function?In Mathematics, an inverse function can be defined as a type of function that is obtained by reversing (undoing) the operation of a given function (f(x)).
Generally speaking, a given function (f(x)) and its inverse function has the following property f⁻¹(f(x)) = x.
In order to determine the inverse of the given function, we would interchange input value (x) and the output value (y) as follows:
y = 16x² + 1
x = 16y² + 1
Subtracting 1 from both sides, we have:
16y² + 1 - 1 = x - 1
16y² = x - 1
Dividing both sides by 16, we have:
y² = (x - 1)/16
Taking the square root of both sides, we have:
y = ±√(x - 1)/16
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PLEEASE HELP ASAP AAA
Stanley ate 3/8 of a pizza. his brother ate 3/4 of a pizza how much pizza did they eat in all
Answer:
The Answer is 1 1/8
Step-by-step explanation:
When Stanley ate 3/8 of a pizza and his brother ate 3/4 of a pizza, the amount eaten in all is 1 1/8 of the pizza.
What is a fraction?A fraction simply means a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
In this case, Stanley ate 3/8 of a pizza and his brother ate 3/4 of a pizza.
Therefore, the amount eaten by both of them will be:
= 3/8 + 3/4
= 3/8 + 6/8
= 9/8
= 1 1/8.
The amount is 1 1/8.
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Order the following expressions from least to greatest.
Answer:
[tex]\boxed{a} \quad \boxed{|b - c|} \quad \boxed{|a - b|} \quad \boxed{|a - c|}[/tex]
Step-by-step explanation:
The bars either side of an expression or a value are the absolute value symbol. "Absolute value" means how far a number is from zero. Therefore, the absolute value of a number is its positive numerical value.
The values of a, b and c are negative. All expressions except "a" are absolute values, and are therefore positive numerical values. Therefore, "a" is the least expression.
The simplest way to calculate each expression's numerical value is by assigning approximate numbers to each value, then carrying out each calculation.
From inspection of the graph:
a ≈ -3.8b ≈ -1.3c ≈ -0.7[tex]\begin{aligned} \implies |a - b| & \approx |-3.8 - (-1.3)|\\ & = |-2.5| \\ &= 2.5\end{aligned}[/tex]
[tex]\begin{aligned} \implies |b - c| &\approx |-1.3 - (-0.7)| \\ &= |-0.6| \\ &= 0.6\end{aligned}[/tex]
[tex]\implies a \approx -3.8[/tex]
[tex]\begin{aligned} \implies |a - c| &\approx |-3.8 - (-0.7)| \\ &= |-3.1| \\ &= 3.1\end{aligned}[/tex]
Therefore: -3.8 < 0.6 < 2.5 < 3.1
Hence, the expressions from least to greatest are:
[tex]\boxed{a} \quad \boxed{|b - c|} \quad \boxed{|a - b|} \quad \boxed{|a - c|}[/tex]
How long should a person cool down after physical activity? responses 1 to 2 minutes 1 to 2 minutes 5 to 10 minutes 5 to 10 minutes 10 to 15 minutes 10 to 15 minutes 15 to 20 minutes
Answer:
15 to 20 minutes
Step-by-step explanation:
Answer:
10-15
Step-by-step explanation:
i took the test
If f(x) = x/2 - 3 and g(x) = 4x^2 + x - 4, find (f +g)(x).
A. 4x^2 + 3/2 x -1
B. 4x^2 + 3/2 x -7
C. 4x^2 + 1/2 x -1
D. 6x^2 -7
Apex Functions!
Answer: B
Step-by-step explanation:
[tex](f+g)(x)=f(x)+g(x)\\\\=\frac{x}{2}-3+4x^2 +x-4\\\\=4x^2 +\frac{3x}{2}-7[/tex]
WILL GIVE BRAINLIEST
The average daily profit of an electronics store is $31,435. The company estimates that 15% is lost each day to returns, with a margin of error of ±4%. What is the maximum the company can expect for returned items?
$3457.85
$4621.13
$5972.65
$6638.22
The maximum that the company can expect for returned items is C. $5972.65
How to calculate the value?From the information, the average daily profit of an electronics store is $31,435 and the company estimates that 15% is lost each day to returns, with a margin of error of ±4%.
In a random survey sample, a margin of error is a statistical measurement that takes into account the discrepancy between actual and anticipated findings. Simply said, you may determine the degree of unpredictability in data and research results using the margin of error.
The maximum the company can expect for returned items will be:
= (15% + 4%) × Profit
= 19% × $31,435
= 0.19 × $31,435
= $5972.65
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-¾ ÷ (-0.06)
Can someone help me with this question please
Answer:
12.5
Step-by-step explanation:
-3\4÷[-0.06]
convert -0.06to fraction
-3\50
then divide
-3\4÷-3\50
sign changes
-3\4 ÷ 50\3
=50\4
=12.5
Write the equation that is the translation of y = |x| left 9 units and up 11 units.
The translation of y = |x| left 9 units and up 11 units is y = |x+9|+11 .
The process of translating an existing graph or equation into a new graph is known as graph translation.
The alteration of algebraic equations is a typical form of algebraic challenge.A translation modifies the graph of a parent function. Dilations, reflections, and translations are the three distinct types of translation. The y-values of a function can be changed vertically, or the x-values can be changed horizontally (affects the x-values).We know that for translation we have to change the x-coordinate and the y-coordinate by the amount that is stated in the translation.
Therefore from the graph we can see that the graph of y =|x| is represented by the blue line and the graph of translation y = |x+9|+11 is represented by the red line.
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Write the equation in slope-intercept form of a line that has a slope of and passes through the point (-6, 0)
3
0 >=²x
xy=
y=x-6
O 0y=x-2
O
0 >=²x+2
The equation of the line in slope intercept form with slope 1/3 and passes through ( - 6, 0) is y = 1/3x + 2.
In mathematics, the slope or gradient of a line is a number that indicates the line's steepness as well as its X and Y directions. The letter "m" stands for slope. The ratio of the "vertical change" to the "horizontal change" between any two separate points on a line is used to compute the slope.
The equation of the line in point-slope form is expressed as:
y - y₁ = m( x - x₁ )
where m is the slope.
So, m = 1/3
( x₁, y₁ ) is the point on the line = ( - 6, 0)
Substituting the values,
y - 0 = 1/3( x + 6 )
y = 1/3( x + 6 )
y = 1/3x + 6/3
y = 1/3x + 2
Hence, the equation in slope-intercept form of the line is y = 1/3x + 2.
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a grocery store sells a bag of 4 oranges for $1.72 . if christopher spent $1.29 on oranges how many did he buy
Christopher would be able to purchase 3 oranges but if the grocery store only sells them in bags of 4 then he would not have enough money to purchase any.
To find our answer we do 4 divided by 1.29 and that is how many he can afford which is 3.1
pls give brainliest
Answer:
He bought 3 oranges
Step-by-step explanation
Divided $1.72 by 4 which gives $0.43
So each orange cost $0.43
0.43 times 3 equals $1.29
a 13-foot ladder is leaning against a wall. if we pull the ladder away from the wall at a rate of 6ft/s, how fast is the top of the ladder moving down the wall when the bottom of the ladder is 12ft from the wall?
Answer:
Below in bold.
Step-by-step explanation:
The relation between the height of the ladder and distance from the ground is given by Pythagoras Theorem:
h^2 = 13^2 - L^2
h = (169 - L^2)^1/2
Finding the derivative:
dh/dL = 1/2(169 - L^2)^-1/2 * -2L
= -L / (169 -L^2)^1/2
dL/dt = 6
So, dh/dt = dh/dL * dL/dt
= -6 * L/ (169 - L^2)^1/2
= -6 * 12 / (169 - 12^2)^1/2
= -72/5 ft /second
= -14.4 ft/second.
It's negative because the distance from the ground is decreasing.
Ramu's sister's age is 28 years old. She is 3 years older than five times Ramu's Age? What is Ramu's age?
Answer:
Ramu's sister's Age= 28
ramus age=×
28=5×+3
5×=28-3
=25
×=25/5
×=5
so the age of Ramu is 5 years old.
Answer:
25 because 5×5= 25 and 25+3=28 so ramu's age is 25
Combine like terms to simplify the expression. 2x - 10 - 5x - 1 + x
Combine X. which is 2x, -5x, x.
we combine -2x and -5x and gives me -3x.
2x -10 -5x -1 +x
now i combine the last x, which is -3x and x and gives us -2x.
-3x -10 -1 +x
now we just combine the rest of the numbers. -10 and -1 and gives me -11.
-2x -10 -1
we have now combine all the numbers and there's nothing else to combine. we're done combining. :))
ANSWER:
-2x-11
I need help on 5,6, and 7 !
In the picture there are 2 problems. The similarity is they two have to find 2 question. The difference is given question are different.
Given that,
In the picture there are 2 problems.
We have to find the difference and similarities of question in the picture.
The similarities are they 2 are word problems.
Another similarity is they two have to find 2 question.
1. How much money for 10 days and How many days to collect the money $1.05?
2.How much gallon of water need for 50 minutes and How much time take to fill the pool?
Another similarity is they two have to justified the answer in a mathematical model.
Now,
The difference is,
First question has given sisters and money problem where as the second has given pool and gallon water problem.
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help me i am helpless.
Answer: -5x >[-3x,4x,1.5x] 10>[11] 6xy>[-7.85xy, -98xy, 155xy]
Step-by-step explanation:
Expand
−
10
(
b
−
9
)
Answer:
Step-by-step explanation:
Expand · Evaluate Fractions · Linear Equations · Quadratic Equations ... 7 + 4 s = 10 ( 6 - 9 s ). 7+4s=10(6−9s) ... 7 + 4 s = 10 ( 6 - 9 s ).
Answer:
-10b × 90
Step-by-step explanation:
-10 * b =-10b
10 *9=90
Your welcome :)
Please help!!! What are the domain and range of the function?
Answer: Option D
Step-by-step explanation:
Step-by-step explanation:
As we know domain of a function is represented by x values on the graph and y values represents the range of the function.
From the given table domain will be the set of all real numbers.
Range of the same function will be y > 4
Option D is the answer. there you go o(*￣︶￣*)o it was hard to but now its easy
In Exercises 12-15, graph the linear function.
12. r(x) = 2
14. g(x) = ²x − 3
How do I graph it? Can someone PLEASE explain!!??
This is due tomorrow so pls help
Answer:
Step-by-step explanation:
Problem 12:
r(x) = 2
Since x will always be 2, it will always be a straight line.
Problem 14:
(I'm assuming the square is on the x)
g(x) = x^2-3
First, start on the y-intercept, and go down 3 as the starting value is -3. You can then substitute a number to find the next point.
For example, if you want to find if x = 1, what y will be:
1^2-3
1-3
-2
You can then do this for the rest of the points to the point.
What is the domain of the following ordered pairs?
(2, 3), (-12, 7), (4, 7)
Answer:
Yes, the relation {(3,2), (4,1), (5,9), (6,12), (7,12)}is a function.
Step-by-step explanation:
Answer:
It's a triangle just like you, except you're acute one.
Step-by-step explanation:
ASAP PLEASE
Solve the following word problem using elimination. Set up a system of equations before solving in order to receive full credit.
The difference between two numbers is 4. The sum of the smaller number and three times the larger number is 36. What are the two numbers?
The two numbers are 10 and 6.
Now, let's take the larger number to be x and the smaller number to be y.
According to the question,
We have the following details:
The difference between two numbers = 4
So, we have the following expression:
(x-y) = 4 .... (1)
The sum of the smaller number and three times the larger number = 36
So, we have the following expression:
(3x+y) = 36 ....(2)
Now, we will use the elimination method to solve these equations. So, we will add equation 1 and 2.
(Please note that the left hand side is added to the left hand side and the right hand side numbers are added to the right hand side numbers.)
(x-y+3x+y) = (4+36)
4x = 40
x = 40/4 (4 is in multiplication on the left hand side. So, it is in the division on the right hand side.)
x = 10
Now, putting the value of x in equation 1,
(x-y) = 4 .... (1)
(10-y) = 4
-y = 4-10
-y = -6
y = 6
Hence, the larger number is 10 and the smaller number is 6.
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What is the image of the point (-5,-7) after a rotation of 270° counterclockwise about the origin?
Answer:
7, -5
Step-by-step explanation:
-5, -7 after a rotation of 270 degrees lands in quadrant 2 left y positive where x negative. while 90 degree clockwise is equal to 270 degree counterclockwise = 7 ,-5 What are the coordinates of the image after a rotation of 90 clockwise?
When the point is rotated through 90° clockwise about the origin, the point M (h, k) takes the image M’ (k, -h). Therefore, the new position of point M (-2, 3) will become M’ (3, 2).
How do you calculate a 90 degree rotation?
The rule for a rotation by 90° about the origin is (x,y)→(−y,x) .
What is the image of point 3/5 If the rotation is?
Answer: The image point will be (-3, -5) .
How do you find the coordinates of the image of a point after a 270 degree rotation?
Answer – To find the coordinates of point (x,y) after a 270° counterclockwise rotation about the origin, multiply the x-coordinate by -1 and then interchange the x- and y-coordinates.
How do you find the rotation point?
The x coordinate of the rotated point is rcos(θ), and the y coordinate is rsin(θ). If you plug in 5 and 66.87 for r and θ, you find that the rotated point (x1,y1) = (1.964, 4.598).
What is 270 degrees rotated?
270 Degree Rotation When rotating a point 270 degrees counterclockwise about the origin our point A(x,y) becomes A'(y,-x). This means, we switch x and y and make x negative.
What is 90 degrees counterclockwise?
90 Degree Rotation When rotating a point 90 degrees counterclockwise about the origin our point A(x,y) becomes A'(-y,x). In other words, switch x and y and make y negative.
How do you rotate a point 90 degrees clockwise?
Answer: To rotate the figure 90 degrees clockwise about a point, every point(x,y) will rotate to (y, -x).
What is a 90 degree rotation clockwise?
Answer: To rotate the figure 90 degrees clockwise about a point, every point(x,y) will rotate to (y, -x). Let’s understand the rotation of 90 degrees clockwise about a point visually.
How do you calculate a 90 degree rotation? The general rule for rotation of an object 90 degrees is (x, y) ——–> (-y, x). You can use this rule to rotate a pre-image by taking the points of each vertex, translating them according to the rule, and drawing the image.
When to rotate point c 180 or counterclockwise?
And this process could be repeated if you wanted to rotation Point C 180 degrees or 270 degrees counterclockwise: Point C after a 180-degree rotation. Point C after a 270-degree rotation. This example should help you to visually understand the concept of counterclockwise geometry rotations.
How to calculate the coordinate point of rotation?
The following formula can be used to calculate the coordinate point in the x-y plane that has rotated by some angle (θ) about the x-axis. Note these formulas are for clockwise rotation. X=xcos (θ)+ysin (θ) Y=−xsin (θ)+ycos (θ) Where X is the new X coordinate. Y is the new Y coordinate. and θ is the angle of rotation.
What is the definition of rotation in geometry?
Rotation Geometry Definition: A rotation is a change in orientation based on the following possible rotations: 90 degrees clockwise rotation 90 degrees
Step-by-step explanation: A standard cube has 6 sides. The spinner has 4 sections. For any section of the spinner you land on, you can land on one of 6 sides of the dice.
The total number of outcomes is 24.
In probability theory, an outcome is a possible result of an experiment or trial.
Each possible conclusion of a particular experiment is unique, and many outcomes are incompatible (only one outcome will occur on each trial of the experiment). All possible outcomes of an experiment make up the elements of a sample space.There is a possibility that events with probabilities between 0 and 1 will occur (inclusively). Each outcome is given a probability inside a discrete probability distribution with a finite sample space. On the other hand, a continuous distribution only permits the assignment of non-zero probabilities to ranges of events, with all individual outcomes having a zero chance.When a number cube is rolled there are 6 distinct outcomes
{1,2,3,4,5,6} = 6
Again when a spinner is spun there are 4 possible outcomes
The total number of outcomes = 6 × 4 = 24
Hence there are 24 distinct outcomes.
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