Answers
A=integral(a,b) [f(x)-g(x)]dx
Since the function is even (the function is mirrored over the y axis) we can evaluate the integral from 0 to 1 and then multiply our answer by 2 since we have the same area on each side of the y axis.
We get A=2*int.(0, 1)[(x^2)-(-2x^4)]dx
Now we can integrate by term.
2*[int.(0, 1)[x^2]dx+int(0, 1)[2x^4]dx]
Now factor out constants.
2*[int(0,1)[x^2]dx+2int(0,1)[x^4]dx]
Now integrate.
2*[(x^3/3)|(0,1) + 2*(x^5/5)|(0,1)]
Now solve.
2*[(1/3)+2*(1/5)]
=22/10
Hope you can decipher what I wrote!
Final answer:
To find the area between two curves, calculate the definite integral of the difference between the two functions over the interval of interest.
Explanation:
To find the area between two curves, you need to calculate the definite integral of the difference between the two functions over the interval of interest. Let's say the two curves are f(x) and g(x), and you want to find the area between them from x = a to x = b. You can write the integral as follows:
Area = ∫(f(x) - g(x)) dx from a to b
Then you can evaluate this integral using integration techniques, such as u-substitution or integration by parts, to find the area between the two curves.
Related Questions
Charlie needs to simplify the
Answers
For example :
(A+B)/C = A/C + B/C.
Then it would be
X^18 y^12/x^3 y^4 + x^9 y^8/x^3 y^4
X^15 y^8 + x^6 y^4.
The solution is D.
Answer:
d
Step-by-step explanation:
John has read the first 114 pages of a novel. He has read 3 pages less than one-third of the novel.
Write an equation to describe the total number of pages p in the novel, and find the value of p.
Answers
novels total page x
1/3x-3=114
1/3x=117
x=3.117
x=351
he says he read 1/3 of his novel. Let x represent number of pages of the novel.
1/3x is one third of that novel.
3 pages less than one third is:
1/3x - 3
and that represents 114 pages that he read.
now we make that equal to 114 and solve for x
1/3x - 3 = 114
1/3x = 114 + 3 = 117
x = 351
Answer is 351 pages
i need help asap
Your cell phone plan costs 55 dollars a month, plus 35 cents per minute. Write an equation to represent the monthly bill of the cell phone plan.
F(x) = 55x + 0.35
F(x) = 55x + 15
F(x) = 0.35x + 55
F(x) = 35x + 55
Answers
so F(x) = 0.35x + 55
(0.35 × minutes in a month)×55
An algebraic expression has parentheses with unlike terms inside. Explain how to simplify this algebraic expression if a minus sign is in front of the parentheses.
Answers
Answer:
The expression can be simplified by distributing the minus sign to each of the terms inside of the expression.
Step-by-step explanation:
Is the following relation a function?
X Y
6 -1
-1 2
4 3
0 3
Yes or no
Answers
40 is rounded to the nearest whole write down the maximum possible length it could have been
Answers
The maximum length the number could have been before being rounded down to 40 is just under 40.5 since that is the point at which it would round up to 41.
Explanation:The question pertains to rounding numbers to the nearest whole number. When rounding the number 40 to the nearest whole, we'd like to find the maximum length it could have been before rounding down. The process of rounding will round a number to the nearest whole number based on the decimal value. For instance, if you are rounding to the nearest whole number, a number with a decimal part of 0.5 or higher will round up, while a number with a decimal part of less than 0.5 will round down.
Given that 40 is already a whole number, this implies it could have been rounded down from a number up to one decimal less than 40.5 since any number 40.5 and above would round up to 41. Hence, the maximum possible length it could have been before rounding down is just under 40.5.
Goran rented a truck for one day. there was a base fee of $15.99, and there was an additional charge of 96 cents for each mile driven. goran had to pay $288.63 when he returned the truck. for how many miles did he drive the truck?
Answers
272.64÷0.96= 284 miles
Calculate the area of a circle with a radius of 5
Answers
A= pi (3.14) x 5^2
A = 78.54
:)
The product of eight minus a number and seven equals forty when decreased by five. Which equation represents the sentence?
Answers
So, you are multiplying (8-n), where n = "a number," by 7.
Then, when you decrease (subtract) this product by 5, you get 40.
So the whole thing looks like
7(8-n) - 5 = 40.
Suppose f is continuous on [1,5] and the only solutions of the equation f(X)= 6 are x=1 and x=4. If f(2)=8, explain why f(3)>6. ...?
Answers
Given the conditions of the continuous function f and the equation f(X) = 6 where X = 1 and X = 4, f(3) must be greater than 6 because of the utilization of the Intermediate Value Theorem.
Explanation:The question is about the function f which is continuous on the interval [1,5]. The given conditions are that the solutions of the equation f(X) = 6 are x = 1 and x = 4 and that f(2) = 8 which is greater than 6. By the Intermediate Value Theorem (IVT), since f is continuous on [1,5] and f(2) = 8 > 6 and we have that f(x) = 6 for x = 1 and x = 4, then by the IVT we should have a point f(c) = 6 for some c in the interval (2,4). Hence, it means that f(3) could be equal to 6 or be more than 6, but since we know the only solutions are x = 1 and x = 4, f(3) cannot be equal to 6 and thus f(3) must be greater than 6.
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Which sequence of transformations creates a similar, but not congruent, triangle?
Rotation and translation
Reflection and rotation
Dilation and rotation
Translation and reflection
Answers
This is not the case with D, however, as length/shape of a triangle is changed, and therefore, it is not a congruent, but a similar triangle.
The correct answer is translation and reflection.
Answer:
I checked and D isn't the right answer I tried it on the test and got it wrong but I guessed the second time and I got it right so the real answer is Dilation and rotation.
__
What is the length of PR?
Answers
The answer is 7 apex
Answer-
The length of PR is 7 units.
Solution-
Given,
in the ΔDEF,
m∠D = 25°, m∠E = 114°, DF = 21, DE = 15
in the ΔPQR,
m∠P = 25°, m∠Q = 114°, PR = x, PQ = 5
So, ΔDEF ~ ΔPQR by AA (Angle-Angle) similarity, as
m∠D = m∠P = 25°m∠E =m∠Q = 114°So, according to similarity
[tex]\Rightarrow \dfrac{DF}{PR}=\dfrac{DE}{PQ}=\dfrac{EF}{QR}[/tex]
Putting the values,
[tex]\Rightarrow \dfrac{21}{x}=\dfrac{15}{5}[/tex]
[tex]\Rightarrow x=\dfrac{21\times 5}{15}[/tex]
[tex]\Rightarrow x=7[/tex]
In a triangle ABC, with angles A, B, and C and sides AB, BC, and AC, angle B is a right (90°) angle. If the sin of angle A is 0.5 and side BC is 8 inches long, what is the length of side AC?
Answers
Write the time 12 hours after 8 p.m. use an or pm
Answers
2)10pm
3)11pm
4)12am
5)1 am
6) 2 am
7) 3 am
8) 4 am
9)5 am
10) 6 am
11) 7 am
12) 8 am
The area of a triangle is 25 sq cm and the base of the triangle is 5 cm. Which equation could be used to find the height of the triangle?
A.
B.
C.
D.
Answers
Area=base×height/2
25=5×height/2
5×2=height
height=10
1/3 and 7/9 rewrite using the least common denominator
Answers
9 is the LCD. So you have to multiply 3 by 3 to get 9, so multiply the numerator (1) by 3. 3/9 is the answer to that.
To rewrite 1/3 and 7/9 using the least common denominator, you need to find the smallest number that both 3 and 9 can divide evenly into. The least common denominator (LCD) of 3 and 9 is 9. Rewrite the fractions as 3/9 and 7/9, respectively.
Explanation:To rewrite the fractions 1/3 and 7/9 using the least common denominator, we need to find the smallest number that both 3 and 9 can divide evenly into. The least common denominator (LCD) of 3 and 9 is 9. We can now rewrite the fractions:
1/3 becomes 3/9 (multiply the numerator and denominator by 3)7/9 remains the sameSo, 1/3 and 7/9 can be rewritten as 3/9 and 7/9, respectively, using the least common denominator.
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Mark is solving the following system.
x+y+z=2 (1)
3x+2y+z=8 (2)
4x-y-7z=16 (3)
Step 1: He multiplies equation (1) by 7 and adds it to equation (3).
Step 2: He multiplies equation (3) by 2 and adds it to equation (2).
Which statement explains Mark’s mistake?
- He added equation (3) instead of equation (2) in step 1.
- He did not multiply equation (3) by the correct value.
- He did not eliminate the same variables in steps 1 and 2.
- He added equation (3) and equation (2) instead of subtracting.
Answers
Solving the system of linear equations Mark tries to apply elementary transformations in order to eliminate one variable.
He makes such steps:
1. He multiplies equation (1) x+y+z=2 by 7 and adds it to equation (3) 4x-y-7z=16. This gives him:
7x+7y+7x+4x-y-7z=14+16,
11x+6y=30.
2. He multiplies equation (3) 4x-y-7z=16 by 2 and adds it to equation (2) 3x+2y+z=8. This step gives him:
8x-2y-14z+3x+2y+z=32+8,
11x-13z=40.
Thus, he did not eliminate the same variables in steps 1 and 2.
Answer: correct choice is C
In which case do you need to reverse the inequality sign when solving an inequality?
when adding or subtracting a negative number
when multiplying or dividing by a negative number
when there is a line under the equality symbol
where there is no line under the equality symbol
Answers
if you DON'T flip the sign, you usually end up with a "backwards" inequality, such as 4 < x, but the rules tell you to write "4 is less than x" as "x is greater than 4" (x > 4) so you end up rearranging the sign anyways--it's just easier to do it as you go.
12x=4(x-5) then x equals?
Answers
distributive property to get rid of parenthesis 12x=4x-20
subtract x from one side to get the variable on one side 8x=-20
divide 8 by -20
x=-2.5
In 1991, the federal minimum wage rate was $4.25 per hour. In 1997, it was increased to $5.15. Find the annual rate of change in the federal minimum wage rate from 1991 to 1997
Answers
1997 = $5.15
1hour = 60min
First you will have to multiply:
4.25 * 60 = 225
5.15 * 60 = 309
Then you subtract the answers you got together
309 - 225 = 84
So the the rate of change increases by 84!!
Hope This Helps!!
:)
The annual rate of change in the federal minimum wage rate from 1991 to 1997 is $0.15 per year.
Explanation:The annual rate of change in the federal minimum wage rate from 1991 to 1997 can be found by calculating the difference between the final and initial values, and then dividing it by the number of years.
Initial value in 1991: $4.25
Final value in 1997: $5.15
Difference: $5.15 - $4.25 = $0.90
Number of years: 1997 - 1991 = 6 years
Annual rate of change: $0.90 / 6 = $0.15
Therefore, the annual rate of change in the federal minimum wage rate from 1991 to 1997 is $0.15 per year.
64% of 596-estimate using a rate per 100
Answers
38144 / 100 = 381.44
What is tangent of 11/6?
Answers
Question. I have some math problems that I really need help with and this is all new to me. The direction are as follows:
Combine like terms 7x4 -5x4 the number four is square root. I don't understand at all what to do. Please help.
Answers
Answer:
-7 + x + 4 + 4x = x - 3 + 6 + 3x
Step-by-step explanation:
Let y represent the total cost of publishing a book (in dollars). Let x represent the number of copies of the book printed. Suppose that x and x are related by the equation.
What is the change in the total cost for each book printed?
What is the cost to get started (before any books are printed)?
Equation: y=1250+25x
Answers
Part 2: the cost to get started before any books are printed. Using the equation, x = 0. So, y =1250+25(0)
y= 1250
So the cost to get started before any books are printed is 1250.
Now, to part 1, let us say, only 1 book is printed. So x=1
y = 1250 +25(1)
y= 1250 +25
y = 1275
So, for 1 book is 1275, and no book is 1250. This gives us the answer that the change in the total cost for each book printed would be $25. Hope this is the answer that you are looking for.
what is the equivalent ratio to 12:20
Answers
3:5
Is this sequence arithmetic, geometric or neither? 4, 8, 16, 32, 64,...
Answers
So, the first value, 4, is 2^(1+1). 8 is 2^(2+1), etc, etc.
Answer:
geometric sequence
How many days equals 7344 minutes??
Answers
Answer:
as a decimal: 5.1
Solve x2 + 10x = −21.
Select one:
a. x = 7 and x = 3
b. x = −7 and x = −3
c. x = −7 and x = 3
d. x = 7 and x = −3
Answers
A college class with 30 sophomores, 18 juniors, and 12 seniors is
divided into project groups where each group has the same number
of sophomores, juniors, and seniors. What is the greatest number of
groups that can be formed? How many sophomores, juniors, and
seniors are in each project group?
Answers
The maximum number of project groups can be formed is 5 and the number of sophomores, juniors, and seniors within each group will be 5, 3 and 2 respectively.
To find the greatest number of groups that can be formed with the given distribution of students,
Identify the common factor: The greatest common factor of 30, 18, and 12 is 6.
Calculate groups: Divide each class by 6: 30 sophomores ÷ 6 = 5, 18 juniors ÷ 6 = 3, and 12 seniors ÷ 6 = 2. Therefore, the maximum number of groups that can be formed is 5.
An angle measure is 6 degrees more than 3 times its compliment. find the measure of the angle.
Answers
The angle which is 6 degrees more than 3 times its complement is found to be 69 degrees.
Explanation:This problem is related to complementary angles in Mathematics. Complementary angles are two angles that add up to 90 degrees. If we denote one angle as x, its complement is 90 - x.
According to the question, an angle measure is 6 degrees more than 3 times its complement. So we write an equation from this: x = 3*(90 - x) + 6. By solving this equation, we can find the value of x which represents the angle.
First, distribute through the parenthesis: x = 270 - 3x + 6. Combine like terms: 4x = 276. Finally, divide both sides by 4 to solve for x: x = 69 degrees.
So, the angle is 69 degrees.
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