Extra Credit : Rewrite the following integral as a product of two one-dimensional integrals. Do not evaluate. (2 points) 5 6 SI €31 +4y (ry+5x+2y+10) dx dy 2 0
Answers
The integral of the product of two one-dimensional integrals is (2r+20)(r+44)
In mathematics, an integral is a mathematical object that represents the area under or between curves. It is used to solve problems in calculus, physics, engineering, and many other fields.
Now, let's take a look at the given integral and see how we can rewrite it as a product of two one-dimensional integrals without evaluating it.
The integral given is:
\(\int^5_6 \int^0_2\) (ry+5x+2y+10) dx dy
To rewrite this integral as a product of two one-dimensional integrals, we need to first separate the variables. This means we need to rewrite the integral in terms of only one variable at a time.
To do this, we can take the integral with respect to x first, treating y as a constant:
\(\int^5_6 \int^0_2\) (ry+5x+2y+10) dx dy
= \(\int^5_6\)[(r/2)x² + (5/1)x + (2y+10)x] from x=0 to x=2 dy
= \(\int^5_6\) [(r/2)(2²) + (5/1)(2) + (2y+10)(2)] - [(r/2)(0²) + (5/1)(0) + (2y+10)(0)] dy
= \(\int^5_6\)(2r+20) dy
= (2r+20)∫5 to 6 dy
= (2r+20)(6-5)
= 2r+20
Next, we take the integral with respect to y, treating r as a constant:
\(\int^5_6 \int^0_2\) (ry+5x+2y+10) dx dy
= \(\int^0_2 \int^5_6\) (ry+5x+2y+10) dy dx
= \(\int^0_2\) [(1/2)ry² + (2y+10)y + 5x(6-5)] from y=5 to y=6 dx
= \(\int^0_2\) [(1/2)r(6²-5²) + (2(6)+10)(6-5) + 5x(1)] dx
= \(\int^0_2\) [(1/2)r(11) + 22 + 5x] dx
= [(1/2)r(11)x + 22x + (5/2)x²] from x=0 to x=2
= (r+44)
Therefore, the original integral can be rewritten as:
\(\int^5_6 \int^0_2\) (ry+5x+2y+10) dx dy = (2r+20)(r+44)
To know more about integral here
https://brainly.com/question/18125359
#SPJ4
Related Questions
determine which of these illustrates two quantities that combine to make 0
Answers
Answer:
D) Marty gets ten dollars for his allowance and then spends ten dollars at the movies.
Step-by-step explanation:
Answer: It is ten degrees below zero and then the temperature rises fifteen degrees.
Step-by-step explanation:
Help please! No file attachments please, only write your answers in response to question.
Answers
AFK,CGJ,DEL,BHM
How can you apply it triangle congruence to real life situation?
Answers
Congruent triangles are also frequently employed in architectural designs, carpet patterns, stepping stone patterns, and geometric art.
The following are the two most typical instances of this: Equilateral triangles are used to make truss bridges, which are built on both sides.
Congruence :
If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved. A term used to describe an object and its mirror counterpart is congruence. If two things or shapes superimpose on one another, they are said to be congruent. They are identical in terms of size and shape. Line segments having the same length and angles with the same measure are congruent in the context of geometric figures.
To learn more about Congruence visit: brainly.com/question/12413243
#SPJ4
the test statistic calculated in the process of a kruskall-wallis test is h.
T/F
Answers
The Kruskal-Wallis test is a non-parametric test used to compare three or more independent groups to determine if there is a significant difference between the medians of the groups. The test statistic used in this test is denoted by the letter "H," which is calculated based on the ranks of the data.
True. The test statistic calculated in the Kruskal-Wallis test is denoted by the symbol H, not to be confused with the Shapiro-Wilk test statistic denoted by W. The Kruskal-Wallis test is a non-parametric test used to compare the median ranks of three or more independent groups. The test statistic H is calculated by comparing the between-group sum of squares to the total sum of squares. H follows a chi-squared distribution with degrees of freedom equal to the number of groups minus one. The p-value obtained from the chi-squared distribution is used to determine whether to reject or fail to reject the null hypothesis that there is no significant difference between the groups.
To learn more about median : brainly.com/question/11237736
#SPJ11
What is the range of the function represented by the graph?
{0,1,2,3} {1,2,3,4} 1
Answers
Answer:
number 3
Step-by-step explanation:
Answer:
number 3 i did it and i got a 100% on it
Step-by-step explanation:
If the first term of a sequence is four and the common difference is -9. Find a40.
(Write your answer as a value without spaces ex. 678, -973, etc.)
Answers
Answer:
an = a1 + d(n - 1)
Step-by-step explanation:
an = 4 + -9(40 -1)
an = 4 + -9(39)
Change the function f(x)=2x^2+4x+3 into vertex form.
Answers
Answer:
f(x) = 2(x + 1)² + 1
Step-by-step explanation:
the equation of a parabola in vertex form is
f(x) = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
given
f(x) = 2x² + 4x + 3 ← factor out 2 from the first two terms
= 2(x² + 2x) + 3
using the method of completing the square
add/subtract ( half the coefficient of the x- term )² to x² + 2x
f(x) = 2(x² + 2(1)x + 1 - 1) + 3
= 2(x + 1)² - 2(1) + 3
= 2(x + 1)² - 2 + 3
= 2(x + 1)² + 1 ← in vertex form
A can of soda weighs 336 grams. Find the weight in kilograms of 15 cans.
Answers
Answer:
5.04
Step-by-step explanation:
1 can equals to 336 grams
so 15 cans will equal to 336 X 15
which is 5040grams
now covert it into kg by dividing it by 1000
which 5.04
Your friend loans you $20,000 for school. In five years he wants
$40,000 back. What is the interest rate he is charging you?
Remember to show your work.
Answers
The interest rate your friend is charging you for the $20,000 loan is 20% per year.
What is the interest rate on the loan?
The simple interest is expressed as;
A = P( 1 + rt )
Where A is accrued amount, P is principal, r is the interest rate and t is time.
Given that;
The Principal P = $20,000
Accrued amount A = $40,000
Elapsed time t = 5 years
Interest rate r =?
Plug these values into the above formula and solve for the interest rate r:
\(A = P( 1 + rt )\\\\r = \frac{1}{t}( \frac{A}{P} -1 ) \\\\r = \frac{1}{5}( \frac{40000}{20000} -1 ) \\\\r = \frac{1}{5}( 2 -1 ) \\\\r = \frac{1}{5}\\\\r = 0.2 \\\\\)
Converting r decimal to R a percentage
Rate R = 0.2 × 100%
Rate r = 20% per year
Therefore, the interest rate is 20% per year.
Learn more about simple interest here: brainly.com/question/25845758
#SPJ1
PLEASE HELP complete the construction a perpendicular line to segment AB through point P.
Answers
Answer:
.
Step-by-step explanation:
sorry i can't help
Which of the following must be used to find the number of bit strings of length seven that either begin with two Os or end with three 1s? a. the inclusion-exclusion principle b. the sum rule c. the product rule d. the division rule
Answers
The correct answer is a. the inclusion-exclusion principle must be used to find the number of bit strings of length seven that either begin with two Os or end with three 1s.
This is because we need to subtract the number of bit strings that both begin with two Os and end with three 1s (which are counted twice if we simply add the number of bit strings that begin with two Os and the number that end with three 1s). The inclusion-exclusion principle allows us to do this by first adding the number of bit strings that begin with two Os and the number that end with three 1s, and then subtracting the number of bit strings that both begin with two Os and end with three 1s.
Learn more about strings here:
https://brainly.com/question/30099412
#SPJ11
I REALLY NEED HELP
How do you know when anexpression is in its simplest form?
Answers
An expression is in its simplest form when it can no longer be simplified or reduced any further.
What happens when an expression is in its simplest form ?When an expression is in its simplest form , it means that it has been reduced to its most basic and concise form, with no unnecessary terms or factors.
This makes it easier to evaluate and work with the expression . In some cases , the simplest form of an expression may also reveal certain properties or relationships that were not immediately apparent in its original form.
Find out more on expressions at https://brainly.com/question/21527775
#SPJ1
pleaseee helpp im giving away good points
Answers
Answer:
x = 1°
Step-by-step explanation:
Bisection means splitting the angle in to 2
So that means 4x-1 = 2x+1
4x-1 = 2x +1
4x = 2x + 2
2x = 2
x = 1°
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
NEED HELP ASAP!!!!!!!!!!!!!!!!!!!!!!
Answers
For what value of x is d || e? Then find the measure of the labeled angles.
Answers
Answer:
THAT QUESTION WILL BE ANSWERED THIS SUNDAY NIGHT!
Express 1/25 as a decimal fraction
Answers
Answer:
0.04
Step-by-step explanation:
I need to show the work. Please help
Answers
Answer:
x=9
Step-by-step explanation:
11x - 47 = 6x - 2 .... if the two lines are parallel the corresponding angles are congruent.
11x - 6x = -2 + 47
5x = 45
\( \frac{5x}{5} = \frac{45}{5} \)
x = 9
hope it helps
for any question comment me ❤❤
Find the integral by using the simplest method. This problem may not require integration by parts. (Use C for the constant of integration.) x sin(5x) dx
Answers
∫x sin(5x)dx = (-x/5)cos(5x) + (1/25)sin(5x) + C.
Integration by parts, also known as partial integration, is a technique used in calculus and more generally in mathematical analysis to determine the integral of a function's product in terms of the integral of the product of the function's derivative and antiderivative.
Integration by parts formula: ∫u dv = uv - ∫v du
Choose u and dv:
u = x, dv = sin(5x) dx
Differentiate u and integrate dv:
du = dx, v = ∫sin(5x) dx = (-1/5)cos(5x)
pply the integration by parts formula:
∫x*sin(5x) dx = uv - ∫v du
= (-x/5)cos(5x) - ∫(-1/5)cos(5x) dx
Integrate the remaining term:
= (-x/5)cos(5x) + (1/25)sin(5x) + C
So, the integral of x*sin(5x) dx using the simplest method (integration by parts in this case) is (-x/5)cos(5x) + (1/25)sin(5x) + C.
To learn more about integration: https://brainly.com/question/30215870
#SPJ11
The price elasticity of demand is defined as Select one: a. the percentage change in price divided by the percentage change in quantity demand. x Incorrect. The two variables should be reversed for the measurement. b. change in quantity demanded divided by quantity supplied. c. change in quantity supplied divided by quantity demanded. d. the percentage change in quantity demanded divided by the percentage change in price. If a small change in price creates a large change in demand, then we would say that the demand is Select one: a. Inelastic. x Incorrect. This is when a large change in price creates a small change in demand. b. elastic. c. Perfectly elastic d. stagnant. Which of the following goods represent a cross-price elasticity likely greater than zero? Select one: a. The complementary goods of hot dog sausages and hot dog buns. x Incorrect. Remember complementary goods are typically negative. b. The complementary goods of printers and printer ink. c. The substitute goods of soda and pizza. d. The substitute goods of blueberries and strawberries.
Answers
The price elasticity of demand is a measure of the responsiveness of quantity demanded to a change in price. It is calculated as the percentage change in quantity demanded divided by the percentage change in price. So, the correct answer is d. the percentage change in quantity demanded divided by the percentage change in price.
When a small change in price creates a large change in demand, we say that the demand is elastic. So, the correct answer is b. elastic.
Cross-price elasticity measures the responsiveness of the quantity demanded of one good to a change in the price of another good. If the cross-price elasticity is greater than zero, it means that the goods are substitutes, meaning that an increase in the price of one good leads to an increase in the demand for the other good. The correct answer is c. The substitute goods of soda and pizza.
To summarize:
- The price elasticity of demand is the percentage change in quantity demanded divided by the percentage change in price.
- When a small change in price creates a large change in demand, we say that the demand is elastic.
- Cross-price elasticity measures the responsiveness of the quantity demanded of one good to a change in the price of another good. If the cross-price elasticity is greater than zero, it means that the goods are substitutes.
To know more about elasticity of demand refer to :
https://brainly.com/question/1048608
#SPJ11
(4) consider three sheep M1,M2,M3 playing leapfrog. We (4). will place the sheep in a flan and characterize them by their coordinates M1=(x10,y10),M2=(x20,y20),M3=(x30,y30) the rules of the game are as follows: - M1 jump over M2 and the new fosition of the first sheep is the mirrol image of M1 by the center symmetry M2. - M M2 jumps above M3 and the new position of the second sheep is the symmetric of M2 by the centas symmetry M3 - M3 Jumps Above M1 and the new position of the second sheep is the symmetry of M by the symmetry of center M1 (Attention M1 has ofready fumped, the symmetry is therefore made with to its mew Position!). We continue the process by following the previous rustes, we denate by (x1m,y1n),(x2n,y2m) and (x3m,y3n) the coordinates of the shcep M1,M2 and M3 after m iterations. Let xm and ym be the vectors defined by xn=⎝⎛x1mx2mx3m⎠⎞ym=⎝⎛y1my2my3m⎠⎞ 1. Give a link between xn+1 and xn for all n∈N. Same question for ym+1 and ym. 2. Deduce a link between xn and x0. Same question for yn and y0 3. Determine an explicit formula for x1n,x2n and x3n and function of x10,x20 and x30 4. Under what condition(s) on the imitial fositions of M1,M2 and M3 con the sheep fump to infinity in a bounded space of the plane?
Answers
The link between xn+1 and xn for all n ∈ N is xn+1 = 2xn - xn-1. The link between yn+1 and yn is yn+1 = 2yn - yn-1. The link between xn and x0 is xn = 2x0 - xn-1. The link between yn and y0 is yn = 2yn - yn-1.
The explicit formula for x1n, x2n, and x3n is as follows:
x1n = 2x10 - x1(n-1)
x2n = 2x20 - x2(n-1)
x3n = 2x30 - x3(n-1)
The sheep can jump to infinity in a bounded space of the plane if and only if the initial positions of M1, M2, and M3 form an equilateral triangle.
The link between xn+1 and xn can be found by considering the symmetry of the leapfrog game. When M1 jumps over M2, the new position of M1 is the mirror image of its previous position with respect to M2. This means that the x-coordinate of M1 will be the same as the x-coordinate of M2, but the y-coordinate will be the negative of the y-coordinate of M2.
The link between yn+1 and yn can be found by considering the symmetry of the leapfrog game. When M2 jumps over M3, the new position of M2 is the mirror image of its previous position with respect to M3. This means that the y-coordinate of M2 will be the same as the y-coordinate of M3, but the x-coordinate will be the negative of the x-coordinate of M3.
The explicit formula for x1n, x2n, and x3n can be found by using the recursive formulas for xn+1 and xn.
The condition for the sheep to jump to infinity in a bounded space of the plane can be found by considering the distance between the sheep. If the initial positions of M1, M2, and M3 form an equilateral triangle, then the distance between the sheep will remain constant. This means that the sheep will continue to jump forever, and they will never reach the boundary of the space.
To learn more about equilateral triangle click here : brainly.com/question/12990950
#SPJ11
the number 3076 written in standard form
Answers
The number 3076 written in standard form as 3000+0+70+6.
What is the standard form of a number?The standard form means the process of writing very large expanded form of a number into small form or small number.
The given number is 3076
Now, in standard form
3×1000+0×100+7×10+6×1
= 3000+0+70+6
Therefore, the standard form is 3000+0+70+6.
To learn more about the standard form of a number visit:
https://brainly.com/question/13139379.
#SPJ1
For f(x) = 2x+1 and g(x) = x^2-7, find (f-g)(x)
Answers
Answer:
(f-g)(x) = - x² + 2x + 8Step-by-step explanation:
f(x) = 2x+1
g(x) = x² - 7
To find (f-g)(x) subtract g(x) from f(x)
That's
(f-g)(x) = 2x + 1 - ( x² - 7)
Remove the bracket
We have
(f-g)(x) = 2x + 1 - x² + 7
Simplify
We have the final answer as
(f-g)(x) = - x² + 2x + 8Hope this helps you
What is x???????????
Answers
Answer:
17
Step-by-step explanation:
6^2 + y^2 = 10^2
36 + y^2 = 100
y^2 = 64
y = 8
y^2 + 15^2 = x^2
64 + 225 = x^2
289 = x^2
x = 17
You are planning to retile the walls around your bathtub. You measure the dimensions of the wall and find that the length of the tub is 7 feet, the width of the tub is 2 feet and the height of the wall is 5 feet. You go to the hardware store to pick out some tile. You find ones that you like. There are 4 sizes of tile and are priced differently. The prices are 1 square inch tile is 10 cents, 6 square inch tile is 25 cents, 8 square inch tile is 75 cents and 18 square inch tile is $1.50. Find the best deal (price) for tile in order to tile your bathroom. How much will you spend? Why is this the best deal? Show ALL OF YOUR WORK and explain how you found the answer.
Answers
Answer:
it is the best deal cause i said
Step-by-step explanation:
Question 5 (1 point) Most fossils are two million years old. True False
Answers
Answer:
False
Step-by:-step explanation
2 million years
The oldest reliably classified fossils belonging to the genus Homo date back to a little over 2 million years ago. They belong to H. habilis, a type of ancient hominin that scientists classify as the first of our genus, and which may have led to H. erectus, one of our direct ancestors
Answer:
false
Step-by-step explanation:
most fossils are muuchhh older
Fred and Wilma are in the 33% tax bracket. Their joint taxable income is $205,375. If the first $16,050 is taxed at 10%, with the remainder at 33%, how much tax will they owe?
Answers
Answer:
$64,082.25
Step-by-step explanation:
$205,375-16,050=189,325
189,325×33% (or .30)=62,477.25
16,050×10% (or .10)=1,605
1,605+62,477.25=$64,082.25
Mckenna was asked to write the following expression in standard form. 3-5(3a 6)3−5(3a 6) when writing the expression in standard form, mckenna made a mistake. \begin{array}{rrr}3-5(3a 6)
Answers
The first mistake McKenna made when change the expression to standard form is in step 2.
What is PEMDAS?PEMDAS in mathematics it is a order of operations that must be prioritize when involving more than one operation. PEMDAS is abbreviation for Parentheses, Exponents, Multiply, Divide, Add, Subtract.
For multiply and divide the priority is for those who come first. Also for add and subtract the priority is for those who come first. And for the rest is the priority in order Parentheses, Exponents, Multiply and Divide, Add and Subtract.
In step 2, McKenna added 3 and -5 first when McKenna should have multiplied -5 by (3a+6). Thus, the step 2 is the first time McKenna made a mistake during change the expression to standard form.
You question is incomplete, but most probably your full question was
McKenna was asked to write the following expression in standard form.
3−5(3a+6)
When writing the expression in standard from, McKenna made a mistake.
3−5(3a+6)
3+(−5)(3a+6) Step 1
−2(3a+6) Step 2
−6a+(−12) Step 3
−6a−12 Step 4
McKenna made her first mistake in
Learn more about PEMDAS here:
brainly.com/question/1094951
#SPJ4
The length (L) of a rectangle of fixed area varies inversely as the width (W).
If the length of a rectangle is 10 ft when the width is 8 ft, find the length
of the rectangle when the width is 5 ft.
Solve for k.
Answers
Answer:
6.25
Step-by-step explanation:
If 10ft=8ft
=5ft
cross multiply
Find the volume of the cylinder.
Either enter an exact answer in terms of T or use 3.14 for T.
8
Answers
Answer: V= 100.48 m^3 or in terms of Pi V = 32 π m^3
Step-by-step explanation:
V = πr^2h
V = π(2)^2(8)
V = π(4)(8)
V = 100.48
or
V = π (4)(8)
V = 32 π m^3
How do you model .7 on a number line
Answers
Answer:
.7 is over 0 and under 1 so u have to make the mark just in between them right I front of the half way mark.
Answer:
(this won't really be good since the
number line would be longer if you are
modeling 7)
Step-by-step explanation:
7
<----------------------------|------------>