The value of [tex]\int\limits^._R {xy^2} \, dA[/tex] is 16.
What is integration?The calculation of an integral is called integration. In math, many useful quantities like areas, volumes, displacement, and so on can be found using integrals. When we discuss integrals, we typically refer to definite integrals. Antiderivatives make use of the indefinite integrals. Apart from differentiation, one of the two major calculus topics in mathematics is integration.
Given xy =3, xy = 7,
xy² = 3, xy² = 7
s = xy and t = xy²
dividing t by s we get
t/s = xy²/xy
y = t/s
and x = s/y = s²/t
now differentiate x and y partially with respect to s and t
∂x/∂s = 2s/t
∂x/∂t = -s²/t²
∂y/∂s = -t/s²
∂y/∂t = 1/s
The Jacobian is
∂(x, y)/∂(s, t) = [tex]\left|\begin{array}{ccc}dx/ds&dx/dt\\dy/ds&dy/dt\end{array}\right|[/tex]
∂(x, y)/∂(s, t) =[tex]\left|\begin{array}{ccc}2s/t&-s^{2}/t^{2} \\-t/s^{2} &1/s\end{array}\right|[/tex]
∂(x, y)/∂(s, t) =2/t - 1/t
∂(x, y)/∂(s, t) = 1/t
so for [tex]\int\limits^._R {xy^2} \, dA[/tex] = [tex]\int\limits^a_b \int\limits^a_b {t}\frac{d(x, y)}{d(s, t) } \, dsdt[/tex]
for (s, t) (3 ≤ s ≤7, 3 ≤ t ≤ 7)
= [tex]\int\limits^7_3 \int\limits^7_3 {t}*1/t } \, dsdt[/tex]
= [tex]\int\limits^7_3ds \int\limits^7_3 dt[/tex]
=[s]₃⁷ [t]₃⁷
= (7 - 3)(7 - 3)
= 16
Hence the value is 16.
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Solve by substitution-5x+4y=22 x - 3y = 0A) No solution.
b. (6, 2)
c. Infinitely many solutions.
d. (-6, 2)
e. (-6, -2)
Given: AB = 12
AC = 6
Prove: C is the midpoint of AB.
Proof:
We are given that AB = 12 and AC = 6. Applying the segment addition property, we get AC + CB = AB. Applying the substitution property, we get 6 + CB = 12. The subtraction property can be used to find CB = 6. The symmetric property shows that 6 = AC. Since CB = 6 and 6 = AC, AC = CB by the property. So, AC ≅ CB by the definition of congruent segments. Finally, C is the midpoint of AB because it divides AB into two congruent segments.
Answer:
Pretty sure its the Transitive Property
Step-by-step explanation:
It's a dropdown on Edge so there's no A B C or D
To prove that point C is the midpoint of segment AB, we apply the segment addition property and the definition of congruent segments.
Explanation:To prove that point C is the midpoint of segment AB, we can use the segment addition property. We are given that AB = 12 and AC = 6. By applying the segment addition property, we get AC + CB = AB. Substituting the given values, we have 6 + CB = 12. Solving for CB using the subtraction property, we find that CB = 6.
Now, by using the symmetric property, we can see that 6 = AC. Since CB = 6 and 6 = AC, we can conclude that AC is congruent to CB by the definition of congruent segments. This implies that C is the midpoint of AB, as it divides AB into two congruent segments.
Kanisha has x green apples and y red apples.
Which statement explains why x + y and y + x will each find the total number of apples that Kanisha has?
In addition, the order of the variables matters in the expression.
The expressions are not equivalent because there are two variables.
The first expression has a greater value than the second expression.
In addition, the order of the variables does not matter in the expression.
Answer:
the answer is in addition the order of the variables does not matter in the expression
Step-by-step explanation:
i took the test
Maya spent her allowance on playing an arcade game a few times and riding the Ferris wheel more than once.Write about what additional information you would need to create a two-variable equation for the scenario. What kind of problem could you solve with your equation?
To write a two-variable equation, I would first need to know how much Maya’s allowance was. Then, I would need the cost of playing the arcade game and of riding the Ferris wheel. I could let the equation be cost of playing the arcade games plus cost of riding the Ferris wheel equals the total allowance. My variables would represent the number of times Maya played the arcade game and the number of times she rode the Ferris wheel. With this equation I could solve for how many times she rode the Ferris wheel given the number of times she played the arcade game u welcome
What is the minimum value for P = x - 2y over the feasibility region defined by the constraints shown below?
A. 8
B. -2
C. -16
D. -14
the answer is -14
Hope this helps : )
HELP PLEASE
Solve the system by substitution
-4.5x - 2y = -12.5
3.25x - y = -0.75
PLEASE HELP!!
What is the length of the midsegment of this trapezoid?
Enter your answer in the box.
Answer:
7 units
Step-by-step explanation:
The length of the midsegment of this trapezoid will be 7 units.
What is mean by Rectangle?
A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
The coordinates of the vertices of the trapezoid are,
A = (-2, 4)
B = (4, 3)
C = (4 , -5)
D = (- 2, - 2)
Now,
Since, We know that;
The length of the midsegment of a trapezoid is always equal to the half of the sum of the parallel sides.
Here, Line AD and BC are parallel lines.
And, The length of AD = √(- 2 - (-2))² + (- 2 - 4)²
= √-6²
= 6
And, The length of BC = √(4 - 4)² + (- 5 - 3)²
= √-8²
= 8
Thus, The length of the midsegment of this trapezoid = (6 + 8)/2
= 14/2
= 7 units.
Therefore, The length of the midsegment of this trapezoid will be 7 units.
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can you please explain to me which functions are odd?
f(x)=-1/2x^4+5
f(x)=-8x^3+5x
f(x)=-4/x^3-x+1
f(x)=x^5/x^4-1
f(x)=-sqrt2x
f(x)=3sqrtx -x^3
thank you!
A chess board has 64 squares. if you put one grain of rice on the first square, two grains on the second square, four grains on the third, eight grains on the fourth, and so on. how many grains are on the last square. no calculators.
Dr. Cheeks tries to run at least 45 rotations on her hamster wheel each week. She has already run 6 rotations. Which inequality shows how many more rotations, r, she would have to run to meet her weekly goal?
A. r-6>45
B. r-6>45
C. r+6>45
D.r+6<45
Answer: C. r+6>45
Step-by-step explanation:
Since, Dr. Cheeks tries to run at least 45 rotations on her hamster wheel each week.
If she runs r rotations then, for the value of r, [tex]45\leq r[/tex]
Since, If she has already 6 rotations
Therefore total rotation she has = r+6
Thus, if [tex]45\leq r[/tex] ⇒[tex]45<x+6[/tex]
So, Option C is the correct option.
The inequality of option C r+6 > 45 shows the rotations, r, she would have to run to meet her weekly goal.
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions.
Dr. Cheeks tries to run at least 45 rotations on her hamster wheel each week.
She has already 6 rotations but if she runs r rotations then, for the value of r, 45 ≤ r
The total rotation she has = r+6
Thus, 45 ≤ r
= 45 < r + 6
or r+6 > 45
So, Option C is the correct option.
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Q.17
Select the correct numerical form of this number written in scientific notation.
1.2 × 10^4
0.00012
120,000
12,000
1,200
Answer:
its 12,000
Step-by-step explanation:
what is 3 divided by 7.71?
Find the slope of the line.
We can use the points (-4, -1) and (0, -2) to solve.
Formula: y2-y1/x2-x1
= -2-(-1)/0-(-4)
= -1/4
Best of Luck!
two chipmunks were collecting acorns for the winter months. the older chipmunk gathered three times as many acorns as the younger chipmunk. together they collected 28 acorns. how many acorns did each chipmunk save for winter?
How to find the angle measure of an isosceles triangle if you only know the side lengths?
Determine if the statement is always, sometimes or never true. A natural number is a whole number.
Solve for x: 3 over 4 x + 5 over 8 = 4x. . x = __________________ Write your answer as a fraction in simplest form. Use the \"/\" symbol for the fraction bar
the sum of twice a number x and 13 is two less than three times x
This is a word problem which requires basic logic or understanding to solve. We can write the equation:
2 x + 13 = 3 x – 2
So calculate for x:
3 x – 2x = 13 + 2
x = 15
Therefore the number is 15.
Please help!
What is the equation of this graphed line?
Enter your answer in slope-intercept form in the box.
Answer:
[tex]y=2x+2[/tex]
Step-by-step explanation:
step 1
Find the slope
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
[tex]A(-4,-6)\ B(2,6)[/tex]
Substitute the values
[tex]m=\frac{6+6}{2+4}[/tex]
[tex]m=\frac{12}{6}=2[/tex]
step 2
we know that
The equation of the line into slope intercept form is equal to
[tex]y=mx+b[/tex]
we have
[tex]m=2[/tex]
[tex]B(2,6)[/tex]
substitute and solve for b
[tex]y=mx+b[/tex] ------> [tex]6=(2*2)+b[/tex]
[tex]6=4+b[/tex]
[tex]b=2[/tex]
The equation of the line is equal to
[tex]y=2x+2[/tex]
The functions f(x) = –(x + 4)2 + 2 and g(x) = (x − 2)2 − 2 have been rewritten using the completing-the-square method. Is the vertex for each function a minimum or a maximum? Explain your reasoning for each function.
Final answer:
The completing-the-square method allows rewriting quadratic functions to determine the vertex. The coefficient of the squared term determines if the vertex is a minimum or maximum.
Explanation:
The completing-the-square method allows us to rewrite quadratic functions in a form that reveals the vertex of the parabola. To determine if the vertex is a minimum or a maximum, we need to consider the coefficient of the squared term. In the function f(x) = –(x + 4)² + 2, the coefficient is negative, indicating that the parabola opens downwards, and the vertex is a maximum. In the function g(x) = (x − 2)² − 2, the coefficient is positive, indicating that the parabola opens upwards, and the vertex is a minimum.
The probability that an individual is left-handed is 0.16. in a class of 10 students, what is the mean and standard deviation of the number of left-handers in the class?
Using the binomial distribution, it is found that:
The mean of the number of left-handers in the class is of 1.6.The standard deviation of the number of left-handers in the class is 1.16.For each student, there are only two possible outcomes, either they are left-handers, or they are not. The probability of a student being a left-hander is independent of any other student, hence the binomial distribution is used to solve this question.
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
The expected value is:
[tex]E(X) = np[/tex]
The standard deviation is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
In this problem:
The probability that an individual is left-handed is 0.16, hence [tex]p = 0.16[/tex].The class has 10 students, hence [tex]n = 10[/tex]Then:
[tex]E(X) = np = 10(0.16) = 1.6[/tex]
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{10(0.16)(0.84)} = 1.16[/tex]
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Using exponents what is the simplified form of the expression 12x^5/6x^2
The required simplified form of the expression 12x⁵/6x² is 2x³.
What are exponential expressions?Exponential expressions, as the name indicates, involve exponents. We already know that the exponent of a number (base) specifies how many times the number (base) has been multiplied. To answer the exponential expressions, we may need to apply the relationship between exponents and logarithms.
The exponential expression is given in the question as:
12x⁵/6x²
To simplify the expression 12x⁵/6x², we can start by dividing 12 by 6 to get:
12x⁵/6x² = (12/6)x⁵/x² = 2x⁵/x²
Then, we can use the quotient of powers rule, which states that when we divide two powers with the same base, we can subtract the exponents to get:
2x⁵/x² = 2x⁵⁻² = 2x³
Therefore, the expression is 2x³ equivalent to the given expression 12x⁵/6x².
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On wensday on a track myles run 7 laps for every 3 laps that elijah run on friday elijahrun 16 more laps than on wensday making the number of laps he run and myles run the same .how many laps did eligah run on wensday
The sum of two numbers is 68 . the smaller number is 12 less than the larger number. what are the numbers?
Final answer:
To solve the problem, we defined two variables for the larger (x) and smaller (y) numbers. Using the provided information, we set up two equations and solved them to find the numbers: x (the larger number) is 40, and y (the smaller number) is 28.
Explanation:
Step-by-Step Solution to Find the Two Numbers
Let's denote the larger number as x and the smaller number as y. We are given two pieces of information:
The sum of the two numbers is 68.
The smaller number is 12 less than the larger number.
These two statements can be turned into two equations:
x + y = 68 (Equation 1)
y = x - 12 (Equation 2)
Now, we can substitute Equation 2 into Equation 1 to find x:
x + (x - 12) = 68
2x - 12 = 68
Add 12 to both sides:
2x = 80
Divide both sides by 2:
x = 40
Now that we know the larger number, x, we can find y using Equation 2:
y = 40 - 12
y = 28
So, the two numbers are 40 and 28
How would I do this? I'll give brainliest!
Make a table of ordered pairs for the equation.
y = 1/2x − 3
Then plot two points to graph the equation.
A customer wants you to enlarge a photo to 2 3/4 its current height. The photo’s current height is 3 1/4 inches. What should its enlarged height be, in inches?
The perimeter of a rectangular field is 320 yd. the length is 80 yd longer than the width. find the dimensions.
The dimensions of a rectangular field is width = 40 yd and length = 120 yd.
What is a rectangle?
A rectangle is one of the types of quadrilaterals in which all four angles are right angles or equal to 90 degrees. It is four-sided polygon in which the opposite sides are parallel and equal to each other.
For the given situation,
Let the width of the rectangle, w = x
The length is 80 yd longer than the width.
The length of the rectangle, l = x + 80.
The perimeter of a rectangular field = 320 yd.
The formula of perimeter of rectangle is
[tex]P=2(w+l)[/tex]
On substituting the above values,
⇒ [tex]320=2(x+x+80)[/tex]
⇒ [tex]320=2(2x+80)[/tex]
⇒ [tex]2x+80=\frac{320}{2}[/tex]
⇒ [tex]2x+80=160[/tex]
⇒ [tex]2x=160-80[/tex]
⇒ [tex]2x=80[/tex]
⇒ [tex]x=\frac{80}{2}[/tex]
⇒ [tex]x=40[/tex]
Thus width = [tex]40[/tex] and
length = [tex]40+80[/tex]
⇒ [tex]120[/tex]
Hence we can conclude that the dimensions of a rectangular field is width = 40 yd and length = 120 yd.
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Two cards are drawn at random without replacement from a standard 52-card deck. what is the probability we see at least one club and at least one ace?
The probability we see at least one club and at least one ace would be 0.019225
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.
The Total number of cards in a deck = 52
Number of aces in a standard deck = 4
Number of clubs in a standard deck = 13
The Probability = required outcome / Total possible outcomes
P(ace) = 4 / 52 = 0.0769
P(club) = 13 / 52 = 1/4 = 0.25
Therefore, the probability we see at least one club and at least one ace
0.0769 x 0.25
= 0.019225
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"if calvin buys 4 pounds of starfruit and 3 pounds of oranges, how much is his total utility"
The Calvin has a total of 252 utility coming from Oranges and Starfruit.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given that oranges cost $2 per pound and starfruit costs $5 per pound.
The utility coming from Oranges and Starfruit, therefore he needs to spend his $26 on buying the oranges and starfruit
Since all in all he also spend $23 on it, and still has remaining $3 in his pocket,
Thus his total utility is 252.
Hence, The Calvin has a total of 252 utility coming from Oranges and Starfruit.
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The complete question is
The oranges cost $2 per pound and starfruit costs $5 per pound. calvin has $26 to spend. if calvin buys 4 pounds of starfruit and 3 pounds of oranges, how much is his total utility?
Four friends purchase 18.4 pounds of peaches. The peaches cost $1.75 per pound. The friends share the cost of the peaches equally. What amount does each person pay? $4.60 $8.05 $24.15 $32.20