The integral in spherical coordinates is:
∫π 0 ∫π/4 0 ∫√(2-r^2)cos(φ) −√(2-r^2)cos(φ) ρ^2 sin(φ) dρ dφ dθ.
To rewrite the given integral in spherical coordinates, we first need to express the integrand in terms of spherical coordinates. We have:
z = ρ cos(φ)
r = ρ sin(φ) cos(θ)
x^2 + y^2 = ρ^2 sin^2(φ) = ρ^2 - z^2
Solving for ρ, we get:
ρ^2 = x^2 + y^2 + z^2 = r^2 + z^2
ρ = √(r^2 + z^2)
Substituting these expressions, we get:
∫2π 0 ∫√2 1 ∫√2−r^2 −√2−r^2 r dz dr dθ
= ∫π 0 ∫π/4 0 ∫√(2-r^2)cos(φ) −√(2-r^2)cos(φ) ρ^2 sin(φ) dρ dφ dθ
So the integral in spherical coordinates is:
∫π 0 ∫π/4 0 ∫√(2-r^2)cos(φ) −√(2-r^2)cos(φ) ρ^2 sin(φ) dρ dφ dθ.
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can you help m with this?
Cody sells sourdough bread by weight. He cuts a 1-lb loaf into 12 equal slices. What is the weight of one slice of Cody’s bread?
Answer:
ewd
Step-by-step explanation:
ewddew
When asked to rewrite $364 + 728 as a product of the GCF and the sum of two numbers a student wrote 364 (1 + 2) is the student correct why or why not?
Answer: The student got the wrong answer. ✅
Step-by-step explanation: When you add 364 and 728 together, you get 1092. To make it easier to understand, it is like having 3 piles of 100, 6 piles of 10, and 4 ones on one side, and 7 piles of 100, 2 piles of 10, and 8 ones on the other side, when you put them together you get 10 piles of 100, 8 piles of 10 and 12 ones.
To find the biggest number they have in common, you can divide both numbers by 2 and you get 182 and 364.
So the correct way to rewrite 364 + 728 is 364 * (3+2) ✅
Polygon ABCD with vertices at A(−4, 6), B(−2, 2), C(4, −2), D(4, 4) is dilated using a scale factor of one fourth to create polygon A′B′C′D′. Determine the vertices of polygon A′B′C′D′.
A′(−0.8, 1.2), B′(−0.4, 0.4), C′(0.8, −0.4), D′(0.8, 0.8)
A′(−1, 1.5), B′(−0.5, 0.5), C′(1, −0.5), D′(1, 1)
A′(−2, 3), B′(−1, 1), C′(2, −1), D′(2, 2)
A′(−3, 4.5), B′(−1.5, 1.5), C′(3, −1.5), D′(3, 3)
After dilatation, the vertices of polygon ABCD with vertices at A (4, 6), B (2, 2), C (4, 2), and D (4, 4) will be
A′(−1, 1.5), B′(−0.5, 0.5), C′(1, −0.5), D′(1, 1) (1, 1)How to determine the image's coordinatesDilation is a transformation technique that can either enlarge or reduce the preimage depending on the scale factor.
The following is the dilation transformation rule:
(x, y) with r as the scaling factor (rx, ry)
Using a similar process for the given issue, we have for r = one fourth
preimage dilation image
A(-4, 6) → (1/4 * -4, 1/4 * 6) → A'(-1, 1.5)
B(−2, 2) → (1/4 * -2, 1/4 * 2) → B'(-0.5, 0.5)
C(4, −2) → (1/4 * 4, 1/4 * -2) → C'(1, -0.5)
D(4, 4) → (1/4 * 4, 1/4 * 4) → D'(1, 1)
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Points P, Q, and R are collinear, with PQ=5, PR=7, and QR=12. Complete the statement.
Point P lies between Q and R
What are collinear points?Collinear points are the points that lie on the same straight line or in a single line. If two or more than two points lie on a line close to or far from each other, then they are said to be collinear, in Euclidean geometry.
Given here: Points P, Q, and R are collinear, with PQ=5, PR=7, and QR=12
Clearly we can observe that QR = PQ+PR
12=5+7
And the three points are collinear therefore we can deduce that Point P must lie between the two points Q,R.
Hence, Point P lies between Q and R
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What are 2 types of images?
In mathematics, the image of a function is the algebraic set of all output values it may generate. Real image and Virtual Image.
More generally, evaluating a given function
f at each element of a given subset
A of its domain produces a set, called the "image of
A under (or through) f
f". Likely, the inverse image (or preimage) of a given subset.
B of the codomain of f
f, is the set of all elements of the domain that map to the members of B.
Both Image and inverse image may also be defined for general binary relations, not just functions.
Image In common language an image is a picture or other visual way of showing something. But in mathematics it is another name for Range of a Function
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Luca decided to walk to a new park in town and estimated how long it would take. When he arrived, it had taken him 20 minutes to walk to the park. His estimate was 25% more than that. How long did Luca estimate it would take him to walk to the park
Answer: If it took Luca 20 minutes to walk to the park and his estimate was 25% more than that, we know that the estimate was 20 * 1.25 = 20 + (20 * 0.25) = 20 + 5 = 25 minutes.
So Luca estimated that it would take him 25 minutes to walk to the park.
Step-by-step explanation:
What is 2 with an exponent of 0?
Therefore, 2 with an exponent of 0 is equal to 1.
When a number is raised to an exponent of 0, the result is 1. This applies to any non-zero number, including 2. Therefore, 2 with an exponent of 0 is equal to 1.
The reason is that any number raised to the power of 0 is 1. This is because any number multiplied by 1 is itself, and any number raised to the power of 1 is itself. Therefore, raising a number to the power of 0 is the same as multiplying it by 1, so the result is 1.
It is also important to note that a number raised to the power of 1 is the number itself, so 2^1=2, 2^2=4, 2^3=8 and so on.
Therefore, 2 with an exponent of 0 is equal to 1.
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What is the relation between ∆ H and ∆ U under what condition the two ate are equal?
Therefore , the solution of the given problem of expressions comes out to be ΔH = ΔU.
By changing each variable with the a number and running arithmetic operations, an algebraic equation must be checked. Since 79 + 8 = 87 , the answer variable in the aforementioned example is the same as 6. We can substitute the variables values with those we know in order to evaluate the expression.
Here,
Given:
During a procedure that takes place in a closed vessel, ΔH = ΔU.
ΔV = 0 denotes that there are no gaseous reactants or products in the reaction, or
that the amount of moles for gaseous products equals the number of molecules of gaseous reactants.
Therefore , the solution of the given problem of expression comes out to be ΔH = ΔU.
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please answer quick!! thank you
Answer:
Question 2 :
[tex]\boxed{-35}[/tex]
Question 3:
[tex]\boxed{7}[/tex]
Question 4:
[tex]\boxed{-5}[/tex]
Question 5:
[tex]\boxed{-5}[/tex]
Step-by-step explanation:
The easiest points to take on the line are those where x =0, y = 35 (0,35) and x = 7, y =0 (7,0)
Question 2.
We can see that between these two points, the y value decreases linearly from 35 to 0. So the rise between (0, 35) and (7,0) = [tex]0 -35 = -35[/tex]
Question 3
[tex]\textrm{Between (0, 35) and (7,0) the x value increases from 0 to 7 so the run is 7}[/tex]
Question 4
[tex]\dfrac{rise}{run}= \dfrac{-35}{7}= -5}[/tex]
Question 5
Slope is the same as rise over run
We can also write this as
[tex]\dfrac{0-35}{7-0} = \dfrac{-35}{7} = -5[/tex]
Though not asked for, the equation of the line is
[tex]y = -5x + 35[/tex]
Look at the following graph of the given equation. Points marked on graph: (1,0), (0,2), (1,4), (2,6). Determine whether the equation is a function. Explain why or why not. y = 2x + 2
The equation y = 2x + 2 is a function. This can be determined by observing that for each x-value, there is exactly one corresponding y-value. In other words, the graph of the equation passes the vertical line test, which states that a graph represents a function if no vertical line intersects the graph more than once.
Additionally, as the given points (1,0), (0,2), (1,4), (2,6) all fall on the same line, all with a slope of 2 and y-intercept of 2, so this confirms that the equation is indeed a function.
graph 2y – 4x < 8 thanksss
The solution is the set of all points (x,y) that satisfy the inequality y < 2x + 4.
What is the graph of a function?
The graph of a function is a visual representation of the relationship between the input values (x-coordinates) and the output values (y-coordinates) of the function. In other words, it is a visual representation of the function's rule.
The graph of a function can take many different forms, depending on the function's rule. Linear functions, for example, will produce a straight line on the graph.
To solve the inequality 2y – 4x < 8, we can start by isolating y by adding 4x to both sides:
2y < 4x + 8
then divide both sides by 2:
y < 2x + 4
This is the solution in slope-intercept form (y = mx + b), where the slope is m = 2 and the y-intercept is b = 4.
To graph the solution, you can pick a few x-values and substitute them into the inequality to find the corresponding y-values.
You can use x = -2, x = -1, x = 0, x = 1, x = 2, for example and find the y-values for each x, y < 2* -2 + 4 = 0, y < 2* -1 + 4 = 2, y < 20 + 4 = 4, y < 21 + 4 = 6 and y < 2*2 + 4 = 8.
Then plot those points on a coordinate plane and draw the line that goes through them, and shade the half-plane that is below the line
Hence, the solution is the set of all points (x,y) that satisfy the inequality y < 2x + 4.
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Proportionalit
26. Bonnie's Boutique had a T-shirt sale to make room for new inventory. At the end of
the sale, 16 T-shirts were left. Of these, 6 were blue. Write the ratio of blue T-shirts to
total T-shirts left as a fraction in simplest form.
ake it for abou
Answer:
3:8
Step-by-step explanation:
The total number of t-shirts is 16. Out of the 16 t-shirts, 6 are blue. We can write this as 6:16, or 6 out of 16. You can simplify this further by dividing the ratio by 2 to get 3:8. I hope this helps!
The equation 3x − 6 = 2(x + 4) has solution(s).
The expression 3x − 6 = 2(x + 4) has one solution of x which is 10
x = 10How to solve the linear equationA linear function consists of functions where the variables has exponents of 1.
The graph of linear functions is a straight line graph
For the given problem, 3x − 6 = 2(x + 4) the solution is sort as thus
3x − 6 = 2(x + 4)
expanding the parenthesis
3x − 6 = 2x + 4
collecting like terms by subtracting 2x from both sides and adding 6 on both sides will result to the equation below
3x - 2x = 6 + 4
x = 10
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I have 2 questions
1. 7/8n³ + 2 -1/2n³
2. 1.4y² + 4.6 +8y - 0.5 -4y + y2
The simplified expressions are given as follows:
1. 3n³/8 + 2.
2. 2.4y² + 7.6y - 0.5.
How to simplify the expression?The expressions are simplified combining the like terms.
The first expression is given as follows:
(7/8)n³ + 2 - (1/2)n³.
The like terms are given as follows:
(7/8)n³ - (1/2)n³ = 7n³/8 - 4n³/8 = 3n³/8.2.Hence the simplified expression is:
3n³/8 + 2.
The second expression is defined as follows:
1.4y² + 3.6y + 8y - 0.5 - 4y + y².
The like terms are given as follows:
1.4y² + y² = 2.4y².3.6y + 8y - 4y = 7.6y.-0.5.Hence the simplified expression is:
2.4y² + 7.6y - 0.5.
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just a challenge. if 10 apples grew on a maple ctree and 3 were picked and 4 more grew
how many apples are thare
Answer:
apples don't grow on maple trees
Step-by-step explanation:
Why do you think you succeeded (or failed) at making money in the stock market?
Answer:
Succeeded because you did the correct research and made educated investments in a reliable company.
Failed because you did not do good and deep research and invested in an unreliable company.
Is a triangle possible with length of the sides as 10.2 cm 5.8 cm and 4.5 cm?
The Triangle with length of the sides as 10.2 cm 5.8 cm and 4.5 cm is possible.
What is Triangle Inequality Theorem?Triangle inequality is a theorem in Euclidean geometry that states any two triangle sides added together must be greater than or equal to the third side; it is represented by the symbols a + b ≥ c. The basic tenet of the theorem is that a straight line connects any two places.
Given:
Sides of triangle is: 10.2 cm 5.8 cm and 4.5 cm
Now, using Triangle inequality "the sum of two sides is greater than the third side of the triangle."
Suppose such a triangle is possible.
4.5 + 5.8 > 10.2
5.8 + 10.2 > 4.5
10.2 + 4.5 > 5.8
Hence, the triangle is possible.
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How do you find the number of functions from class 11 to B?
Number of functions. It is an important topic in sets and relation. A relation in which each input has a specific output is called a function. If f is a function from set A to set B, then each element of A will be plot with only one element in B.
1. Number of possible functions: If a set A has j elements and set B has k elements, then the number of functions possible from A to B is j ^k.
2. Number of Injective Functions (One to One): If set A has j elements and set B has k elements, j ≥k, then the number of injective functions or one to one function is given by j! / (j-k)!
3. Number of Bijective functions: If there is bijection between two sets A and B, then both sets will have the same number of elements. If n(A) = n(B) = m, then number of bijective functions = m!
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Help please I don’t understand
Answer:
(1, -2)
Systems of Equations
The solution to a system of equations is the point where the 2 lines intersect.
Q)Examine the graph. Where do the 2 lines intersect?
(1,-2)
The answer is:
(1, -2)Work/explanation:
This system has been solved by the graphing method; both equations have been graphed, and to find the solution, I need to find the point where both graphs intersect. And the graphs are the lines.
The x co-ordinate of the point is the solution for x, and the y co-ordinate of the point is the solution for y.
In our case, the lines intersect at (1, -2), which means that the value of x is 1, and the value of y is -2.
Select the correct answer.
While feeding a patient, Nadine, a nurse's aide, twists her upper body as she turns to retrieve a piece of tissue to help the patient wipe hands. She
sprains her neck muscles and so has to leave work and go home to rest. How could Nadine have correctly turned using the principles of body
mechanics?
O A.
O B.
OC.
O D.
by moving her shoulders and stretching out her arms
by moving her shoulders and neck and keeping hips still
by moving only her neck and stretching out her arms
by moving her feet and hips along with the upper body
Where while feeding a patient, Nadine, a nurse's aide, twists her upper body as she turns to retrieve a piece of tissue to help the patient wipe hands. She sprains her neck muscles and so has to leave work and go home to rest. Note that Nadine could have correctly turned the body using the principles of body mechanics: "by moving her feet and hips along with the upper body" (Option D)
What are the principles of body mechanics?Employee well-being depends on maintaining good body mechanics at work. Every employee should adhere to the four body mechanics principles. They are as follows:
Keeping a constant center of gravityKeeping a broad base of supportKeeping a line of gravityKeeping optimal body alignmentWhen these body mechanics principles are followed, employees are less likely to get injured at work and are more productive.
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-4>n or 3n+1>-2 solve equation or inequality
graph it too
The value of n is -1 < n < -4.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
-4>n or 3n+1>-2
now, solving the above inequality
3n+1>-2
3n > -2-1
3n > -3
n > -1
So, the value of n varies -1 < n < -4.
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How do you change the base value?
The base value of a number can be changed by using a base conversion calculator. This calculator can convert a number from one base to any other base. It can also be changed manually by using the rules of base conversion.
Changing the Base Value of a NumberBase conversion is the process of changing a number from one numerical base to another.
For example, converting a decimal number to a binary number or a hexadecimal number.This can be done manually by using the rules of base conversion or by using a base conversion calculator. When using a calculator, the user will enter the number, the current base, and the desired base and the calculator will output the number in the desired base.
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Janice and her family went on a backpacking trip. They started hiking at 4:22 P.M. It took 2 hours and 22 minutes to reach their campsite. After they arrived, it took 57 minutes to set up the campsite. What time was it when Janice and her family finished setting up their campsite?
A quadratic equation has zero real number solutions. Which could be the discriminant value associated with this equation?
–5
0
1
6
The discriminant value associated with this quadratic equation when it has zero real number solutions is -5.
Option A is the correct answer.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 8 is an equation.
We have,
In a quadratic equation when the discriminant is 0 we get one real solution.
In a quadratic equation when the discriminant is positive we get two real solutions.
In a quadratic equation when the discriminant is negative we get a complex solution.
A complex solution is not a real solution.
So,
The discriminant value must be -5.
Thus,
The discriminant value associated with this equation is -5.
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Answer: It’s A: -5
Step-by-step explanation:
on edge 2020
(Took test)
Plssss helpppp!!!!!!
The graph shows the distance y (in miles) that a bus travels in x hours. Find and interpret the slope of the line.
A line graph titled "Bus Trip"
The x-axis is labeled time, in hours. The y-axis is labeled distance, in miles. A line begins at ordered pair (0, 0 )and goes through ordered pair (1, 60) and ordered pair (2, 120).
The slope of the line is __ The bus is traveling at a speed of __ miles per hour.
The slope of the line is 60 The bus is traveling at a speed of 60 miles per hour.
What is the slope?A line's steepness is determined by its slope. Slope can be computed mathematically as "rise over run" (change in y divided by change in x). In the slope-intercept form, the equation for the line is expressed as follows: y = mx + b, where m denotes the slope and b the y-intercept. When the slope of the line being studied is known, and the provided point is also the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b). Its y value of the y intercept point is represented by b in the equation.
Given that,
A line begins at ordered pair (0, 0) and goes through ordered pair (1, 60) and ordered pair (2, 120).
Slope of the line (m) = (y₂ - y₁) / (x₂ - x₁)
m = 120 - 60 / 2 - 1
m = 60
thus, slope of the line = 60
The bus is travelling at a speed of 60 miles per hour.
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How do you divide division?
The division is performed by dividing the dividend by the divisor. This helps to find the quotient and remainder.
Along with addition, subtraction, and multiplication, the fourth main operation in mathematics is division. There are five main division techniques used in arithmetic calculations: long division, short division, dividing fractions, dividing exponents, and dividing decimals.
For example, to divide 500 by 5 we use the following steps using short division. Here, the divisor is 5 and the dividend is 500. Doing the division we get, the quotient is 100, and the remainder is 0. This is represented in the attached image. Here, the answer for the division of 500 by 5 is 100.
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Noah ia taking a multiple choice tet with a total of 20 point available. Each quetion i worth exactly 1 point. What would be Noah' tet core (out of 20) if he got 3 quetion wrong? What would be hi core if he got quetion wrong?
Noah's total score is 17 out of 20 since he answered 3 questions wrong.
A word problem is a short passage presenting a "real-life" situation where an issue has to be solved using math.
Word problems are seen as an essential component of learning in the elementary curriculum because they require students to apply their understanding of various concepts to situations that are representative of "real-life" situations.
Given that,
Total multiple choice questions = 20
The score of answering one question correctly = 1
Total number of questions Noah wrongly answered = 3
Therefore, his score out of 20 = 20 - 3 = 17
Thus, Noah's total score is 17 out of 20 since he answered 3 questions wrong.
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Study the equation.
2(x+6)=mx+12
Which value of m results in the equation having infinitely many solutions?
Responses
m=0m is equal to 0
m=2m is equal to 2
m=6m is equal to 6
m=12
The value of m = 2 results in the given equation having infinitely many solutions.
What is an Equation?An equation is the mathematical statement of two expressions situated on two sides connected with an equal to sign.
The two sides of an equation is usually called as left hand side and right hand side.
Given the equation,
2(x + 6) = mx + 12
Applying the distributive property a(b + c) = a b + a c on the left hand side,
2x + 12 = mx + 12
Two equations have infinitely many solutions when both the equations are same.
Left and right side are equal if m = 2.
Hence there are infinitely many solutions when m = 2.
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6-4 Additional Practice Proving a Quadrilateral Is a Parallelogram Is there enough information to prove each quadrilateral is a parallelogram? Explain: For what values of and b is each quadrilateral parallelogram? (I2b 26 + 45 2u + 14 Understand Margaret says there is not enough information to show that WXYZ is parallelogram: Explain why Margaret is incorrect: 10. Apply A hazard sign has_ identical parallelogram-shaped stripes as shown: Charles must outline each stripe with reflective tape: Is one roll of 144 inches of tape enough to finish the job? Explain: 6I_3n 6n enVision" Geometry * Teaching Resources'
Margaret is incorrect because the given information does not include enough details to determine if the quadrilateral WXYZ is a parallelogram.
To prove that a quadrilateral is a parallelogram, the four sides must be equal in length and the opposite angles must be congruent. The given information does not include any measurements or angles, so it is not possible to determine if the quadrilateral is a parallelogram.
No, 144 inches of tape is not enough to finish the job. The hazard sign has two identical parallelogram-shaped stripes, and each stripe will require more than 144 inches of tape to outline. The area of a parallelogram can be calculated using the formula A = bh, where b is the base and h is the height. In order to determine how much tape is needed to outline the stripes, the base and height of the parallelograms must be known.
There is not enough information to prove that a quadrilateral is a parallelogram, as all four sides must be equal in length and the opposite angles must be congruent. Additionally, 144 inches of tape is not enough to outline the hazard sign's two identical parallelogram-shaped stripes, as the base and height of the parallelograms must be known in order to calculate the area.
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