The integral, when rewritten using the indicated order of integration, is ∫₀¹ ∫₀¹-y² ∫₀¹-x² dz dy dx, and the value of the resulting integral is 2/3.
To rewrite the given integral in the indicated order of integration, we integrate with respect to 'z' first, then 'y', and finally 'x'. The given integral is triple nested, and each integral has specific limits.
integrate with respect to 'z':
∫₀¹ ∫₀¹-y² (z ∣₀¹-x²) dy dx
∫₀¹ ∫₀¹-y² (1-x²) dy dx
integrate with respect to 'y':
∫₀¹ (y ∣₀¹) (1-x²) dx
∫₀¹ (1-x²) dx
(x - x³/3) ∣₀¹
evaluate the result:
(1-1/3) - (0-0) = 2/3
Thus, the integral rewritten and evaluated using the indicated order of integration is 2/3. However, this is not the final answer as we still need to perform one more integration with respect to 'y':
∫₀¹ (2/3) dy = (2/3) * (y ∣₀¹) = 2/3 * (1 - 0) = 2/3
Thus, the final result after evaluating all integrals is 2/3 * 1 = 2/3.
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URGENT URGENT URGENT!!!
HELP PLEASE!!
Answer:
Step-by-step explanation:
I think it’s b correct me if I’m wrong
Answer:
I think it is b im pretty sure
O No; there are y-values that have more than one x-value.
• No; the graph fails the vertical line test.
• Yes; the graph passes the vertical line test.
Yes; there are no y-values that have more than one x-value.
The graph meets the vertical line test requirement, it must represent a function (C) The vertical line test shows that the graph is correct, hence the answer is yes.
How do functions work?According to the function, every value in the domain is associated to exactly one value in the range, and they have a predefined domain and range. It is characterized as a certain kind of relationship.
Please refer to the image instead of the graph, which is related to it.
The graphic displays a graph.
A parabola is seen on the graph.
The vertical line test determines if a graph can be a function, as is common knowledge.
The graph passes the vertical line test option, indicating that it does in fact represent a function (C) The vertical line test shows that the graph is correct, hence the answer is yes.
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What is the value of k?
(Not multiple choice)
Answer:
k is 10
Step-by-step explanation:
Finding the missing length in a figure
Answer:
6 ft
Step-by-step explanation:
Solve the problem PDE: Utt = 9uxx, 0 0. BC: u(0, t) = u(1, t) = 0; IC: u(x,0) = 8 sin(2πx), ut (x,0) = 4 sin(3πx). u(x, t) = ___
To solve the partial differential equation (PDE) Utt = 9uxx, subject to the boundary conditions u(0, t) = u(1, t) = 0 and initial conditions u(x, 0) = 8sin(2πx) and ut(x, 0) = 4sin(3πx), we can use the method of separation of variables.
Assuming a solution of the form u(x, t) = X(x)T(t), we substitute it into the PDE:
T''(t)X(x) = 9X''(x)T(t).
Dividing both sides by X(x)T(t) and rearranging, we have:
T''(t)/T(t) = 9X''(x)/X(x) = -λ².
Solving the time part, we have T''(t)/T(t) = -λ². This yields T(t) = Acos(3λt) + Bsin(3λt), where A and B are constants.
Solving the spatial part, we have X''(x)/X(x) = -λ²/9. This leads to X(x) = Ccos(λx/3) + Dsin(λx/3), where C and D are constants.
Applying the boundary conditions u(0, t) = u(1, t) = 0, we obtain C = 0 and λ = nπ, where n is a positive integer.
Thus, the solution is u(x, t) = ∑(Aₙcos(nπx/3) + Bₙsin(nπx/3))(Cₙcos(3nπt) + Dₙsin(3nπt)), where n ranges from 1 to infinity.
To find the coefficients Aₙ and Bₙ, we use the initial conditions. Plugging in u(x, 0) = 8sin(2πx) and ut(x, 0) = 4sin(3πx), we can determine the coefficients.
The final solution is the sum of all the terms: u(x, t) = ∑(Aₙcos(nπx/3) + Bₙsin(nπx/3))(Cₙcos(3nπt) + Dₙsin(3nπt)), where the coefficients Aₙ, Bₙ, Cₙ, and Dₙ are determined from the initial conditions.
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The cost of rice is proportional to its weight. Rice costs $0.71 per 16 ounces.
Part A.
Create an equation to represent the cost, c, of w ounces, of the rice.
PLS ANSWER THIS ASSIGNMENT IS DUE TODAY
Answer:
c = .71(16w)
Step-by-step explanation:
c is the unknown cost because it has to depend on the amount of ounces
.71 multiplies the amount of ounces
16 is the amount of ounces
What is the effect on the graph of f(x) if it is changed to f(x) + 2 and f(x + 2)?
Answer:
For f(x)+2, it goes along the y axis, 2 units.
For f(x+2), it goes along the x axis, -2 untis.
Step-by-step explanation:
hich of these sequences is the order of the steps below in the iterative problem-solving process? a) formulate and test hypothesis b) collect information c) analyze results d) consider alternative explanations
The order of the steps in the iterative problem-solving process is: a) collect information, b) formulate and test hypothesis, c) analyze results, and d) consider alternative explanations. (option c)
The iterative problem-solving process is a cycle that involves gathering information, forming hypotheses, testing hypotheses, analyzing the results, and then considering alternative explanations.
The second step is to formulate and test hypotheses. Hypotheses are educated guesses about what might be causing the problem or why the problem is occurring.
The third step is to analyze the results. This involves interpreting the data and determining if the hypothesis was correct or incorrect.
The final step is to consider alternative explanations. This involves looking at the data and considering other potential causes for the problem.
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Complete Question:
Which of these sequences is the order of the steps below in the iterative problem-solving process? a) formulate and test hypothesis b) collect information c) analyze results d) consider alternative explanations.
Option:
a,b,c,da,c,d,bb, a,c,dd,b, a,cto make a strawberry banana smoothie, a recipe calls for 1.75 cups of strawberries and some bananas. to make the recipe taste more like banana, 12 cup more banana was added to the blender. the smoothie now has 1.4 cups of bananas. how many cups of bananas were in the original recipe?
The original recipe had 0.9 cups of bananas.
Using only fresh ingredients, strawberry banana smoothie is a simple, nutritious dish. It is creamy, sweet, nutritious, and dairy- or dairy-free can be used to make it. The ideal summertime smoothie. Putting the strawberries, frozen banana, milk, and yoghurt in a blender and mixing until smooth and creamy is all that is required to make it.
Cups of strawberries = 1.75
No. of cups added of banana = 1/2
= 0.5
No. of cups of banana smoothie have = 14.
The original recipe had = 1.4 - 0.5
= 0.9
Hence, the original recipe had 0.9 cups of bananas.
Correct Question :
to make a strawberry banana smoothie, a recipe calls for 1.75 cups of strawberries and some bananas. to make the recipe taste more like banana, 1/2 cup more banana was added to the blender. the smoothie now has 1.4 cups of bananas. how many cups of bananas were in the original recipe?
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I need help with this
1. Since triangle ABC and DEF are congruent, the value of x is -3
2. length AB = 24
length DE = 24
What are congruent triangles?If the three angles and the three sides of a triangle are equal to the corresponding angles and the corresponding sides of another triangle, then both the triangles are said to be congruent.
Since triangle ABC is congruent to triangle DEF , then we can say that line AB is equal to line DE
therefore;
12- 4x = 15-3x
collect like terms
12 -15 = -3x +4x
x = -3
therefore the value of x is -3 and
AB = 12 - 4x
AB = 12 -4( -3)
AB = 12 +12 = 24
DE = 15-3x
= 15-3(-3)
= 15 + 9
= 24
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The average weight of a package of rolled oats is supposed to be at least 18 ounces. A sample of 18 packages shows a mean of 17.78 ounces with a standard deviation of 0.41 ounce. (a) At the 5 percent level of significance, is the true mean smaller than the specification? Clearly state your hypotheses and decision rule.
At the 5% level of significance, there is not enough evidence to suggest that the true mean weight of the packages is smaller than the specification of 18 ounces.
To determine whether the true mean weight of a package of rolled oats is smaller than the specification of 18 ounces, we can perform a one-sample t-test.
Hypotheses:
- Null Hypothesis (H0): The true mean weight of the packages is equal to or greater than 18 ounces.
- Alternative Hypothesis (H1): The true mean weight of the packages is smaller than 18 ounces.
The decision rule for hypothesis testing at a 5% level of significance is to reject the null hypothesis if the test statistic falls in the critical region, which is determined by the critical value.
In this case, since we are testing if the true mean is smaller, it is a one-tailed test with a significance level of 0.05.
The test statistic can be calculated as:
t = (sample mean - hypothesized mean) / (standard deviation / sqrt(sample size))
Plugging in the values:
sample mean = 17.78 ounces
hypothesized mean = 18 ounces
standard deviation = 0.41 ounce
sample size = 18
t = (17.78 - 18) / (0.41 / sqrt(18))
Calculating this value, we find t ≈ -1.222
Next, we need to find the critical value corresponding to a 5% significance level and (n-1) degrees of freedom, where n is the sample size (18 - 1 = 17).
Using a t-table or a t-distribution calculator, the critical value is approximately -1.746.
Since the calculated test statistic (-1.222) does not fall in the critical region (less than -1.746), we fail to reject the null hypothesis.
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For a standard normal random variable, what z-score has: __________
a) The z-score corresponding to the probability of 0.2000 to the right is z = 0.84.
b) The z-score corresponding to the probability of 0.9000 to the left is z = -1.28.
a) To find the z-score corresponding to a probability of 0.2000 to the right, we need to use the fact that the area under the standard normal distribution to the right of z is equal to 1 minus the area to the left of z.
In other words, we need to find the z-value such that the area to the left of it is equal to 1 - 0.2000 = 0.8000. Consulting a standard normal distribution table or using a calculator, we find that this z-value is approximately 0.84. Therefore, the answer is z = 0.84.
b) Similarly, to find the z-score corresponding to a probability of 0.9000 to the left, we need to find the z-value such that the area to the left of it is equal to 0.9000. Consulting a standard normal distribution table or using a calculator, we find that this z-value is approximately 1.28. Therefore, the answer is z = -1.28.
In both cases, we used the fact that the standard normal distribution has a mean of 0 and a standard deviation of 1, and we transformed the probability into an area under the curve.
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Complete question is:
For a standard normal random variable, what z-score has:
a) probability 0.2000 to the right? z = _____
b) probability 0.9000 to the left? z = _________
Which description represents this equation? 7x-2=33
Answer:
Step-by-step explanation:
pull up in a monsta automobile gangsta
Answer:
7x = 33+2
7x = 35
x = 5
Step-by-step explanation:
A SIMPLE EQUATION
Help please I don’t know how to solve this !!!!!!!
Answer: its 40 because its a whole number
Step-by-step explanation:
students are conducting an experiment to determine if the amount of sunlight affects the size of clover leaves. they plant clover in two identical pots, placing one next to a window and one inside a cupboard. they water each pot daily with 10 ml of water. which is the independent variable?
In the experiment, the independent variable is the amount of sunlight received by the clover plants.
The amount of sunlight the clover plants receive throughout the experiment serves as the independent variable, as it is being manipulated by the experimenters to determine its effect on the size of the clover leaves.
The dependent variable is the size of the clover leaves, which is being measured as a result of the change in the independent variable (amount of sunlight). The water is a controlled variable, as it is kept constant across both conditions to eliminate its effect on the outcome.
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A standard number cube is rolled and a card is drawn from a deck of cards numbered 1 to 12. Find P(2 on the number cube and 10 on the card).
Answer:
1/72
Step-by-step explanation:
P(2 on number cube) = 1/6
P(10 on the card) = 1/12
To get the probability of two events at the same time you multiply the probability of the events on their own
\(\frac{1}{6}\times\frac{1}{12} =\frac{1}{72}\)
∴ P(2 on the number cube and 10 on the card) = \(\frac{1}{72}\)
5. Find the measure of arc AC.
Find mAC
A) 52
B) 72
C) 92
D) 112
Answer:
B: 72
Step-by-step explanation:
Here, we want to find the measure of arc AC
Mathematically, we will use an angle arc relationship here
The angle arc relationship to use here is that the arc AC is twice the measure of angle ABC
Thus, we have the arc AC as 2 * 36 = 72 degrees
Hillary exercises Monday through Friday for 5/6 hours per day how many hours does she exercise per week
Answer: 4 hours and 10 minutes per week
Step-by-step explanation:
She exercises for 5 days per week (week days only).
(5/6 hr/day) x 5 days = 25/6 = 4.17 hours = 4 hours and 10 minutes per week
How to find the height of a cone when only radius is given
Answer:
upload the actually picture of the math problem young lady
fill in the missing values in the table
minutes miles
10. 2
8
10
A line that includes the point (10,7) has a slope of 1. What is it's equation in slope-intercept form?
Find the truth set of 2y+4 > -6
Answer:
Let's solve your inequality step-by-step.
2y+4>−6
Step 1: Subtract 4 from both sides.
2y+4−4>−6−4
2y>−10
Step 2: Divide both sides by 2.
2y /2 > −10 /2
y>−5
Answer:
y>−5
Answer:
\(y = - 5\)
Step-by-step explanation:
\(2y + 4 > - 6 \\ 2y > - 6 - 4 \\ 2y > - 10 \\ \frac{2y}{2} > \frac{ - 10}{2} \\ y > - 5\)
hope this helps you.
solve on the interval [0,2pi] 3(sec x)^2 -4=0
Answer:
pi/6, 5pi/6, 7pi/6, 11pi/6
Step-by-step explanation:
3(sec x)^2 -4=0
Add 4 on both sides:
3(sec x)^2=4
Divide 3 on both sides:
(sec x)^2=4/3
Take square root of both sides:
sec x=plus/minus sqrt(4/3)
Reciprocal identity:
cos x=plus/minus sqrt(3/4)
Simplify the radical:
cos x=plus/minus sqrt(3)/2
So we are looking on the unit circle where the first coordinate of the order pair is either sqrt(3)/2 or -sqrt(3)/2.
This happens at pi/6, 5pi/6, 7pi/6, 11pi/6
Answer:
\(\sf \boxed{\sf x = \dfrac{\pi}{6},\dfrac{5\pi}{6},\dfrac{7\pi}{6},\dfrac{11\pi}{6}}\)
Step-by-step explanation:
A trigonometric equation is given to us , and we need to find the solutions of the equation within the interval [ 0,2π ]
The given equation is ,
\(\sf\longrightarrow 3(sec x)^2-4=0 \)
This can be written as ,
\(\sf\longrightarrow 3sec^2x - 4 = 0 \)
Add 4 to both sides of the equation ,
\(\sf\longrightarrow 3sec^2x = 4 \)
Divide both sides by 3 ,
\(\sf\longrightarrow sec^2x =\dfrac{4}{3} \)
Put squareroot on both sides ,
\(\sf\longrightarrow sec \ x =\sqrt{\dfrac{4}{3} }\)
Simplify ,
\(\sf\longrightarrow sec\ x =\pm \dfrac{2}{\sqrt3} \)
Multiply numerator and denominator by √3 ,
\(\sf\longrightarrow \bf sec(x) = \dfrac{ 2\sqrt3}{3},-\dfrac{2\sqrt3}{3} \)
Solve for x ,
\(\sf\longrightarrow x = \dfrac{\pi}{6} +2\pi n , \dfrac{11\pi}{6}+2\pi n , \textsf{ for any integer n } . \)
Therefore all the possible solutions are ,
\(\sf\longrightarrow \boxed{\blue{\sf x = \dfrac{\pi}{6},\dfrac{5\pi}{6},\dfrac{7\pi}{6},\dfrac{11\pi}{6}}} \)
Find the value of the expression 5x7-4x4
A cell phone plan charges a $30 activation fee plus $19.50 a month. If Ellie has a maximum of $200 to spend, how many months of the cell phone plan can she afford?
Answer: 3 months
Step-by-step explanation: if you had $30 + $19.50
you get 49.50 if you add 49.50+ 49.50 you get 99.00 add another 49.50 you get 148.50 add another 49.50 you get 198 and you cant keep going
49.50= the total for 1 month
Pls help I dont under stand this at all
Answer:
0.5 = 0.25
1=2
2=4
2.5=5
3=6
Step-by-step explanation:
distance divided by 2 equals the time
i hope this helps!
What are the factors of 2x^2 - 7x - 4?*
\(y = 2 (x^2 - \frac{7}{2} x - 2)\) ⤵️
\(y = 2 (x - 4)(x + \frac{1}{2} )\)
An investment of \$2,500 doubles in value every 15 years. The function f defined by f(x) = 2, 500(2 ^ (rx)) represents the value of the investment , in dollars, years after the investment is made , where r is a constant. What is the value of r? R =
Answer:
\(\dfrac{1}{15}\)
Step-by-step explanation:
Given that:
Investment amount = $2500
Time in which it gets doubled = 15 years
Amount after 15 years = $5000 (As per given statement as it gets doubled)
Value of investment in dollars after \(x\) years if investment:
\(f(x) = 2, 500(2 ^ {rx})\)
\(r\) is a constant.
To find:
Value of \(r\).
Solution:
We are given that:
\(f(x) =\$5000\)
\(x=15\ years\)
Putting all the values in the given equation:
\(5000 = 2500(2 ^ {r\times 15})\\\Rightarrow 2 = 2 ^ {r\times 15}\\\Rightarrow r\times 15=1\\\Rightarrow r =\bold{\dfrac{1}{15}}\)
Therefore, the value of \(r\) is:
\(\dfrac{1}{15}\)
Ashley had 4/ 5 of a spool of yarn. She used 2/5 of it for her project. What fraction of the spool was used for her project? Write your answer in simplest form
Ashley used 8/25 of the spool for her project.
To determine the fraction of the spool that Ashley used for her project, we need to multiply the fraction of the spool she had (4/5) by the fraction she used (2/5):
(4/5) * (2/5) = 8/25
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Explain how you decided to divide your wholes into fractional parts and how you decided where your number scale should begin and end. Due 1-2-23
On solving the provided question, we can say that - on doing the fraction we have \(\frac{1}{10} ; \frac{1}{100} ; \frac{1}{10000}\)
what is fraction?Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.
here we have,
0.1 = 1/10
0.01 = 1/100
0.0001 = 1/10000
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