Evaluate the following integral. TT i sin x SSS sin y dz dx dy π/2 Ο Ο TT i sin x SS S siny dz dx dy = 1 n/20 0 (Simplify your answer. Type an exact answer, using a as needed. Use integers or fract
Answers
The value of the given integral is (i + 1).
To evaluate this integral, we start by integrating with respect to z first since we have a function of z only.
∫[0, π/2] ∫[0, sin(x)] ∫[0, sin(y)] i sin(x) sin(y) dz dx dy
= ∫[0, π/2] ∫[0, sin(x)] i sin(x) sin(y) dy dx
= ∫[0, π/2] i sin(x) ∫[0, sin(x)] sin(y) dy dx
= ∫[0, π/2] i sin(x) [-cos(y)] [0, sin(x)] dx
= ∫[0, π/2] i sin(x) (1-cos(x)) dx
= i [∫[0, π/2] sin(x) dx - ∫[0, π/2] sin(x) cos(x) dx]
= i [-cos(x)] [0, π/2] - i ∫[0, π/2] cos(x) d(sin(x))
= i (1 - 0) - i sin(x) [0, π/2]
= i - i(sin(π/2) - sin(0))
= i - i(1-0)
= i(1-i)
= i - i^2
= i + 1
Therefore, the value of the given integral is (i + 1).
In summary, we evaluated the given integral by first integrating with respect to z, then simplifying the resulting expression using trigonometric identities, and finally obtaining the exact value of the integral. The final answer is
(i + 1).
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Related Questions
The side length of each square is 6 units. Find the areas of the inscribed shapes.
Answers
Answer:
a) A₁ = 18 unit²
b) A₂ = 20 unit²
c) A₃ = 12 unit²
d) A₄ = 12 unit²
Step-by-step explanation:
a) Given that the side length of square is 6 units, we have;
The height of the square = The height of the triangle = 6 units
The base of the triangle = The side length of the square = 6 units
The area of a triangle A₁ = 1/2×base×height = 1/2×6×6 = 18 unit²
b) The side of the square A₂ forms an hypotenuse side to the side length 2 and 4 on sides of the circumscribing square
The length of the side = √(4^2 + 2^2) = 2·√5
A₂ = The area of a square =Side² = (2·√5)² = 20 unit²
c) The base length of the triangle, A₃ + 2 = The side length of the circumscribing square = 6 units
∴ The base length of the triangle, ₃₂ = 6 - 2 = 4 units
The height of the triangle, A₃ = The side length of the circumscribing square = 6 units
The area of a triangle A₃ = 1/2×base×height = 1/2×4×6 = 12 unit²
d) Figure, A₄, is a parallelogram;
The area of a parallelogram = Base × Height
The base of the parallelogram, A₄ + 4 = 6 units
Therefore, the base of the parallelogram, A₄ = 6 - 4 = 2 units
The height of the parallelogram = The side length of the circumscribing square = 6 units
The area of a parallelogram A₄ = 2× 6 = 12 unit².
FIRST PERSON TO ANSWER CORRECTLY GETS BRAINLIEST AND 10 POINTS!!!!!!! Click an item in the list or group of pictures at the bottom of the problem and holding the button down drag it into the correct position in the answer box. Release your mouse button when the item is placed if you change your mind drag the item to the trashcan. Click the trashcan to clear all your answers.
Evaluate the following expression. 7^0
Answers
Answer:
The answer is 1
Step-by-step explanation:
Jasim works in a restaurant.
The table shown gives his rates of pay.
Day
Mon to Fri
Weekend
Jasim worked for a total of 30 hours last week.
He worked 12 of these hours at the weekend.
Work out Jasim's pay for last week.
Rate of pay
£8.70 per hour
£10.80 per hour
Answers
Answer:
Step-by-step explanation:
The option that is most suitable for tabular data will be provided by-
Jasim's last week's total pay was £286.2.
Describe tabular data.Tabular data is data presented in the form of rows and columns.
Here,
Total time for which Jasim works last week = 30 hours
Time for which Jasim works at the weekend = 12 hours
Time for which Jasim works at the weekdays = (30 - 12) hours
= 18 hours
Jasim's pay during weekdays = £8.70
Jasim's pay during weekends = £10.80 per hour
Jasim's pay during weekdays last week = £8.70 \(\times\) 18
= £156.6
Jasim's pay during weekends = £10.80
Jasim's pay during weekends = £10.80 per hour
Jasim's pay during weekdays last week = £10.80 \(\times\) 12
= £129.6
Total pay of Jasim for last week = £(156.6 + 129.6)
= £286.2
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a right triangle is a removed from a rectangle to create the shaded religion shown below. Find the area of the shaded region. Be sure to include the correct unit in your answer.
Answers
Answer:
63
Step-by-step explanation:
help i need help with this question fast!!!!
Answers
The solution set of the inequality is (- ∞, - 1].
What is the solution set of simultaneous inequality?
In this problem we have an inequality formed by two linear equations of the form f(x) ≥ g(x), whose solution set has to be found by using algebraic procedures:
- 1.5 · (4 · x + 1) ≥ 4.5 - 2.5 · (x + 1) Given
- 6 · x - 1.5 ≥ 4.5 - 2.5 · x - 2.5 Distributive property / (- 1) · a = - a / Definition of multiplication
- 3.5 ≥ 3.5 · x Compatibility with addition / Existence of the additive inverse / Modulative and associative properties / Definitions of addition and subtraction
- 1 ≥ x Compatibility with multiplication / Existence of multiplicative inverse / Modulative property / - a / b = a / - b = - (a / b)
x ≤ - 1 Trichotomy / Result
The solution set of the inequality is (- ∞, - 1].
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The manager would like to know the probability of a stockout during replenishment lead-time. in other words, what is the probability that demand during lead-time will exceed 25 gallons?
Answers
The probability that demand during this period will exceed 25 gallons depends on the distribution of demand.
To calculate the probability of a stockout during the replenishment lead-time, we need to consider the distribution of demand during this period. If the demand follows a known probability distribution, such as the normal distribution, we can use statistical methods to estimate the probability.
First, we need to determine the parameters of the distribution, such as the mean and standard deviation of the demand during the lead-time. Once we have these parameters, we can calculate the probability of demand exceeding 25 gallons using the cumulative distribution function (CDF) of the chosen distribution.
For example, if the demand during lead-time follows a normal distribution with a mean of 20 gallons and a standard deviation of 5 gallons, we can use the normal distribution table or statistical software to find the probability of demand exceeding 25 gallons.
Alternatively, if we have historical data on demand during lead-time, we can use that data to estimate the probability. We can calculate the proportion of instances where the demand exceeded 25 gallons and use this as an estimate of the probability of a stockout during the lead-time.
Overall, the probability of a stockout during replenishment lead-time depends on the distribution of demand and can be determined using statistical techniques or historical data.
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Find the degree of the monomial.
7a765
Answers
Answer: 1^ degree
Step-by-step explanation: because A is raised to 1 and being the only literal part the degree is one
Jon sells books on the internet for $12
each and spent $180 on shipping last
month. Represent on a number line the
number of books, x, he sold last month
if he earned a total of $720.
Answers
Answer:
60 books
Step-by-step explanation:
12x=720
Take 720 and divided by 12, so you got 60.
==> Jon sold 60 books last month.
Don't mind the answer i picked i accidently clicked it
Answers
Answer:
a ball resting on the edge of a cliff
Suppose a product's revenue function is given by R(q) = - 7q + 600qr. Find an expression for the marginal revenue function, simplify it, and record your result in the box below. Be sure to use the proper variable in your answer. (Use the preview button to check your syntax before submitting your answer.) Answer: MR(q) =
Answers
The expression for the marginal revenue function is MR(q) = 600r - 7.
The given product's revenue function is R(q) = - 7q + 600qr.
To find an expression for the marginal revenue function, we can use the following steps:
Step 1: Take the first derivative of the revenue function with respect to q to obtain the marginal revenue function MR(q).
Step 2: Simplify the expression for MR(q) to record the final result.
In other words, the marginal revenue function MR(q) is the derivative of the revenue function R(q) with respect to q. Here, R(q) = - 7q + 600qr.
So, we have to differentiate R(q) with respect to q to get MR(q).
The derivative of - 7q with respect to q is - 7.
The derivative of 600qr with respect to q is 600r because the derivative of q with respect to q is 1.
MR(q) = dR(q) / dq
= (d/dq)(- 7q + 600r)
= (- 7) + (600r)
= 600r - 7
The equation that represents the marginal revenue function is MR(q) = 600r - 7.
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Which number best represents the slope of the graphed line?
A. -3 -3
B. -1/3 -1/3
C. 1/3 1/3
D. 3 3
Answers
Because you go up 1 over 3 in the negative direction starting from (0,0)
Will mark brainliest
question-
jack jogs and rides his bike for a total of 75 minutes every day. he rides his bike 15 minutes more than he jogs.
part a: write a pair of linear equations to show the relationship between the number of minutes jack jogs (x) and the number of minutes he rides his bike (y) every day.
part b: how much time does jack spend jogging every day?
part c: is it possible for jack to have spent 60 minutes riding his bike every day? explain your reasoning.
Answers
The answers have been shown below.
To find the answers:Questions regarding the time spent by Jack jogging and bike riding are needed to be answered.
(A) The equations are \(x+y=75, y=15+x\)
Time spent jogging is 30 minutes
The total time would be \(45+60=105\) minutes which is not equal to 75 minutes.
(B) Let \(x\) be the time spent jogging.
\(y\) be the time spent bike riding.
\(x+y=75\\y=15+x\\x+15+x=75\\2x+15=75\\x=\frac{75-15}{2} =30\)
Time spent jogging is 30 minutes.
\(y=60\\x+y=75\)
(C) If he rides his bike 15 minutes longer than he jogs then he would have to jog \(60-15 = 45\) minutes.
Therefore, the total time would be \(45+60=105\) minutes which is not equal to 75 minutes.
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a random sample of 64 students at a university showed an average age of 23 years and a sample standard deviation of 3 years. what is the 95% confidence interval for the true average age of all students in the university?
Answers
As per the 95% confidence interval, the true average age of all students in the university is approximately 23 to 24.
Confidence interval
Confidence interval means the interval calculation, obtained from the observed data that holds the actual value of the unknown parameter.
Given,
A random sample of 64 students at a university showed an average age of 23 years and a sample standard deviation of 3 years.
And we need to find the 95% confidence interval for the true average age of all students in the university.
While we looking through the given question we have identified the following,
Number of samples = 64
Average age = 23
Standard deviation = 3
Confidence interval = 95%
Based on this confidence interval, the z score is 1.96
According to the formula,
u = 23 ± 1.96 x 3/√64
u = 23 ± 1.96 x (3/8)
u = 23 ± 1.96 x 0.375
u = 23 ± 0.735
u = 23.735, 22.635
Therefore, the average age of the student is approximately 23 to 24.
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In this problem, we'll discover why we always see quadratic functions for equations of motion. Near the surface of the earth, the acceleration due to gravity is almost constant - about 32 ft/sec^2. Velocity is an antiderivative of acceleartion. Determine the "general antiderivative" of the acceleartion function a(t) = −32. v(t) = [The variable is t, not x, and don't forget +C!] Now consider a chem student who shows up to chem lab without proper footwear. The chem prof, in a fit of rage, throws the student (or just their shoes) out of the lab window. Let's assume the prof threw the shoes straight up with a velocity of 20 ft/sec, meaning v(0) = 20. Find the exact formula for the velocity v(t) of the shoes at second t after they were thrown. [Hint: what do you need +C to be?] v(t) = For the velocity function you just found, write its general antiderivative here. s(t) = = The window where the shoes were thrown from is about 30 feet above the ground. Find the equation s(t) that describes the position (height) of the shoes. s(t) =
Answers
The general antiderivative of the acceleration function a(t) = -32 is given by integrating with respect to time:
v(t) = ∫(-32) dt = -32t + C
Given that v(0) = 20, we can substitute t = 0 and v(t) = 20 into the velocity equation and solve for C:
20 = -32(0) + C
C = 20
Thus, the exact formula for the velocity v(t) of the shoes at time t after they were thrown is:
v(t) = -32t + 20
To find the general antiderivative of v(t), we integrate the velocity function with respect to time:
s(t) = ∫(-32t + 20) dt = -16t² + 20t + C
Since the shoes were thrown from a window 30 feet above the ground, we set s(0) = 30 and solve for C:
30 = -16(0)² + 20(0) + C
C = 30
Therefore, the equation s(t) that describes the position (height) of the shoes is:
s(t) = -16t² + 20t + 30
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Mike wants to save $1,750 in the next 12 months. He plans to save $150 each month for the first 11 months. What is the total amount of money Mike will save during the first 11 months if he saves $150 each month?
Please need steps
Answers
Answer:
$1650
Based on the question, we don't need the information that Mike wants to save 1750 in 12 months.
We just need to focus on how he is saving 150 every month, for 11 months.
150*11=1650
He will save $1650 if he saves $150 every month for 11 months.
Step-by-step explanation:
Can i get brainiliest plz
Samir works as a salesperson at an electronics store and sells phones and phone accessories. Samir earns a $8 commission for every phone he sells and a $4 commission for every accessory he sells. On a given day, Samir made a total of $216 in commission from selling a total of 39 phones and accessories. Graphically solve a system of equations in order to determine the number of phones sold. 2, and the number of accessories sold, y.
Answers
The number of phones sold is 15 and the number of accessories sold is 24, and the graph is attached below.
What is a graph?A graph is a structure made up of a collection of things, where some object pairs are conceptually "connected." The items are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.
Given:
Samir earns an $8 commission for every phone he sells and a $4 commission for every accessory he sells,
Total money earned = $216,
Total number of phones and accessories sold = 39
Write the equation of the above statement as shown below,
8x + 4y = 216,
x + y = 39
Assume the number of phones sold is x and the number of accessories sold is y,
Solve the equation by elimination as shown below
x = 15,
y = 39 - 15 = 24
The graph is also attached below,
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Box of 36 rubber bands he used 1/4 of the rubber bands in the box how many rubber bands did use
Pleas help
Answers
Answer:
He used 9 rubberbands.
pls give me brainliest if correct.
Step-by-step explanation:
Answer:
9
Step-by-step explanation:
36 divided by 1 over 4 equals 9
9+9+9+9=36
1+1+1+1=36
-----------
4 4 4 4
Pls help im am struggling i will give brainliest !!!!!!!!!
Answers
They are extremely similar but a(x) has a greater y-intercept!
If you look at the y axis, a(x) simply intercept it higher than b(x)
Hope this helps!
Answer:
a(x)
because the greater is a(x)
PLEASE HURRY XX
Find a equation that matches the graph.
Answers
Answer:
x ≥ 3
Step-by-step explanation:
The closed dot represents ≥ and ≤
The dot is located on the number "3"
The closed dot essentially shows that the solution is nothing more than 3 and up.
Let "x" be the variable we use.
x ≥ 3
Best of Luck!
The above never line shows the possible values of an variable in any expression.
Through Observation:
The arrow pointing from 3 to infinity.3 is represented by a closed dot.The value is starting from 3 to infinity.Hence, the required value of the variable can be equal to 3 or greater than 3 for that expression. This can be written as:
\( \large{ \boxed{ \rm{ x\geqslant 3}}}\)
Carry On learning !
Keenan got 13 /25 for his Mathematics Test write this as a decimal fraction
Answers
Answer: Answer is 0.52
Step-by-step explanation:
So we have the fraction 13 Out of 25.
step 1: here we divide numerator(which is 13) by denominator(which is 25).
step 2: first we make denominator 100 by multiplying by 25 with 4 and also 13 with 4.
ie. \(\frac{13 * 4}{25 * 4}\)
step 3: we get \(\frac{52}{100}\)
step 4: now we can easily write the decimal fraction. ie. 0.52
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2H2 + O2 yields 2H2O How many grams of water will be produced if 2. 6 grams of oxygen gas reacts
Answers
While 2.6 grams of oxygen gas reacts, 2.925 grams of water will be produced.
The balanced chemical equation for the reaction is
2H2 O2 → 2H2O
According to the stoichiometry of the reaction, 1 mole of oxygen gas reacts with 2 moles of hydrogen gasoline to give 2 moles of water. The molar mass of oxygen gasoline( O2) is 32 g/ spook, and the molar mass of water( H2O) is 18 g/ mol.
To decide the quantum of water produced whilst 2.6 grams of oxygen gas reacts, we need to follow the subsequent way
Convert the presented mass of oxygen gas to moles
g O2 ×( 1 mol O2/ 32 g O2) = 0.08125 mol O2
Use the mole ratio from the balanced equation to decide the moles of water delivered
mol O2 ×( 2 mol H2O/ 1 mol O2) = 0.1625 mol H2O
Convert the moles of water produced to grams
mol H2O ×( 18 g H2O/ 1 mol H2O) = 2.925 g H2O
Accordingly, 2.925 gram of water will be produced while 2.6 gram of oxygen gas react.
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A store sells a certain tile for $2 per tile and a pint of paint for $3. A second store sells the same items for $1 per tile and $4 per pint of paint. Ari bought the same number of tiles and pints of paint at both stores, costing him $26 at the first store and $18 at the second store, before tax. Which system of equations can be used to find the number of tiles, x, and the number of pints of paint, y, that Ari bought at each store? A system of equations. 3 x plus 4 y equals 18. X plus 2 y equals 26. A system of equations. X plus 3 y equals 18. 2 x plus 4 y equals 26. A system of equations. 2 x plus 3 y equals 26. X plus 4 y equals 18. A system of equations. 3 x plus 2 y equals 26. 4 x plus y equals 18.
Answers
Answer:
2 x plus 3 y equals 26. X plus 4 y equals 18
Step-by-step explanation:
Number of tiles, = x
Number of pints of paint, = y
Store 1:
Cost per tile = $2 ; cost per pint = $3 ; total cost = $26
Store 2 :
Cost per tile = $1 ; cost per pint = $4 ; total cost = $18
System of equation:
2x + 3y = 26 - - - (1)
x + 4y = 18 - - - - - (2)
Pand Q are points on the line
3x + 2y = 6
(a)
Complete the coordinates of P and Q.
Answers
Answer:
you are multiplying baceicly
Step-by-step explanation:
3×2=6
You roll a red-sided die and a white-sided die. Find the probability. P(red is less than 3 and white is less than 3) Simplify the answer.
Answers
Answer:
1 on 3
Step-by-step explanation:
The red dice has 6 faces. The number you have to obtain is less than 3. So your answers must be 1 and 2. The numbers 1 and 2 are two solutions out of six. Now the same goes with the white dice. Two solutions out of six. You combine them and obtain 4 on 12. Then, you reduce the answer in minimal terms and finally obtain 1 on 3.
calculate the angular area of the hst’s field of view in square degrees.
Answers
The angular area of the HST's field of view is 25 square degrees.
The field of view is the extent of the sky that the Hubble Space Telescope (HST) can observe at a given time. It is usually measured in degrees.
To calculate the angular area, we can use the formula for the area of a circle:
Area = π * (angular size/2)^2
Where π is a mathematical constant approximately equal to 3.14, and the angular size is in degrees.
Let's say the angular size of the HST's field of view is 10 degrees.
First, we divide the angular size by 2:
10 degrees / 2 = 5 degrees
Next, we square the result:
5 degrees * 5 degrees = 25 square degrees
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variables y and x have proportional relationship and y=21 when x=14 what is the value of x when y=12
Answers
Answer:
x = 8
Step-by-step explanation:
Formula: y = kx
21 = k(14) --> k = 21/14 = 3/2
y = 3/2 x
When y = 12:
12 = 3/2 x
24 = 3x
x = 8
The value of x is 8 when y = 12 if variables x and y have proportional relationship.
According to the given question.
Variables y and x have proportional relationship.
⇒ y ∝ x
Let k be the constant of proportionality.
⇒ y = kx
Also, it is given that
y = 21 when x = 14
Substitute the value of y = 21 and x = 14 in y = kx to find the value of k.
21 = k(14)
⇒ k = 21/14
⇒ k = 3/2
Therefore, the value of x when y = 12
y = kx
⇒ 12 = (3/2)x
⇒ 12 × 2 = 3x
⇒ 24 = 3x
⇒ x = 24/3
⇒ x = 8
Hence, the value of x is 8 when y = 12.
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The volume of the triangular pyramid below is 256 units 3 . Find the value of x.
Answers
Answer:
Step-by-step explanation:
We can use the formula for the volume of a pyramid, which is:
V = (1/3) * B * h
where V is the volume, B is the area of the base, and h is the height.
In this case, we have a triangular pyramid, so the base is a triangle. Let's call the length of the base x, and the height of the pyramid h. Then, the area of the base is:
B = (1/2) * x * h
Substituting into the formula for the volume, we get:
256 = (1/3) * (1/2) * x * h * h
Simplifying and solving for h, we get:
256 = (1/6) * x * h^2
h^2 = (256 * 6) / x
h = sqrt((256 * 6) / x)
Now, let's use the given information that the three sides of the base have lengths x, 2x, and 3x, to find the area of the base:
B = (1/2) * x * (2x + 3x) / 2
B = (5/4) * x^2
Substituting this and the expression for h into the formula for the volume, we get:
256 = (1/3) * (5/4) * x^2 * sqrt((256 * 6) / x)^2
Simplifying, we get:
256 = (5/4) * x^2 * sqrt(1536 / x)
256 = (5/4) * x^2 * (sqrt(1536) / sqrt(x))
256 = (5/4) * x^2 * (12 / sqrt(x))
256 = 15 * x * sqrt(x)
Squaring both sides, we get:
65536 = 225 * x^3
Dividing both sides by 225, we get:
x^3 = 65536 / 225
Taking the cube root of both sides, we get:
x = (65536 / 225)^(1/3)
x ≈ 6.4
Therefore, the value of x is approximately 6.4 units.
find the area of equilateral triangle whose median is X cm
options:
a.x^2
b.(x^2)/2
c.(x^2)/√3
d.(x^2)/3
Answers
Explanation:
Since all the sides of equilateral triangle are the same and x is the median. Meaning that all the other sides are also X.
We can use the formula:
Area = (b x h)/2
A = (x • x)/2
A = (x^2)/2
For his long distance phone service, tony pays $3 monthly fees plus 11 cents per minute. Last month, Tony's long distance bill was $22.03. For how many minutes was tony billed
Answers
Answer:
173 minutes
Step-by-step explanation:
Total fees= monthly fees + $0.11(number of minutes)
$22.03= $3 +$0.11(number of minutes)
$0.11(number of minutes)
= $22.03 -$3
= $19.03
= 1903¢
11¢ (number of minutes)= 1903¢
Number of minutes
= 1903¢ ÷11¢
= 173
Thus, Tony was billed for 173 minutes.
True or False: In –6x – 20 = –2x + 4(1 – 3x)
Answers
Given \(-6x-20\)
Proof that it is equal to the \(-2x + 4(1 - 3x)\) or not
\(-2x + 4(1 - 3x)\)
Distribute
\(-2x+ 4-12x\)
\(4-14x\)
Not equal to the \(-6x-20\) \(\neq\) \(4-14x\)
So, it is false
What is Distribute in math?
To "distribute" anything is to divide it up or to give someone a piece of it.
What does the mathematical distributive property mean then?
The distributive property is the distributive law of multiplication over operations in fundamental arithmetic, such as addition and subtraction.
Distributive property: What Is It?
This property states that multiplying the total of two or more addends by a number will provide the same outcome as multiplying each addend by the number separately and then adding the results together.
In other words, an expression of the type A (B + C) can be resolved as A (B + C) = AB + AC in accordance with the distributive property.
This characteristic also holds for subtraction.
A(B-C) = AB-AC
This demonstrates that the other two operands share operand A.
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