The value of the integral is: πcos(16)- πcos (81)
What are polar coordinates?The polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a from a reference point and an angle from a reference direction.
Given:
∫∫ r sin(x²+y²)dA and 16≤x²+y²≤81.
Now,
x =rcosϕ
y=rsinϕ
I=r
Find the integration limits:
ϕ∈[0,2π]
16≤x²+y²≤81
16≤r² cos² Ф + r²sin² Ф≤81
16≤r²≤81
4≤r≤9
So, r∈[4,9]
Now,
∫∫ r sin(x²+y²)dA=
= [tex]\int\limits^9_4 {dr} \int\limits^{2\pi}_0 {rsin \;(r^{2}) } \, d\phi[/tex]
=2π [tex]\int\limits^9_4 {rsin \;(r^{2}) } \, dr[/tex]
Let r² = u
2rdr=du
Also, limit will change from 16 to 25.
5→25
4→16
So,
= π[tex]\int\limits^{81}_{16} {sin \;(u) } \, du[/tex]
=−π|cos (u)∣[tex]^{81}_{16}[/tex]
= πcos(16)- πcos (81)
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What is the interquartile range of 4 5 7 9 10 14 16 24
Answer:
The answer is 9
Step-by-step explanation: ? i did the the tetst or whatever and 9 is the correct answer.
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Carlos has 7 times as many red toy cars as blue toy cars. He has 56 total cars. How many more red cars does he have?
let x = blue cars
so 7x = red cars
x +7x = 56
8x = 56
x = 56/8 =7 blue cars
7*7 =49 red cars
49-7 =42 more red cars
Twenty different books are to be put on five book shelves, each of which holds at least twenty books.
What is the value of mc009-1.jpg?
–34
–2
10
34
the pic is the .jpg
The value of the expression -4²+(5-2)(-6) is -34 when following the standard rules of arithmetic.
Explanation:The value of the expression −4²+(5−2)(−6) can be determined by first calculating the power and then performing the operations inside the parentheses, followed by the multiplication and addition/subtraction.
The power of −4² is 16 because the negative sign is not inside the parentheses, so it is not squared, and 16 will be considered as a negative number here (-16).
Next, we calculate the value within the parentheses (5−2), which gives us 3.
Then we multiply 3 by −6, which equates to −18. Finally, we add the two results: −16 + (−18) = −16 −18 = −(16 + 18) = −(34), resulting in the value −34.
A= P(1+nr) ; solve for r
mr. renato had $150 in his bank account. he deposited $50. acuple of days later he withdrew $20. a week later he deposited $75 .the next week he withdrew $100. what is mr. Renato balance after all the transactions
The median for the given set of 6 ordered data values is 32.5.
9, 12, 25, _, 41, 48
What is the missing value?
Given that the volume decreases at a rate of 3 cubic meters per minute, find the rate of change of an edge, in meters per minute, of the cube when the volume is exactly 64 cubic meters
Th local park has 4 bike racks. Each bike rack can hold 15 bikes. There are 16 bikes in the bike racks. What expression shows the total number of empty spaces in the bike racks?
Order these numbers from least to greatest. 14325 , 5.753 , 534 , 5.34
the GCF of the following numbers. 32 and 40
Consider the following equation:
f′(a)=limh→0 (f(a+h)−f(a))/h
Let f(x)=3√x If a≠0, use the above formula to find f′(a)=
Show that f′(0) does not exist and that f has a vertical tangent line at (0,0)
Final answer:
To find the derivative of f(x) = 3√x at a nonzero point, use the definition of the derivative with limits. The derivative at x=0 does not exist because the function has an infinite slope at this point, demonstrated by the absence of a limit, signifying a vertical tangent line at (0,0).
Explanation:
To find f'(a) for f(x) = 3√x when a ≠ 0, we can use the given definition of the derivative:
f'(a) = limh→0 (f(a+h) – f(a)) / h.
To show that f'(0) does not exist and that f has a vertical tangent line at (0,0), we need to evaluate the limit as h tends to zero for the derivative definition applied at a = 0. Since the square root function is not differentiable at 0 (due to the function having an infinite slope at this point), the limit will not exist, indicating that the derivative at 0 does not exist, and the graph of f exhibits a vertical tangent at that point.
Determine whether the fractions -4/5, -4/6, -4/7, and -4/8 are arranged in order from least to greatest. explain
scuba diver is swimming 30 feet below sea level . A hand glider passes over the position of the scuba diver. The hand glider is 215 ft above sea level.
draw a number line to represent the distance between the scuba diver and the hand glider (include sea level at zero feet)
Is it possible to construct a triangle with side lengths of 11 cm, 15 cm, and 21 cm? Why or why not?
Which BEST describes the construction of a triangle if given one side length of 10 cm and one right angle?
A)
Unique triangle
B)
More than one triangle
C)
Triangle not possible
D)
Cannot be determined
Answer:
b
Step-by-step explanation:
write the number 1,744,326 in expanded form
katie and carol bought toys for charity toy drive.katie bought 125 dolls for 13$ each. carol bought 65 toy boats for 32$ each.who spent more money altogher
Don tracked the price of gas for several months. In January gas cost $2.65, in February the price had risen $0.56, in March decreased $0.23, in April risen $1.02, and in May decreased $0.48. By how many dollars has the price of gas changed from January to May?
The solution is, By $.87 dollars has the price of gas changed from January to May
What is Subtraction?Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.
here, we have,
given that,
Starting price is 2.65, increased by .56
2.65+.56=3.21
Price is 3.21, decreased by .23
3.21-.23=2.98
Price is 2.98, increased by 1.02
2.98+1.02= 4
Price is 4, decreased by .48
4-.48=3.52
Now find the difference from the starting price (January) from the end price (May)
3.52-2.65=.87
The difference from gas prices is $.87.
Hence, The solution is, By $.87 dollars has the price of gas changed from January to May.
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FREE POINTS!!!!!!!!!! 10 POINTS Len's recipe for blueberry muffins calls for 110.25 grams of brown sugar for the muffin batter and an additional 55.45 grams of brown sugar for the topping. Len wants to make 4.5 batches of muffins. Enter the total amount of brown sugar that Len will need
the answer is 745.65
hope i helped:)
Differentiate f and find the domain of f. (enter the domain in interval notation.)f(x) = ln(x2 − 12x)derivative f '(x) = 2x−12x2−12x correct: your answer is correct.domain
Shelly used exactly 1/ 3 of a cup of oil and 3/ 8 of a cup of water in a recipe. How many cups of liquid did Shelly use in all?
Answer: =[tex]\dfrac{17}{24}[/tex]
Step-by-step explanation:
Given : The amount of oil is used in a recipe. = [tex]\dfrac{1}{3}[/tex]
The amount of water used in a recipe = [tex]\dfrac{3}{8}[/tex]
The total number of cups of liquid used by Shelly:-
[tex]\dfrac{1}{3}+\dfrac{3}{8}=\dfrac{8+3\times3}{24}\\\\\=\dfrac{8+9}{24}=\dfrac{17}{24}[/tex]
Hence, the total number of cups of liquid used in all =[tex]\dfrac{17}{24}[/tex]
ABCD is a trapezoid. = 2.5 cm, and = 4 cm, and the area = 6.5 cm2. What is the altitude of the trapezoid?
Answer:
Altitude of the trapezoid is 2 cm.
Step-by-step explanation:
ABCD is a trapezoid. Since two bases of the trapezoid are
B1 = 2.5 cm and B2 = 4 cm.
Area given is 6.5 cm²
Then we have to calculated he altitude of the trapezoid.
Now we know the formula of area of the trapezoid = [tex]\frac{1}{2}[/tex] ( Base1 + Base2)
By putting the values in the formula
6.5 = [tex]\frac{1}{2}[/tex] ( 2.5 + 4 ) × h
6.5 = [tex]\frac{6.5}{2}[/tex] × h
h = \frac{2\times 6.5}{6.5} = 2 cm.
Answer is altitude of the trapezoid is 2 cm.
Translate the phrase to mathematical language. Then simplify the expression.
Subtract 81 from −55.
What is a numerical expression for the phrase?__
(Do not simplify.)
Simplify the expression.__
Which of the following is a sample of the population of bookstores on the West Coast of the United States? I. All book stores in California II. Randomly selected children's book stores III. Internet book stores A. I only B. II only C. I and III D. III only E. I and II
Answer:
It would be I - All bookstores in California
Step-by-step explanation:
Internet book stores and random children's bookstores do not specify that they're on the West Coast and could be taken from anywhere
Which of the following is the simplified form of the seventh root of x times the seventh root of x times the seventh root of x ?
Jason bought 5 movie tickets and a bag of popcorn Jeremy bought 2 movie tickets they spent 54$ total. If the popcorn cost 5$, how much did each movie ticket cost?
The volume of this rectangular prism is 6x3. What does the coefficient 6 mean in terms of the problem?
A. The total volume of the prism is 6 cubic units.
B. The length is 6 times the width.
C. The width is 6 times the height and the length.
D. The length of the prism is 6 units.
Answer:
B. The length is 6 times the width
Step-by-step explanation:
The proper solution is choice B. The length is 6 times the width.
How do you resolve rectangular prisms?
To find the quantity of a rectangular prism, multiply its 3 dimensions: duration x width x height. The volume is expressed in cubic gadgets.
What are examples of square prisms?Right rectangular prisms or cuboids are all around us. a few examples are books, packing containers, homes, bricks, forums, doorways, containers, cabinets, mobiles, and laptops.
What does the coefficient mean?Any of the elements of a product taken into consideration with regards to a specific element particularly: a constant thing of a term as outstanding from a variable.
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what is -8 3/4 + -11 1/3
A soccer coach purchased one goal and some soccer balls for the team. The expression 180 + 15x represents the cost before tax. What do the different parts of the expression model? Drag the parts of the expression into the boxes to match each description.
The expression [tex]180+15x[/tex] consists of ONE CONSTANT [180] and another VARIABLE EXPRESSION [15x].
Since the coach purchased ONE GOAL, this corresponds to the CONSTANT, which is 180. 180 is the price of the goal.
Since coach purchased several soccer balls, but doesn't say how many, it is the variable part, 15x, where
either 15 is price of ball and x is the number of balls, OR15 is the number of balls and x is the price of eachANSWER:
180 represents the price of the goal
15x represents the total price of the soccer balls
Answer:
180 represents the price of the goal
15x represents the total price of the soccer balls
Step-by-step explanation: