Answer:
The result of the integral is [tex]\frac{\pi}{4}(-\cos{16} + \frac{9})[/tex]
Step-by-step explanation:
Polar coordinates:
In polar coordinates, we have that:
[tex]x^2 + y^2 = r^2[/tex]
And
[tex]\int \int_{dA} f(x,y) da = \int \int f(r) r dr d\theta[/tex]
In this question:
[tex]\int \int_{dA} \sin{(x^2+y^2)} dA = \int \int_{dR} = \sin{r^2}r dr d\theta[/tex]
Region in the first quadrant between the circles with center the origin and radii 3 and 4
First quadrant means that [tex]\theta[/tex] ranges between [tex]0[/tex] and [tex]\frac{\pi}{2}[/tex]
Between these circles means that r ranges between 3 and 4. So
[tex]\int \int_{dR} = \sin{r^2}r dr d\theta = \int_{0}^{\frac{\pi}{2}} \int_{3}^{4} \sin{r^2} r dr d\theta[/tex]
Applying the inner integral:
[tex]\int_{3}^{4} \sin{r^2} r dr[/tex]
Using substitution, with [tex]u = r^2, du = 2rdr, dr = \frac{du}{2r}[/tex], and considering that the integral of the sine is minus cosine, we have:
[tex]-\frac{\cos{r^2}}{2}|_{3}{4} = \frac{1}{2}(-\cos{16} + \frac{9})[/tex]
Applying the outer integral:
[tex] \int_{0}^{\frac{\pi}{2}} \frac{1}{2}(-\cos{16} + \frac{9}) d\theta[/tex]
Has no factors of [tex]\theta[/tex], so the result is the constant multiplied by [tex]\theta[/tex], and then we apply the fundamental theorem.
[tex]\frac{\theta}{2}(-\cos{16} + \frac{9}) = \frac{\pi}{4}(-\cos{16} + \frac{9})[/tex]
The result of the integral is [tex]\frac{\pi}{4}(-\cos{16} + \frac{9})[/tex]
Find a polynomial that represents the perimeter of the rectangle.
Hi there!
[tex]\large\boxed{P = 4x^2 + 12x + 22}[/tex]
The perimeter of a rectangle is:
P = 2l + 2w
Thus, plug in the given length and width:
P = 2(2x² + 5x + 8) + 2(x + 3)
Distribute:
P = 2(2x²) + 2(5x) + 2(8) + 2(x) + 2(3)
Simplify:
P = 4x² + 10x + 16 + 2x + 6
Combine like terms:
P = 4x² + 12x + 22
Answer:
[tex]4x^2+12x+22[/tex]
Step-by-step explanation:
The perimeter of a rectangle is equal to [tex]2l+2w[/tex] where l is the length and w is the width. So, this rectangle would be equal to [tex]2\left(x+3\right)+2\left(2x^2+5x+8\right)[/tex]. Then, to find the polynomial simplify the expression. To do this first distribute the two 2s. This equals [tex]2x+6+4x^2+10x+16[/tex]. Then, add like terms to finish simplifying. This gives you the final answer of [tex]4x^2+12x+22[/tex].
there is a safety fence around a circular pool with a gate the gate is 150cm wide
Answer:
The length of the fence is 6.28x-150 cm.
Step-by-step explanation: ... Since the pool is in a circular shape so the circumference will be the length of the fence.
Cassandra baked a cake measuring 13 in. x 9 in. x 2 in. She wants to add frosting to the cake. The only side that will not be frosted is the bottom of the cake.
What is the surface area that will be frosted with icing?
O A 24 in. ^2
O B 117 in. ^2
O C 205 in. ^2
O D 322 in. ^2
DO NOT ANSWER IF YOU DO NOT KNOW THE ANSWER! Whoever answers correctly will get Brainliest! :)
Answer:
C
Step-by-step explanation:
The cake has a shape of a rectangle prism
first of all we can find the base area, that represents the top of the cake
base area = base x width = 13 x 9 = 117 in^2
Now we have to find the lateral area
base perimeter = (base + width) x 2 = (13 + 9) x 2= 44 in
LA = base perimeter x height = 44 x 2 = 88 in^2
total icing surface:
base area + LA = 117 + 88 = 205 in^2
Hey guys! I need some help
Answer:
D
Step-by-step explanation:
8x+12y-2y+3x=11x+10y
Answer:
answer D
Step-by-step explanation:
8x+12y-2y+3x
11x+ 10y
Peter received a $40 gift card to Starbucks for his birthday. He
spends the same amount every time he goes and has gone 5
times so far. On one of his trips he also got a $3 drink for his
brother. What is the most he could have spent per trip? Choose
the inequality that describes his situation. Let xramount per trip
Answer:
xr ≤ 7
Step-by-step explanation:
He must spend less than or equal to 7$ to account for 5 trips and 3 extra dollars for 1 trip.
This is the graph of a quadratic function i need help
Answer:
vertex: (-1,-2)
roots: (-3,0);(1,0)
axis of symmetry is: x=-1
Jenny calculated the probabilities of pulling chops of different colors out of a bag.
Which color chip is MOST LIKELY to be pulled from the bag?
DON’T ANSWER IF YOU DO NOT KNOW THE ANSWER! Whoever answers correctly will get Brainliest! :)
Answer:
I'm really sorry if i am wrong but i think Gold chip is most likely to be pulled from the bag.
Step-by-step explanation:
Let's convert each fraction given to the decimal form:
(Purple) [tex]\frac{1}{5}[/tex] = 0.2
(Gold) [tex]\frac{6}{10}[/tex] = 0.6
(White) [tex]\frac{1}{10}[/tex] = 0.1
(Red) [tex]\frac{2}{20}[/tex] = 0.2
=> since Gold chips' value is the most, the answer would be Gold Chip.
Hope this helps!
#6 for the function f(x) = x² what is the
Max. domain if y is restricted to; f(x) = 144 and
f(x) =1286?
Answer:
Step-by-step explanation:
or the function f(x) = x² what is the
Max. domain if y is restricted to; f(x) = 144 and
f(x) =1286?
A person is using a new teenis ball launching machine that is 15 inches by 14. Assuming the machine uses tennis balls that are spherical and 2.7 inches in diameter, how many tennis balls should fit in one of the top of the machine?
The number of tennis ball fit in the machine are 305 balls.
What is volume?Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.
Finding an object's volume can help us calculate the quantity needed to fill it, such as the volume of water needed to fill a bottle, aquarium, or water tank.
given dimensions of machine 15 x 15 x 14
volume of machine is 15 x 15 x 14 = 3150 cubic inches
and shape of ball is spherical,
with dia = 2.7 inches
radius of ball = 2.7/2 = 1.35 inches
volume of sphere is 4/3πr³
V = 4/3πr³
V = 4/3(3.14)(1.35)³
V = 4/3(3.14)(2.46)
V = 10.30 cubic inches
the area covered by 1 ball is 10.30 cubic inches
the number of ball in machine is 3150/10.30
the number of ball in machine = 305.82 = 305 approx
Hence 305 balls can be fit in machine.
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A parent function is a linear function of the form y=b true of false
False
Step-by-step explanation:The parent function is the simplest function within a family of functions that defines the general form of that family.
Parent Functions
Parent functions are given in terms of y and x, where y is the output and x is the input. In linear functions, b represents a constant, specifically the y-intercept. Since the form y=b does not have an input it cannot be the parent function of linear lines. The graph of y=b would be a horizontal line with no slope. This does not define the general form of most linear functions. Additionally, since the slope has been changed to zero, it is not considered the simplest form of linear functions.
Linear Parent Function
The true parent function of linear functions is y=x. This function is the simplest linear function and has no transformations. Additionally, when graphed it is a diagonal line that defines the general shape of lines.
To create new linear functions the parent function, y=x, can be transformed by changing the coefficient of x to change the slope or by adding a constant to shift the graph vertically.
8. If you got 27 questions correct on
a test that has 32 questions, what
percent of the questions did you
correct on the test?
please help middle school math
Answer:
Step-by-step explanation:
1）√320=8√5
（√125+√45）=8√5
（√500-√20）=8√5
ABC is an equilateral triangle.
2) area=1/2 lengh * h
1/2 * 4√15 * 8√5
=2√15 * 8√5
=80√3
Solve Using substitution 3x+5y=-28 Y=x+4
Answer:
(-6, -2) x=-6, y=-2
Step-by-step explanation:
3x + 5(x+4) = -28
3x + 5x+20=-28
8x+20=-28
8x=-48
x=-6
Y=-6+4
y=-2
16. The side length of a square ABCD is 18 inches. What is the side length of the square formed by joining the
midpoints of the sides of ABCD, to
the nearest tenth?
Therefore , the solution of the given problem of square comes out to be the ABCD square is 18 inches
what is the side of length of square ABCD?The side length of a square ABCD is 18 inches Each side of square ABCD is 18 inches The midpoints of ABCD are joined to form a square MNOP The figure is attached below
Here,
We need to find the side length of square MNOP
AMN form a Right angle triangle
We know AM =9 and AN= 9
To find MN , use Pythagoreans theorem
MN2=AM2+AN2
MN2=9square+9 square
MN2=162
Take square root on both sides
MN=9 root 2
so the side of the square MNOP is 9 square root 2 inches
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find the first term in geometric sequence if the 11th term is -160 and the ratio is -1/3
Answer:
-9447840
Step-by-step explanation:
You want the first term of a geometric sequence whose 11th term is -160 and whose common ratio is -1/3.
N-th termThe n-th term of a geometric sequence is ...
an = a1·r^(n-1)
where a1 is the first term and r is the common ratio.
Using the given values, we have ...
-160 = a1·(-1/3)^(11 -1)
a1 = (-160)·(-3)^10 = -9447840
The first term is -9447840.
Who is your favorite red dead character I need to see if u are smart
Answer: Dutch
Step-by-step explanation: He just needs the money
Answer:
Uncle
Step-by-step explanation:
If a pair of shoes was discounted from an original price of P5000 to P2800 what is the percent decrease or discount
Work Shown:
a = old price = 5000
b = new price = 2800
c = change in price
c = b-a
c = 2800-5000
c = -2200
The value of c is negative to indicate a price decrease.
d = percent change
d = (c/a)*100%
d = (-2200/5000)*100%
d = -44%
There is a 44% decrease or discount.
An unusually wet spring has caused the size of a mosquito population in some city to increase by 7 â% each day. If an estimated 18â0,000 mosquitoes are in the city on May 6. Find how many mosquitoes will inhabit the city on May 17 . Use y =18â0,000(1.07 )^ x where x is number of days since May 6 .
Answer:
378873
Step-by-step explanation:
Using the relation :
y = 180000(1.07)^x
x = Number of days since May 6 ;
y = Number of mosquitoes after x days
x = May 17- May 6 = 11 days
Therefore, number of mosquitoes inhabiting the city on May 17 will be :
y = 180000(1.07)^11
y = 180000 * 2.1048519522998348950643
y = 378873.351413970281111574
y = 378873 (nearest whole number).
Is the set of rational expressions closed under division
Answer:
Step-by-step
Closure property is true for division except for zero.
A family of 3 goes to a fair. Tickets cost $5 each, but
each person has a coupon. They pay $7 altogether.
How much money does each person save on buying
their ticket?
5x - 7 = 3
7 = 3(5 + x)
3x + 5 = -7
x + 7 = 3 x 5
Answer: $105
Step-by-step explanation:
Answer:
$2.66
Step-by-step explanation:
Step 1: Multiply the $5 to the family of 3
[tex]5 \times 3 = 15[/tex]
That's what they would have paid if they did not have a coupon. Now they have a coupon and only pay $7.
Step 2: Subtract what they paid from the result
[tex]15 - 7 = 8[/tex]
Now we have found how much they save altogether. To find how much they saved each;
Step 3: Divide the result found in step 2 by the family of 3
[tex]8 \div 3 = 2.66666\dots[/tex]
Each person saves approximately $2.66
HELPPP PLEASE ASAPPP 20 POINTS!
The U.S. produces 9.08 million barrels of crude oil per day. It consumes 19.7 million barrels per day. How many barrels of oil have to be imported each day from other oil-producing countries?
help me pls if you cant and dont help me then. no links or report. pls help me giving brainless.
Answer:
pls give brainless
Step-by-step explanation:
How many barrels of oil does the US use per year?
The U.S. uses about 6.6 billion barrels per year. That is only enough oil to last the U.S. about three and a half years without importing oil from other countries. 84% of the reserves are concentrated in four states.
Write 162 as a product of primes.
Use index notation when giving your answer.
On one day at a local minigolf course, there were 320 customers who paid a total of $2,900. If the cost for a child is $7 per game and the cost for an adult is $10 per game, write a system of equations to model this scenario, where x represents the number of children and y represents the number of adults who played that day.
7x + 10y = 2900
x + y = 320
7x + 10y = 320
x + y = 2900
10x + 7y = 2900
x + y = 320
10x + 7y = 320
x + y = 2900
Brainiest for correct answer
A system of equations to model this scenario is given as follows -
x + y = 320
7x + 10y = 2900
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.The general equation of a straight line is → y = mx + c{m} - slope {c} - intercept along the y - axis.
Given is that on one day at a local minigolf course, there were 320 customers who paid a total of $2,900. The cost for a child is $7 per game and the cost for an adult is $10 per game.
Let {x} represents the number of children and {y} represents the number of adults who played that day. We can write the given system of equations as -
x + y = 320
7x + 10y = 2900
Therefore, a system of equations to model this scenario is
x + y = 320
7x + 10y = 2900
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Set X is the set of all multiples of 6 between 15 and 70.
Which set is equivalent to set X?
A. {6, 12, 18, 24,...}
B. {6, 12, 18, ...,66}
C. {18, 24, 30, 36,...}
D. {18, 24, 30, ..., 66}
E. {18, 24, 30, ..., 70}
Answer:
D
Step-by-step explanation:
we have 2 conditions
1. to be a multiple of 6
2. to be between 15 and 70
A and B are not correct because have numbers les than 15
C is not correct because the numbers keep on going passed 70
E is not correct because 70 is not a multiple of 6
D is correct because has both conditions meet
Pls help. Cindi wants to cover the top and sides of this box with glass tiles that
are 1 cm square. How many tiles will she need?
Answer:
300 square centimeters
Surface area of box:
= 2(lb + bh +hl)
= 2(20×15 + 15×9 + 9×20)
= 2(300 + 95 + 180)
= 2 × 575
= 1,150 cm³
Area of tiles:
= 1 × 4 = 4 cm
No of tiles:
= 1,150/4
= 287.5 = 288
Total 288 tiles will be needed
X+X+X+Y+Y=
im doing algebra and cant understand the above question
Answer:
3x + 2y
Step-by-step explanation:
X+X+X+Y+Y=
you simply count equal letters and add them x+x+x is 3x and y + y = 2y.
x + x + x + y + y =
3x + 2y
not knowing the value of x or y we stop hereWhich of the following points are solutions to the equation 3x - 4y - 8 = 12?
Select all that apply.
(0-5)
(4-2)
(8.2)
(-16-17)
(-1.-8)
(-40,-34)
If 3n+5=23 what is the value of 2n-3
Answer:
3n + 5 = 23,
3n = 18
n = 6
since "n" = 6,
2n - 3
= 2×6 - 3
12 - 3
= 9
please help guys ASAP
Answer:
180
Step-by-step explanation:
You do 24 x 4 + 64 which is = to 176 then rounded is 180