Answer:
The result of the integral is [tex]\frac{\pi}{4}(\cos{4}-\cos{1})[/tex]
Step-by-step explanation:
Polar coordinates:
In polar coordinates, we have that:
[tex]r^2 = x^2 + y^2[/tex]
[tex]\int \int_{R} dA = \int \int_{R} r dr d\theta[/tex]
In which r is related to the radius values, while [tex]\theta[/tex] is related to the angles in the trigonometric circle.
In this question:
R is the region in the first quadrant
In the first quadrant in the trigonometric circles, the angles go from 0 to [tex]\frac{\pi}{2}[/tex], which means that this are the outer limits of integration.
Between the circles with center the origin and radii 1 and 2
This means that the inner limits of integration are between 1 and 2.
The integral will be given by:
[tex]\int \int_{R} \sin{x^2+y^{2}} dA = \int_{0}^{\frac{\pi}{2}} \int_{1}^{2} \sin{r^2} r dr d\theta[/tex]
Inner integral:
[tex]\int_{1}^{2} \sin{(r^2)} r dr[/tex]
By substituion,
[tex]u = r^2[/tex]
[tex]du = 2r dr[/tex]
[tex]dr = \frac{du}{2r}[/tex]
So
[tex]\int_{1}^{2} \sin{(r^2)} r dr = \int_{1}^{2} \sin{u} r \frac{du}{2r}[/tex] = \frac{1}{2} \int_{1}^{2} \sin{u} du[/tex]
Integral of sine is minus cosine. So
[tex]\frac{1}{2}(\cos{u})|_{1}^{2}[/tex]
Before replacing, we substitute back u.
[tex]\frac{1}{2}(\cos{r^2})|_{1}^{2} = \frac{1}{2}(\cos{4}-\cos{1})[/tex]
Outer integral:
[tex]\int_{0}^{\frac{\pi}{2}} \frac{1}{2}(\cos{4}-\cos{1}) d\theta[/tex]
[tex]\frac{\theta}{2}(\cos{4}-\cos{1})_{0}^{\frac{\pi}{2}}[/tex]
[tex]\frac{\pi}{4}(\cos{4}-\cos{1})[/tex]
The result of the integral is [tex]\frac{\pi}{4}(\cos{4}-\cos{1})[/tex]
1) f(x) = x 2+ 3x - 18 2) g(x) = x 2+ 2x - 120 3) h(x) = x 2+ 7x - 17 4) k(x) = x 2+ 9x + 20.25 5) s(x) = 4x 2– 5x - 21 6) t(x) = 16x 2+ 9x + 20 7) f(x) = -2x 2+ 10x - 5 8) r(x) = -3x 2- 5x + 2
Which ordered pair is in the solution set for y>-3/4x+6
Answer:
where are the choices?
Step-by-step explanation:
I'll invent one...(4, 3)
Answer:
B
Step-by-step explanation:
graph it and see which points match the graph.
Ten people will equally share three pizzas. How much will each person receive?
3 because 1 person out of the 10 will receive 3/10 of the pizza.
Classify each number as an integer or a not an integer.
-2.5
Integers
3
8.1
-5
Answer:
3
Step-by-step explanation:
an integer is a number without any decimals or fractions like 7 or 3.
An integer does not include decimals or fractions.
Integer: -5 and 3
Not an integer: -2.5 and 8.1
Please help me find the correct answers
Answer:
1) 63cm²
2)28.27cm²
(dont put the cm² in your answer though since its already there)
Step-by-step explanation:
Surface area of the cardboard part formula :
Base × Height
you have the radius going half way so add another 3cm to make it 6cm so you have the full length
6 x 10.5= 63cm²
Plastic part of the can :
[tex]\pi \: r^{2} [/tex]
3cm is your radius so.
[tex]\pi \times 3 ^{2} = 28.27433388[/tex]
but its asking you to round to the nearest hundredth so
28.27cm²
Write the equation for the line.
Find the number of square tiles required to tile a floor of dimensions 10m and 9m if the
side of the tile is 75cm. *
(1 Point)
140
150
0 160
Answer:
160 tiles
Step-by-step explanation:
1000cm×900cm=900000cm²
75cm×75cm=5625cm²
900000cm²÷5625cm²=160 tiles
WHY IS IT SO HARD FOR PPL TO HELP ONE LITTLE GIRL THAT IS ONLY 11 ALL SHE ASK IS PPL NICE PPL TO HELP HER SHE NEEDS HELP ITS NOT THAT HARD JUST HELP HER JEZZ
pls solve this for me i need help bad
Answer:
1 1/4 In
BTW the image is clear now so I can actually see it
Find the value of x. Round the nearest tenth
Answer:
x ≈ 30.7
Step-by-step explanation:
Reference angle = 61°
Opposite side length = x
Adjacent side length = 17
Applying the trigonometric function TOA, we have:
Tan 61 = opp/adj
Tan 61 = x/17
17 × Tan 61 = x
x ≈ 30.7
Enter the equations of the asymptotes for the function f(x).
f(x)=−2x+4−6
Vertical asymptote:
Horizontal asymptote:
Answer:
Vertical Asymptote: -4
Horizontal Asymptote: -6
Step-by-step explanation:
Using it's concepts, it is found that:
There is a vertical asymptote at x = 4.There is a horizontal asymptote at y = -6.What are the asymptotes of a function f(x)?The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity.In this problem, the function is given by:
[tex]f(x) = -\frac{2}{x + 4} - 6[/tex]
Hence:
[tex]x + 4 = 0 \rightarrow x = 4[/tex]
There is a vertical asymptote at x = 4.
As for the horizontal:
[tex]y = \lim_{x \rightarrow 0} -\frac{2}{x + 4} - 6 = -\frac{2}{\infty + 4} - 6 = -0 - 6 = -6[/tex]
There is a horizontal asymptote at y = -6.
More can be learned about asymptotes at https://brainly.com/question/16948935
Distributive Property. Show work below.
1/5(5r+10) - 3(r-2)
Answer:
The answer is -2r + 8.
Step-by-step explanation:
1) Simplify 1/5(5r + 10) to 5r + 10/ 5.
[tex] \frac{5r + 10}{5} - 3(r - 2)[/tex]
2) Factor out the common term 5.
[tex] \frac{5(r + 2)}{5} - 3(r - 2)[/tex]
3) Cancle 5.
[tex]r + 2 - 3(r - 2)[/tex]
4) Expand by distributing terms.
[tex]r + 2 - (3r - 6)[/tex]
5) Remove parentheses.
[tex]r + 2 - 3r + 6[/tex]
6) Collect like terms.
[tex](r - 3r) + (2 + 6)[/tex]
7) Simplify.
[tex] - 2r + 8[/tex]
Thus, the answer for this equation is -2r + 8.
Please help me with this
Answer: It would be the second answer that says SSS.
Step-by-step explanation: Side MK and MN are congruen. Side JN and JK are also congruen. Since both triangles share the line MJ, it’s congruent based on the reflexive property.
The length of a rectangle is 7 inches and the width is (x + 2) inches. Write an expression in simplest form that represents the area of a rectangle.
Answer:
7(x+2)
Step-by-step explanation:
7x +14 is that eventually equals out to
Linear expression - The area of rectangle is (7x + 14) square inches.
What do you mean by the linear expression?An algebraic expression known as a linear expression has terms that are either constants or variables raised to the first power. Alternatively stated, none of the exponents can be greater than 1. Both positive and negative values can be used as coefficients. The exponent is important. Polynomial with the variable raised to the first power, also known as the linear expression
Using, Area of a rectangle = Length × width
Length = 7 inches
Width = (x + 2) inches
Area of a rectangle = Length X Width
= 7 × (x + 2)
= (7x + 14) square inches
Hence, Area of a rectangle = (7x + 14) square inches
Learn more about the linear expression form from the link.
https://brainly.com/question/2030026
#SPJ2
kirans mother gets a restaurant bill for $25. He has a coupon for 15% of the as the discount is applied she adds 20% as tip. What is the total after the discount and tip explain how or show resoning
Tom has 28 milk chocolates and Emily has 24 dark chocolates. They have to divide these chocolates into small packets that each have the same
number of dark chocolates and the same number of milk chocolates. They also want to use all of the chocolates,
The maximum number of packets they can make is
To make the maximum number of packets, each packet should have
milk chocolates and
dark chocolates
Answer: The answer is 4
Step-by-step explanation: In this problem, all you have to do is find the GCF and that is the max amount
Answer:
The correct answer is 4 :)
Step-by-step explanation:
Find the volume of the beach ball and the volume of the toy ball. How many times greater is the volume of the beach ball than the volume of the toy ball?
A.THE VOLUME OF THE BALL IS 904 CUBIC INCHES. b. THE VOLUME OF THE BEACH BALL IS 678 CUBIC INCHES. c.the volume of the beach ball is 452 cubic inches
Answers:
Volume of beach ball = 904 cubic inchesVolume of toy ball = 113 cubic inchesThe beach ball is 8 times greater compared to the toy ball===============================================
Work Shown:
Beach ball
V = volume of sphere
V = (4/3)*pi*r^3
V = (4/3)*3.14*(6)^3 .... the beach ball has diameter 12, so radius is 6
V = 904.32
V = 904 cubic inches is the approximate volume of the beach ball
------------------------
Toy ball
V = volume of sphere
V = (4/3)*pi*r^3
V = (4/3)*3.14*(3)^3 .... the toy ball has diameter 6, so radius is 3
V = 113.04
V = 113 cubic inches is the approximate volume of the toy ball
--------------------------
Divide the two volumes to find that 904/113 = 8
This means that the beach ball is 8 times greater in volume compared to the toy ball
We can say
[tex]\text{Beach ball volume} = 8*\left(\text{toy ball volume}\right)[/tex]
The beach ball's volume is 7238.23and if we round that would be 7238 and the volume for the toy ball is 904.78 and if we round that it would be 905.So, it's around 7 times greater. The difference after they are rounded is 6,333.
Hope this helps.
The half-life of a radioactive kind of barium is 3 minutes. How much will be left after 6
minutes, if you start with 80 grams of it?
Answer:
20 Grams will be left after 6 minutes.
Step-by-step explanation:
In ΔPQR, the measure of ∠R=90°, the measure of ∠P=40°, and QR = 5.1 feet. Find the length of RP to the nearest tenth of a foot.
Answer:
The answer is 6.1 feet
Step-by-step explanation:
Answer:6.1
Step-by-step explanation:
Free brainliest
ᵀʰᵉ ᵗʰʳᵉᵉ ˢᶦᵈᵉ ˡᵉⁿᵍᵗʰˢ ᵒᶠ ᶠᵒᵘʳ ᵗʳᶦᵃⁿᵍˡᵉˢ ᵃʳᵉ ᵍᶦᵛᵉⁿ. ᵂʰᶦᶜʰ ᵗʳᶦᵃⁿᵍˡᵉ ᶦˢ ᵃ ʳᶦᵍʰᵗ ᵗʳᶦᵃⁿᵍˡᵉˀ
ᵀʳᶦᵃⁿᵍˡᵉ ¹: √¹³, ⁶, ⁷
ᵀʳᶦᵃⁿᵍˡᵉ ²: ⁷, ⁸, ¹³
ᵀʳᶦᵃⁿᵍˡᵉ ³: ¹⁰, ¹¹, ¹²
ᵀʳᶦᵃⁿᵍˡᵉ ⁴: √¹⁰, ⁹, ⁸
A baseball team offers a promotion. Normally it’s $12 for bleacher seats, but every specially marked soda can takes $0.50 off the price.
Make a table with the following information:
Cans: 0, 2, 4, 6
Cost:
Equation:
Answer:
$12,$11,$10,$9
Step-by-step explanation:
As the starting price is $12, the first piece of information they give you is the number of cans + the discount each one gives, meaning that the table should have two titles being cost and cans. The number of cans should be at the top with the price being put below for example.
cans: 0 2 4 6
cost: 12 11 10 9
that is the table; the equation to figure this out would be
if you say that 1 can is = to "x"
then the equation becomes much easier to write down and you can simply write it down for each price
cost = 12
cost = 12 - 2x = 11
cost = 12 - 4x = 10
cost = 12 - 6x = 9
making x worth 0.5
Answer: $12,$11,$10,$9
Step-by-step explanation:
As the starting price is $12, the first piece of information they give you is the number of cans + the discount each one gives, meaning that the table should have two titles being cost and cans. The number of cans should be at the top with the price being put below for example. cans: 0 2 4 6 cost: 12 11 10 9 that is the table; the equation to figure this out would be if you say that 1 can is = to "x" then the equation becomes much easier to write down and you can simply write it down for each price cost = 12 cost = 12 - 2x = 11 cost = 12 - 4x = 10 cost = 12 - 6x = 9 making x worth 0.5
Four times a number, minus 8, is equal to three times the number plus 4
Answer:
4n-8=3n+4
Step-by-step explanation:
4n-8=3n+4
+8 +8
4n=3n+12
-3n -3n
n=12
Step-by-step explanation:
correct equation is
(4x - 8 ) =(3x + 4)
4x - 3x = 8 + 4
x = 12
hope it helps
PLZ ANY HELPPP I WILL MARK YOU BRILLLLLLL
Answer:
27
Step-by-step explanation:
Answer:
27
Step-by-step explanation:
-5a -b
-5(-6) -3
30 -3 = 27
A very, very hungry guy goes to a fast food place and orders 2 chicken sandwiches
and 4 tacos, at a total cost of $6.60. Three days later, he's ready to eat again. This
time, he buys 5 chicken sandwiches and 2 tacos, at a total cost of $9.30. Write and
solve a system of linear equations. Identify the cost of one chicken sandwich, and the
price of one taco.
Answer:
Step-by-step explanation:
Huhuj
How does the graph of the function g(x) = 5x + 1 differ from the graph of f(x) = 5*?
A.
It is translated right 1 unit
O
B. It is translated left 1 unit
O
C. It is translated up 1 unit.
D. It is translated down 1 unit.
Answer:
C. It is translated up 1 unit.
Step-by-step explanation:
Translations of a function f(x)
To translate a function f(x) a units to the right, we have f(x-a)
To translate a function f(x) a units to the left, we have f(x+a)
To translate a function f(x) a units up, we have f(x) + a
To translate a function f(x) a units down, we have f(x) - a
In this question:
g(x) = 5x + 1
f(x) = 5x
This means that the function g(x) is 1 added to the function f(x), that is, it is translated up 1 units, and the correct answer is given by option c.
Find the product of 2/3 and 9/10
4 points
Answer:(2/3) + (9/10) = 47/30
= 1 17/30
Step-by-step explanation:
Answer:
Step-by-step explanation:
2/3 x 9/10
=(2x9)/ (3x10)
=18/30
The simplest form of 18/30 is 35.
How I got this answer: First you need to write out your equation, Then you need to multiply like so, Take the first number of your first equation and multiply it by the first number in the second equation then do that for your second like this (2x9) and take (3x10) mulitply both and you get 18 for the first then 30 for the second, if you need that in simplest form. then it will be 35. Hope this helps Have a wonderful day
please help me find the values!!! I need to submit this soon
Answer:
b = 2
c = 2√2
Step-by-step explanation:
when an exponential expression is raised to another exponent the exponent is______
Answer:
Step-by-step explanation:
When raising a power to a power in an exponential expression, you find the new power by multiplying the two powers together. For example, in the following expression, x to the power of 3 is being raised to the power of 6, and so you would multiply 3 and 6 to find the new power.
Use the conversion that 1 ounce is approximately 28.35 grams to calculate the unit price per ounce for 283.5 grams at $5.48.
a.
$0.06
b.
$0.55
c.
$5.48
d.
$54.80
Answer: B
Step-by-step explanation:
10 ounces in 283.5
5.48/10=0.548
reduce to 0.55
Answer:
Use the conversion that 1 ounce is approximately 28.35 grams to calculate the unit price per ounce for 283.5 grams at $5.48.
a.
$0.06
b. <<<<<<<-------CORRECT
$0.55
c.
$5.48
d.
$54.80
Step-by-step explanation:
eDGE 2021
need help!! what is the ewuation of the like shown?
Answer:
An equation is y = 2x + 4.
Step-by-step explanation:
ANOTHER equation is y - 2 = 2(x + 1)
If 1/3 of a factory is female and we want to sample workers at this factory, then approximately 1/3 of the sample should be female. True or False?