The value of the integral is 343π/3 by changing to polar coordinates. √(49 − x2 − y2) dA where r = (x, y) | x2 y2 ≤ 49, x ≥ 0
What is integration?It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.
We have the integral:
[tex]\int\limits \int\limits_R {\sqrt{49-x^2-y^2}} \, dA[/tex]
Where, r = (x, y) | x2 y2 ≤ 49, x ≥ 0
The polar coordinate will be:
x = rcosθ
y = rsinθ
Where x²+y²= r²
Put the value of x and y in the integral, and the limits will be:
r²≤49 or 0≤r≤7, -π/2≤θ≤π/2 ( since x ≥0)
dA = rdrdθ
[tex]\int\limits \int\limits_R {\sqrt{49-x^2-y^2}} \, dA = \int\limits^{\dfrac{\pi}{2}}_{\dfrac{-\pi}{2}} \int\limits^7_0 {\sqrt{49-r^2]} \, rdrd\theta[/tex]
After solving the double integration, we will get:
[tex]\int\limits \int\limits_R {\sqrt{49-x^2-y^2}} \, dA = \dfrac{343}{3} \pi[/tex]
Thus, the value of the integral is 343π/3 by changing to polar coordinates. √(49 − x2 − y2) dA where r = (x, y) | x2 y2 ≤ 49, x ≥ 0
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What is the surface area of the rectangular prism?
a. 144 m 2
b. 288 m 2
c. 128 m 2
d. 256 m 2
Answer: B. 288m 2
Step-by-step explanation:
A = 2 (wl+hl+hw)
2 · (4 · 16 + 4 · 16 +4 · 4) = 288m 2
A. 225
B. 25
C. 150
D. 50
Step-by-step explanation:
V=1/3hπr².
(h=3cm, r=5²cm
V= 1/3 x 3 x π x 5²
V= 25π
HELPPPPP QUICKLYYY !!! The picture shows a cylinder of height x which has been inscribed in a sphere of radius r. Find the volume of a cylinder in terms of x.
See attached. We can draw a right triangles contained within both shapes.
The triangle has height x (same as the cylinder), base 2r (same as the diameter of the cylinder), and hypotenuse 6 (same as the diameter of the sphere).
Since it's a right triangle, the Pythagorean theorem holds and we have
x² + (2r)² = 6²
which we solve for r to get
x² + 4r² = 36
4r² = 36 - x²
r² = 9 - x²/4
r = √(9 - x²/4)
Then the volume of the cylinder, whose height is x and whose base has radius r, is
π r² x = π (9 - x²/4) x = (36x - x³) π/4
Many large cities have considered or passed proposals that ban the use of plastic grocery bags in stores. A concerned student would like to measure if residents of her hometown would consider a similar ban on plastic bags. Standing in a busy shopping area, the student approaches adults and asks, "Items made of plastics are a dangerous, growing source of pollution to our world’s oceans and threaten many animal species. Given this, would you support a ban on plastic shopping bags in our city stores?” How might the results of this survey be biased in estimating the proportion of all town residents who would support a ban on plastic bags?
The student may overestimate support for a plastic bag ban because only adults in the shopping area were chosen to participate.
The student may overestimate support for a plastic bag ban because the wording of the question may influence adults to support a ban.
The student may underestimate support for a plastic bag ban because the wording of the question may influence adults to not support a ban.
The student may underestimate support for a plastic bag ban because some adults may not want to answer questions about the environment.
Answer: The student may overestimate support for a plastic bag ban because the wording of the question may influence adults to support a ban.
Step-by-step explanation:
jake has an account that is compounded every month at a rate of 3.5%.if he invests $20,000,what will the balance be after 5 years
Libby built a fence that was 56 \text { feet}56 feet56, start text, space, f, e, e, t, end text long over 444 days. She built the same length of fence each day.
How many inches of fence did Libby build each day?
Answer:
168 inches
Step-by-step explanation:
To find the fence made each day by Libby, we will divide 56 by 4.
convert the length of fence into inches.
1 foot = 12 inches.
the volume of a cube with edge lengths of 2/3 units
What is the edge length of a cube with volume 27/64 cubic units?
Pleas helppppppppppppp
Answer:
[tex]a=\sqrt[3]{\frac{27}{64}} = 0.75[/tex]
edge length = 0.75
Equation: [tex]a=\sqrt[3]{V}[/tex]
1. How many triangles are congruent to AABC?
А.
2
В.
3
С.
4
D.
5
Answer:
Answer: 3, 3 of them are translated
Answer:
B. 3 triangles are congruent to ABC
Step-by-step explanation:
2 triangles are congruent if all corresponding side lengths are equal, or using SAS (Side-Angle-Side theorem) to confirm 2 corresponding sides & the included angle is equal those of another triangle.From the picture, triangle ABC is not a right triangle. The length of AB is graphed with a length of 4. From point C to segment AB is a height of 3. The triangle in quadrant I (top right) has both of these dimensions.
Similarly, the triangle on the x-axis (positive side) below it (between Q1 and Q4) is also congruent to ABC.
The triangle fully in quadrant III (bottom left) is congruent to ABC with a height of 3 and base length of 4.
The triangle in the bottom right corner (Q4) has a height of 4, therefore it is not congruent to ABC which has a height of 3.
The triangle on the x-axis (negative left side) is also not congruent to ABC. It may have a height of 3 and base length 4, but the angles are different which means the other side lengths don't correspond to ABC.
[+ I'm not sure if your teacher would consider this a real answer but I figured I'd mention that in proofs tri.ABC is also congruent to tri.ABC.]
Write the equation in standard form using integers. y=3x + 4
To write the equation in standard form
⇒ must know the standard form:
⇒ Ax + By = C
⇒ essentially move all the variables to one side and constant to
the other
Let's solve:
[tex]y = 3x + 4\\-3x+y=4[/tex]
Standard form: [tex]-3x+y=4[/tex]
Answer: [tex]-3x+y=4[/tex]
Hope that helps!
PLS HELP PLS ANSWER AS SOON AS POSSIBLE
Answer:
y>1/3x-3
Step-by-step explanation:
The slope for this equation is 1/3x-3. Because the line is dashed, we know that we're dealing with either < or >. The shading goes upwards, so it's greater than. That means, we would get y>1/3x-3.
Hope this helps!
If an item has a retail price = $475 and a discount of $45, what percentage discount is offered?
Answer:
A 9.47% discount was given
Step-by-step explanation:
The question is asking us to find how much percent of 475 is 45. Therefore we do the following:
[tex] \frac{45}{475} \times \frac{100}{1} = \frac{4500}{475} [/tex]
after dividing we get 9.473 which is approximately 9.47%
To check if what we got is correct we do the opposite and instead find 9.47% of 475.
[tex] \frac{475}{1} \times \frac{9.47}{100} = \frac{4498.25}{100} [/tex]
After dividing we find that is equal to 44.98 which is approximately 45.
I need help please help out dudeeeeeeeeee
Answer: heyaa!!
Your Answer Is 6/25Step-by-step explanation:
Simplify the expression.
Hopefully this helps you <3
- Matthew :)
Nyla compared 790 and 709.her work is shown at the right. Is Nyla comparison correct ? If not, correct her mistake
Answer:
its correct so you don't need to do anything
Step-by-step explanation:
The solution is, result of subtraction = 81.
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,
Nyla compared 790 and 709.
so, we have,
790 - 709
=81
Hence, The solution is, result of subtraction = 81.
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f(x)=4x-1. g(x)=-2|x+3|. what is the y value when f(x)=g(x)
..............................................................
9) How much ice cream can the sugar cone hold if
you only fill the inside? Round your answer to the
nearest cubic millimeter.
60 mm
136 mm
140 mm
Answer:
13188mm^2
Step-by-step explanation:
D=60mm
H=136mm
L=140mm
then v=1/3xd^2x h= 1/3x3.14x60^2x136
SA=tc pl/2
=3.14x60x140= 13188mm^2
hope this helps!
Simplify and she the steps how to solve this
(5t^2 + 4) - (6t^2 - 7t + 1)
Answer:
11t² + 7t + 3
Step-by-step explanation:
⇒ (5t² + 4) - (6t² - 7t + 1)
⇒ 5t² + 4 - 6t² + 7t - 1
⇒ 11t² + 7t + 3
Answer: [tex]-t^2 + 7t + 3\\\\[/tex]
Work Shown:
[tex](5t^2 + 4) - (6t^2 - 7t + 1)\\\\5t^2 + 4 - 6t^2 + 7t - 1\\\\(5t^2 - 6t^2) + 7t + (4-1)\\\\-t^2 + 7t + 3\\\\[/tex]
What is the height of a cone if the radius is 3 and the volume is 40π
WILL GIVE BRAINLIEST Drag the values into the boxes to classify each number as rational or irrational.
Answer:
See below ~
Step-by-step explanation:
5/4 = 1/25 ⇒ Rational√100 = 10 ⇒ Rational7.3 ⇒ Rational0.00247 ⇒ Rational√4/9 = 2/3 = 0.66666... ⇒ Rational√2/24 = 1/2√1/6 ⇒ Irrational0.01.... ⇒ RationalMath in My World
Example 1
Blair is arranging 18 cupcakes on a shelf. Find the
factors of 18. Use arrays to find the factors.
Answer:
445455
Step-by-step explanation:
How many possible outcomes if I choose an odd number between 0 and 10 and a letter of an alphabet?
Answer:
104, with the assumption that "an alphabet" is the English alphabet
Step-by-step explanation:
26*4
A 10 inch long piece of string is approximately 25.4 centimeters long.
What is the length, in centimeters, of a string that is 45 inches long, rounded to the nearest tenth?
If 10 inches is equal to 25.4 centimeters. Then the 45 inches will be equal to 114.3 centimeters.
What are ratio and proportion?A ratio is an ordered set of integers a and b expressed as a/b, with b never equaling 0. A percentage is a mathematical expression in which two things are equal.
A 10 inches long piece of string is approximately 25.4 centimeters long.
If the length of the string is 45 inches. Then the length in cm will be
Let x be the length. Then we have
x/45 = 25.4/10
x = 114.3 cm
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A middle school took all of its 6th grade students on a field trip to see a symphony at a theater that has 3080 seats. The students filled 1078 of the seats in the theater. What percentage of the seats in the theater were filled by the 6th graders on the trip?
Answe
about 30-45 Percent.
Step-by-step explanation:
The square root of 83
Answer:
The answer would be 9.1104335791443.
A star with an initial radius of r=1. 0108 m and a period of 30. 0 days collapses suddenly to a radius of r=1. 0104 m
The initial angular velocity of the star will be [tex]w=2.4\times 10^{-6} \ \frac{rad}{sec}[/tex].
What is angular velocity?Angular velocity refers to how fast an object rotates or revolves relative to another point. It is a rate of change of angle.
Here for the 30 days period the angular velocity will be calculated as:
[tex]W=\dfrac{2\pi}{T}=\dfrac{2\times \pi}{30\times 24\times 3600}=2.4\times 10^{-6} \ \frac{rad}{sec}[/tex]
So the initial angular velocity of the star will be [tex]2.4\times 10^{-6} \frac{rad}{sec}[/tex]
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The smallest angle of rotational symmetry for a regular polygon is 30°. how many sides does the regular polygon have? 9 12 20 30
The regular polygon must have 12 sides so the smallest angle of rotational symmetry is 30°
How many sides the polygon have?We know that the smallest angle of rotational symmetry is 30°, then the exterior angles must measure that.
Remember that the sum of the exterior angles of a regular polygon must be equal to 360°, then we have:
360° = n*30°
Where n is the number of sides
Solving for n we get:
n = 360°/30° = 12
We conclude that the regular polygon has 12 sides.
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Answer: B. 12
Step-by-step explanation: On Edge!!!
A letter is chosen at random from the word CALIFORNIA. Find the probability of all the letters in the word
Answer:
C - 1/10A - 2/10L - 1/10I - 2/10F - 1/10O - 1/10R - 1/10N - 1/10Do not put A and I more than once, we already measured it before.
10 letters in all
Find how many there are per letter
C - 1/10
A - 2/10
L - 1/10
I - 2/10
F - 1/10
O - 1/10
R - 1/10
N - 1/10
A chemist is mixing a 50% salt solution with an 18% salt solution to make 40 L of a new solution that will contain 30% salt. How much of each of the original solutions should the chemist use?
Answer:
See below
Step-by-step explanation:
Sum of ingredients = sum of final solution
.50 x where x = 50 percent amount then 40 - x = 18% amount
.50 x + .18(40 - x) = .30 ( 40 )
.50 x + 7.2 - .18x = 12
.32x = 4.8
x = 15 L of 50% 25 liters of 18%
Does anybody know this? I followed the example and did the formula and it told me it was 11.99 but it was wrong. Find the length of the radius if the area of the sector is 361.6 and the central angle is 288 use 3.15 round your answer to the neatest whole number
Hi Student!
The first step that we need to take to solving this problem (and almost any problem), is to concentrate the important information for the problem that is provided. Looking at the problem we can see that we are trying to determine what the length of the radius is. In order to solve this problem we are provided with the area of a sector of 361.6 meters squared and a central angle of 288 degrees.
Now that we have the important information taken care of, we can move onto the part of actually solving the problem. We must first convert our degrees to radians because the equation that we will be using can only use radians for the angle and not degrees. We can simply convert our angle to radians by multiplying it by π/180.
[tex]288\ degrees\ *\ \frac{\pi }{180\ degrees}[/tex]
[tex]288\ degrees\ *\ \frac{3.14}{180\ degrees}[/tex]
[tex]\frac{288\ degrees\ *\ 3.14}{180\ degrees}[/tex]
[tex]5.024\ radians[/tex]
After completing this step, we have converted our degrees to radians and now we can move onto the step where we plug in our information into an equation and solve for our unknown.
[tex]Sector\ Area = radius^2\ *\ \frac{angle}{2}[/tex]
[tex]361.6\ m^2 = radius^2\ *\ \frac{5.024}{2}[/tex]
[tex]361.6\ m^2 = radius^2\ *\ 2.512[/tex]
[tex]\frac{361.6\ m^2}{2.512} = \frac{radius^2\ *\ 2.512}{2.512}[/tex]
[tex]143.949\ m^2 = radius^2[/tex]
[tex]\sqrt{143.949\ m^2} = \sqrt{radius^2}[/tex]
[tex]12\ m = radius[/tex]
Therefore, after solving our equation for our unknown, we can see that our radius is really close to 12 meters (so we can just round up as the problem stated).
does anyone know how to do bearings
answer as many as you like
I need help with all of these questions you see on the top. there the red squares. please someone smart. this is one of the problems I need to finish this tonight.
Answer:
49°
Step-by-step explanation:
The marked angles are "vertical" angles. They have the same measure.
∠TGF = ∠HGM = 49°
_____
You don't need to know the value of p to answer this question. It is 7.
Answer:
∠TGF = 49°
Step-by-step explanation:
From the diagram, we get that ∠TGF is equal to ∠MGH because they are vertical angles.
Hence,
⇒ ∠TGF = ∠MGH
⇒ ∠TGF = 49°