Answers
Answer:
[tex]\int\limits^\pi_0 {\int\limits^{7cos(\theta)}_0 {r} \, dr } \, d\theta = \frac{49 \pi}{4}[/tex]
Top Right (Selected) Sketch
General Formulas and Concepts:
Calculus
Fundamental Theory of Calculus: [tex]\int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]Reverse Power Rule: [tex]\int {x^n} \, dx = \frac{x^{n+1}}{n+1}[/tex]Integration Property: [tex]\int {cf(x)} \, dx = c\int {f(x)} \, dx[/tex]Trig Reduction Formula: [tex]\int\limits {cos^n(x)} \, dx = \frac{n-1}{n} \int {cos^{n-2}(x)} \, dx + \frac{cos^{n-1}(x)sin(x)}{n}[/tex]Multivariable Calculus
Sketching the Region REvaluating Double IntegralsStep-by-step explanation:
Step 1: Define
[tex]\int\limits^\pi_0 {\int\limits^{7cos(\theta)}_0 {r} \, dr } \, d\theta[/tex]
Step 2: Integrate Pt. 1
Evaluate the inner integral.
Define: [tex]\int\limits^{7cos(\theta)}_0 {r} \, dr }[/tex]Integrate [Reverse Power Rule/FTC]: [tex]\int\limits^{7cos(\theta)}_0 {r} \, dr } = \frac{r^{1+1}}{1+1} | \limits^{7cos(\theta)}_0[/tex] Simplify: [tex]\int\limits^{7cos(\theta)}_0 {r} \, dr } = \frac{r^2}{2} | \limits^{7cos(\theta)}_0[/tex]Evaluate [FTC]: [tex]\int\limits^{7cos(\theta)}_0 {r} \, dr } = \frac{(7cos(\theta))^2}{2} - \frac{0^2}{2}[/tex]Simplify: [tex]\int\limits^{7cos(\theta)}_0 {r} \, dr } = \frac{49cos^2(\theta)}{2}[/tex]Step 3: Integrate Pt. 2
Evaluate Double Integral.
[Inner Integral] Back-Substitute: [tex]\int\limits^\pi_0 {\int\limits^{7cos(\theta)}_0 {r} \, dr } \, d\theta = \int\limits^\pi_0 {\frac{49cos^2(\theta)}{2} } \, d\theta[/tex][Integral] Integration Property: [tex]\int\limits^\pi_0 {\int\limits^{7cos(\theta)}_0 {r} \, dr } \, d\theta = \frac{49}{2} \int\limits^\pi_0 {cos^2(\theta) } \, d\theta[/tex][Integral] Trig Reduction Formula: [tex]\int {cos^2(\theta) } \, d\theta = \frac{2-1}{2} \int {cos^{2-2}}(\theta) \, d\theta + \frac{cos^{2-1}(\theta)sin(\theta)}{2}[/tex][TRF Integral] Simplify: [tex]\int {cos^2(\theta) } \, d\theta = \frac{1}{2} \int {1 \, d\theta + \frac{cos(\theta)sin(\theta)}{2}[/tex][TRF Integral] Integrate: [tex]\int {cos^2(\theta) } \, d\theta = \frac{1}{2}(\theta) + \frac{cos(\theta)sin(\theta)}{2}[/tex][TRF Integral]: Simplify: [tex]\int {cos^2(\theta) } \, d\theta = \frac{cos(\theta)sin(\theta)}{2} + \frac{\theta}{2}[/tex][Double Integral] Back-Substitute/FTC: [tex]\int\limits^\pi_0 {\int\limits^{7cos(\theta)}_0 {r} \, dr } \, d\theta = \frac{49}{2} (\frac{cos(\theta)sin(\theta)}{2} + \frac{\theta}{2} ) | \limits^\pi_0[/tex][Double Integral] Evaluate FTC: [tex]\int\limits^\pi_0 {\int\limits^{7cos(\theta)}_0 {r} \, dr } \, d\theta = \frac{49}{2} [(\frac{cos(\pi)sin(\pi)}{2} + \frac{\pi}{2} ) - (\frac{cos(0)sin(0)}{2} + \frac{0}{2} )][/tex][Double Integral] Evaluate/Simplify: [tex]\int\limits^\pi_0 {\int\limits^{7cos(\theta)}_0 {r} \, dr } \, d\theta = \frac{49}{2} [\frac{\pi}{2} - 0][/tex][Double Integral] Evaluate: [tex]\int\limits^\pi_0 {\int\limits^{7cos(\theta)}_0 {r} \, dr } \, d\theta = \frac{49 \pi}{4}[/tex]Sketching out the Region R for this, we use our polar coordinate plane. Our angle Θ is 0 and our radius r is 0.
We look at the limits of integration for the radius r. Our r has to be between 0 and 7cos(Θ). The lowest possible value that can be attained by radius r is 0. The region has to be outside the circle r = 0. The largest possible value that can be attained by radius r is 7cos(Θ). Our region has to lie in this shape.
We now look at the limits of integration for the angle Θ. Our Θ has to be between 0 and π. Our region has to lie in that angle.
The top right graph (the one selected) is the correct sketch of the shaded region R.
Attached image is how we graph the region. Special thanks to ASimpleEngineer:
Related Questions
help me plsssssssssssss!Of the 420 students enrolled in advanced math at college, only 30% are first-year students.
How many are first-year students?
Answers
Answer:
126 students are first-year students.
Step-by-step explanation:
The answer is 126 because 30% of 420 is 126.
P.S Can I have brainliest?
What is 293.61 in expanded form?
Answers
Answer:
293.61 =
200
90
3
0.6
0.01
Step-by-step explanation:
Which statement about the equation y = 5x – 8 is correct?
A. The equation represents a linear function because the equation is in the form y = mx + b.
B. The equation represents a linear function because the equation has two variables, x and y.
C. The equation does not represent a function because some x-values have more than one y-value.
D. The equation does not represent a linear function because the equation is in the form y = mx – b, not y = mx + b.
Answers
Answer:
Option A
Step-by-step explanation:
It is a straight line which is in the form y = mx + b
9514 1404 393
Answer:
A. The equation represents a linear function because the equation is in the form y = mx + b
Step-by-step explanation:
A linear function does not have to be in the form y = mx + b, but if a function is in that form, it is a linear function.
choice A is appropriate
__
A function may have two variables, x and y, and not be a linear function. For example, y = x² is not a linear function. The fact that it has two variables is not what makes it linear.
The National History Museum has collected 125 dinosaurs. Cole has collected 3/5 of this amount. How many dinosaurs has Cole collected?
Answers
Answer:
75
Step-by-step explanation:
125 divided by 5 = 25
25 x 3 = 75
Please help!! Will mark brainilest ☺️☺️☺️
Answers
Answer:
2.25
so first I think
Step-by-step explanation:
sorry if it didn't help
Answer:
x-intercept=(4,0)
y-intercept=(0,3)
Slope=-3/4
Step-by-step explanation:
the last number is the y-intercept. The y-intercept is 3. Starting at that point, you know that 3/4 is the slope. So count up 3 (rise is 3) and count left 4 (run is 4) to find x. X-intercept would meet at (4,0)
I've added a picture to give you a visual.
If you have any further questions, don't be afraid to reach out! Hope this helps!
Need answer plz —————
Answers
What is the square foot of a Room with a length 10 3/4 and a wish of 8 1/2 feet
Answers
Answer: 91 3/8 ft^2
Step-by-step explanation:
i assume is a width of 8 1/2 ft
we have a rectangle and the area is A=L*W
we have 8 1/2 x 10 3/4= 17/2 x 43/4= 731/8= 91 3/8 ft62
Find the reciprocal.
72a
72a
−72a
−2a7
2a7
Answers
Answer:
[tex]Reciprocal = \frac{1}{72a}[/tex]
Step-by-step explanation:
Given
Expression: 72a
Required:
Determine the reciprocal
Represent the expression with n
[tex]n = 72a[/tex]
The reciprocal is the calculated as thus:
[tex]Reciprocal = \frac{1}{n}[/tex]
Substitute for n
[tex]Reciprocal = \frac{1}{72a}[/tex]
The price of a new cell phone is $199. Eduardo’s cell phone carrier is offering a 15% off coupon, and the store is offering a $50 rebate. How much will Eduardo pay for the cell phone?
Answers
Write a ratio that can be expressed in lowest terms as 4:3
Answers
Answer:
12:9
/3 =
4:3
Step-by-step explanation:
Given the figure below, which statement correctly completes the following?
A - consecutive interior angles
B - alternate interior angles
C - alternate exterior angles
D - corresponding angles
Answers
∠GCB and ∠HCB are consecutive interior angles. Option A is correct.
What are parallel lines?Parallel lines are lines in a plane that are always the same distance apart. Parallel lines never intersect. Perpendicular lines are lines that intersect at a right (90 degrees) angle.
given, A figure, in that
∠GCB and ∠HCB are consecutive interior angles
Since, Consecutive interior angles are a pair of angles formed when a line, known as the transversal line, crosses two lines. The angles created on the inside of the two lines and are on the same side of the transversal line are known as the consecutive interior angles or co-interior angles for short.
Facts about consecutive interior or co-interior angles:
These angles lie between two lines. Consecutive interior angles are non-adjacent angles. If a transversal is drawn on two parallel lines, then the sum of co-interior angles formed are always added up to 180 degrees.
Therefore, we can say that ∠GCB and ∠HCB are consecutive interior angles.
Learn more about parallel lines here:
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$1,200 is deposited into an account with 4.5% simple interest. How much would it earn in interest after 3 years?
Answers
Answer:
$162
Step-by-step explanation:
$1200 x .045 = $54 x 3 years = $162
what is the greatest common factor of 29,29, and 58
Answers
A factor of n is a number that when multiplied by another number gives us the number n. The greatest common factor of 29 and 58 is 29.
What is a factor?A factor of n is a number that when multiplied by another number gives us the number n.
The factors 29 and 58 can be written as:
29 = 1 × 29
58 = 1 × 2 × 29
Hence, the greatest common factor of 29 and 58 is 29.
Learn more about Factors:
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write 400.000+60.000+5.000+200+30+4 as a base-ten number
Answers
4060520304;
I don't know if I am write or wrong
1.
6x+2y=- 4
3x+4y=-17
Answers
Answer:
x=1
y=-5
P.S. hope it helped. If you have any questions, I'll be glad to answer them.❤
Please help me ...........
Answers
The circumference of the circle is is 6.18 miles.
Explanation:
Circumference=(Pi)*(diameter)
C=3.14*2
C=6.18 miles
I hope this helps! Please comment if you have any questions :)
Find f(6) if f(x) = x^2 ÷ 3 + x
Answers
Answer:
18
Step-by-step explanation:
6^2 / 3 + 6
36 / 3 + 6
12 + 6 = 18
Answer: 18
Step-by-step explanation:
(6)^2 / 3 + 6
36 / 3 + 6
18
The science club went on a two-day field trip. The first day the members paid $62 for transportation plus $15 per ticket to the planetarium. The second day they paid $95 for transportation plus $12 per ticket to the geology museum. Simplify the expression (15n + 62) + (12n + 95).
Answers
Let S={v1,v2,v3} be a linearly independent set of vectors in
. Determine whether T={2 v1+ v2 - 2 v3, 4v1+ 3v2 ,3 v1+ 2 v2- v3} is linearly independent.
Answers
S = {v₁, v₂, v₃} is linearly independent, which means
c₁v₁ + c₂v₂ + c₃v₃ = 0
if and only if c₁ = c₂ = c₃ = 0.
T = {w₁, w₂, w₃} = {2v₁ + v₂ - 2v₃, 4v₁ + 3v₂, 3v₁ + 2v₂ - v₃}
is linearly independent if the same is true for the vectors w₁, w₂, w₃, i.e.
c₁w₁ + c₂w₂ + c₃w₃ = 0
iff c₁ = c₂ = c₃ = 0.
Expanding this equation, we get
c₁ (2v₁ + v₂ - 2v₃) + c₂ (4v₁ + 3v₂) + c₃ (3v₁ + 2v₂ - v₃) = 0
(2c₁ + 4c₂ + 3c₃) v₁ + (c₁ + 3c₂ + 2c₃) v₂ + (-2c₁ - c₃) v₃ = 0
Put the coefficients of v₁, v₂, v₃ in this expansion into an augmented matrix and solve the linear system:
[tex]\left[\begin{array}{ccc|c}2&4&3&0\\1&3&2&0\\-2&0&-1&0\end{array}\right][/tex]
Row-reduce the matrix:
• Replace row 2 with [row 1 + (-2) row 2]:
[tex]\left[\begin{array}{ccc|c}2&4&3&0\\0&-2&-1&0\\-2&0&-1&0\end{array}\right][/tex]
• Replace row 3 with [row 1 + row 3]:
[tex]\left[\begin{array}{ccc|c}2&4&3&0\\0&-2&-1&0\\0&4&2&0\end{array}\right][/tex]
Right away, we see that row 3 is a scalar multiple of row 2, since row 3 = -2 (row 2), so T is not linearly independent.
Continuing with the row reduction, we'd end up with
[tex]\left[\begin{array}{ccc|c}2&0&1&0\\0&2&1&0\\0&0&0&0\end{array}\right][/tex]
so if we choose, for instance, c₃ = 1, so that c₁ = c₂ = -1/2, we get
-1/2 (2v₁ + v₂ - 2v₃) - 1/2 (4v₁ + 3v₂) + (3v₁ + 2v₂ - v₃)
= (-v₁ - 1/2 v₂ + v₃) + (-2v₁ - 3/2v₂) + (3v₁ + 2v₂ - v₃)
= (-1 - 2 + 3) v₁ + (-1/2 - 3/2 + 2) v₂ + (1 - 1) v₃) = 0
The graph of a quadratic relationship has a y-Intercept of 16, and a vertex at the point (4,0). Which function does the graph represent?
Answer choices in picture.
Answers
Answer: A
f(x)=(x-4)^(2)
Step-by-step explanation:
A cell phone carrier charges a fixed monthly fee plus a constant rate for each minute used. Part 1. In January, the total cost for 300 minutes was $ 68 while in February, the total cost for 275 minutes was $ 66.5 . The constant charge for each minute used is:
Answers
Answer:
The constant charge for each minute used is $50
Step-by-step explanation:
In order to solve this problem we will need to set two variables up. In this case:
F = constant Fee
R = rate per minute used
So the cost for the month of January is calculated like this:
F+300R=68
and the cost for February is calculated like this:
F+275R=66.5
So no we have a system of equations we can solve simultaneously. This can be solved by using different methods, elimination, substitution, graphically or by using matrices. I will solve this by substitution.
So let's solve the first equation for R:
[tex]R=\frac{68-F}{300}[/tex]
and let's substitute this first equation into the second equation:
[tex]F+275(\frac{68-F}{300})=66.5[/tex]
and now we can solve this for F:
[tex]F+11(\frac{68-F}{12})=66.5[/tex]
We can multiply both sides by 12 so we get:
12F+11(68-F)=798
12F+748-11F=798
F= $50
A rectangular box with a square base and no top is being constructed to hold a volume of 120 cm3. The material for the base of the container costs $18/cm2 and the material for the sides of the container costs $3/cm2. Find the dimensions of the cheapest possible box
Answers
Answer:
Base=3.42cm
Height = 10.26 cm
For a total cost of $631.59
Step-by-step explanation:
In order to solve this problem we can start by drawing what the box will look like. (See attached picture).
So, the problem mentions that the box will have a volume of [tex]120cm^{3}[/tex]. Since the box has a squared base, we can calculate its volume by using the following formula:
[tex]V=b^{2}h[/tex]
we can turn this into an equation by substituting the corresponding volume:
[tex]b^{2}h=120[/tex]
now, the problem tells us that the base of the box will cost [tex]$18/cm^{2}[/tex] so first, we need to calculate the area of the base of the box. Its area can be calculated by using the following formula:
[tex]A_{base}=b^{2}[/tex]
so the cost of the base is calculated with the following equation:
[tex]C_{base}=18b^{2}[/tex]
we can find the cost of the sides of the box by following a similar procedure:
[tex] A_{side}=bh[/tex]
since there are 4 sides to the box, then we can calculate the total area of the sides by multiplying the formula by 4.
[tex]A_{sides}=4bh[/tex]
the problem tells us that the cost of the sides of the container is: [tex]$3/cm^{2}[/tex] so the cost of the sides will be:
[tex]C_{sides}=3(4)bh[/tex]
[tex]C_{sides}=12bh[/tex]
So the total cost of the box is found by adding the two costs we just found:
[tex]C_{total}=C_{base}+C_{sides}[/tex]
[tex]C_{total}=18b^{2}+12bh[/tex]
so we can take the volume equation to find an equation we can substitute for h on the cost equation:
[tex]h=\frac{120}{b^{2}}[/tex]
when substituting we get:
[tex]C_{total}=18b^{2}+12b(\frac{120}{b^{2}})[/tex]
Which simplifies to:
[tex]C_{total}=18b^{2}+\frac{1440}{b}[/tex]
or:
[tex]C_{total}=18b^{2}+1440b^{-1}[/tex]
In order to minimize the costs we will now take the derivaative of this function and set it to be equal to zero:
[tex]C'=36b-1440b^{-2}[/tex]
[tex]36b-1440b^{-2}=0[/tex]
and now we solve for b:
[tex]36b=\frac{1440}{b^{2}}[/tex]
[tex]36b^{3}=1440[/tex]
[tex]b^{3}=\frac{1440}{36}[/tex]
[tex]b^{3}=40[/tex]
[tex]b=\sqrt[3]{40}[/tex]
b=3.42 cm
so now we can use this value to find the height:
[tex]h=\frac{120}{3.42}[/tex]
h=10.26 cm
the total cost is found by using the cost equation:
[tex]C_{total}=18b^{2}+1440b^{-1}[/tex]
[tex]C_{total}=18(3.42)^{2}+1440(3.42)^{-1}[/tex]
[tex]C_{total}=$631.59[/tex]
Is 5.3 - 5.3 negative, positive, or zero? *
Answers
Answer:
0 (zero)
Step-by-step explanation:
5.3 - 5.3 = 0
5 - 5 = 0 0.3 - 0.3 = 0
5.3 - 0.3 = 5 5 - 5 = 0
Factor the following. Check using FOIL then
solve for x:
x^2 + 3x + 2 = 0
Answers
Answer:
x = -2 and -1
Step-by-step explanation:
x^2 + 3x + 2 = 0
Factorizing the given equation:
x^2 + 3x + 2 = 0
x^2 + 2x + x+ 2 = 0
x(x+2)+1(x+2) = 0
(x+2) (x+1)= 0
x+2 = 0 and x+1 = 0
x = -2 and -1
Tell whether the order pair is a solution of the equation, y=6x;(0,3) (yes or no) please explain this i don't get it I'll give brainliest
Answers
Answer:
Assuming I didn't misunderstand your question, the answer is no.
Step-by-step explanation:
The given equation is y=6x. The ordered pair is (0, 3). 0, the first of the two numbers, represents the x coordinate. Therefore, you can replace the x in the equation with 0.
3, the second number of the ordered pair, represents the y coordinate. Therefore, you can replace the y in the equation with 3.
You should end up with 3=6(0)
Simplified, the equation is 3=0, which is false.
Casey builds the gate shown to the right, with two solid triangular panels. Each support post runs 10 cm above and below the gate. Are the solid panels congruent? Explain
Answers
Answer:
Congruent
Step-by-step explanation:
There are two triangular panels ΔABC and ΔDBE used in the gate.
Since, ∠ABC ≅ ∠DBE [Given]
∠ACB ≅ ∠DBE [Given]
AB ≅ DE [Given]
Therefore, by AAS postulate of congruence, both the triangles will be congruent.
ΔABC ≅ ΔDBE
Hence, we can say that the solid panels used in the gate are congruent.
The two solid triangular panels are congruent by the AAS Congruence Theorem.
What is the AAS Congruence Theorem?
When two angles and a non-included side of a triangle are congruent to two angles and a non-included side of another, the triangles are congruent by the AAS Congruence Theorem.
In the image given, we have the following:
Two angles in one triangle that are congruent to two angles in the other (30 and 90 degrees).One non-included side length in one that is congruent to another in the other triangle.Therefore, the two solid triangular panels are congruent by the AAS Congruence Theorem.
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Which of the following arguments proves that the statement is false if a decimal is non-terminating then it is irrational 0.25 is non-terminating but is not irrational 1.125 is non-terminating but is not irrational 2.42513654 is non-terminating but is not irrational square root of 7 is non-terminating but is not irrational
Answers
Answer:
we did it,yes we made it
Step-by-step explanation:
Answer:
the correct answer to the question you asked is B.
Step-by-step explanation:
I dont need the work i just the need the answer fast
Answers
Answer:
60
Step-by-step explanation:
you have to add 30 plus 30
the prime number which is also even is
a) 0
b) -2
c) 2
d) 6
Answers
Answer:
c) 2
Step-by-step explanation:
a prime number is a number which is only completely divisible by 1 and itself
Answer:
the answer is 2
good luck bro
Step-by-step explanation:
C) 2
Use the cosine ratio or the inverse cosine to solve forx. Round your answer to the nearest tenth.
Answers
Answer:
The value of x = 175.4 mm
Step-by-step explanation:
The given triangle is a right-angled triangle.
Given
Ф = 70
To determine
hypotenuse = x
We know that the trigonometric cosine ratio can be represented as
cos Ф = adjacent / hypotenuse
here
adjacent = 60 mmФ = 70hypotenuse = xsubstituting the values
cos Ф = adjacent / hypotenuse
cos 70 = 60 / x
x = 60 / cos 70
x = 175.4 mm
Therefore, the value of x = 175.4 mm
