I think the given integral reads
[tex]\displaystyle \int_{-3}^3 \int_0^{9-x^2} \int_{x^2+y^2}^{9-x^2-y^2} \mathrm dz\,\mathrm dy\,\mathrm dx[/tex]
In cylindrical coordinates, we take
x ² + y ² = r ²
x = r cos(θ)
y = r sin(θ)
and leave z alone. The volume element becomes
dV = dx dy dz = r dr dθ dz
Then the integral in cylindrical coordinates is
[tex]\displaystyle \boxed{\int_0^\pi \int_0^{(\sqrt{35\cos^2(\theta)+1}-\sin(\theta))/(2\cos^2(\theta))} \int_{r^2}^{9-r^2} r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta}[/tex]
To arrive at this integral, first look at the "shadow" of the integration region in the x-y plane. It's the set
{(x, y) : -3 ≤ x ≤ 3 and 0 ≤ y ≤ 9 - x ²}
which is the area between a paraboloid and the x-axis in the upper half of the plane. So right away, you know θ will fall in the first two quadrants, so that 0 ≤ θ ≤ π.
Next, r describes the distance from the origin to the parabola y = 9 - x ². In cylindrical coordinates, this equation changes to
r sin(θ) = 9 - (r cos(θ))²
You can solve this explicitly for r as a function of θ :
r sin(θ) = 9 - r ² cos²(θ)
r ² cos²(θ) + r sin(θ) = 9
r ² + r sin(θ)/cos²(θ) = 9/cos²(θ)
(r + sin(θ)/(2 cos²(θ)))² = 9/cos²(θ) + sin²(θ)/(4 cos⁴(θ))
(r + sin(θ)/(2 cos²(θ)))² = (36 cos²(θ) + sin²(θ))/(4 cos⁴(θ))
(r + sin(θ)/(2 cos²(θ)))² = (35 cos²(θ) + 1)/(4 cos⁴(θ))
r + sin(θ)/(2 cos²(θ)) = √[(35 cos²(θ) + 1)/(4 cos⁴(θ))]
r = √[(35 cos²(θ) + 1)/(4 cos⁴(θ))] - sin(θ)/(2 cos²(θ))
Then r ranges from 0 to this upper limit.
Lastly, the limits for z can be converted immediately since there's no underlying dependence on r or θ.
The expression above is a bit complicated, so I wonder if you are missing some square roots in the given integral... Perhaps you meant
[tex]\displaystyle \int_{-3}^3 \int_0^{\sqrt{9-x^2}} \int_{x^2+y^2}^{9-x^2-y^2} \mathrm dz\,\mathrm dy\,\mathrm dx[/tex]
or
[tex]\displaystyle \int_{-3}^3 \int_0^{\sqrt{9-x^2}} \int_{x^2+y^2}^{\sqrt{9-x^2-y^2}} \mathrm dz\,\mathrm dy\,\mathrm dx[/tex]
For either of these, the "shadow" in the x-y plane is a semicircle of radius 3, so the only difference is that the upper limit on r in either integral would be r = 3. The limits for z would essentially stay the same. So you'd have either
[tex]\displaystyle \int_0^\pi \int_0^3 \int_{r^2}^{9-r^2} r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta[/tex]
or
[tex]\displaystyle \int_0^\pi \int_0^3 \int_{r^2}^{\sqrt{9-r^2}} r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta[/tex]
A diameter perpendicular to a chord
that chord
Select one:
a. is parallel to
b. bisects
c. is equal to
A committee on community relations in a college town plans to survey local businesses about the importance of students as customers. From the 10,000 businesses listed in the telephone book, the committee chooses 150 businesses at random. Of these, 72 return the questionnaire mailed by the committee. The nonresponse rate is ______ percent. (Give your answer as a whole number.)
Answer:
The nonresponse rate is 52 percent.
Step-by-step explanation:
150 sampled:
72 returned and 150 - 72 = 78
The nonresponse rate is
Percentage that 78 is out of 150, that is:
78*100%/150 = 52%
The nonresponse rate is 52 percent.
In a certain animal species, the probability that a healthy adult female will have no offspring in a given year is 0.24, while the probabilities of 1, 2, 3, or 4 offspring are respectively 0.25, 0.19, 0.17, and 0.15. Find the expected number of offspring.
Answer:
The expected number of offspring is 2
Step-by-step explanation:
The given parameters can be represented as:
[tex]\begin{array}{cccccc}x & {0} & {1} & {2} & {3} & {4} \ \\ P(x) & {0.24} & {0.25} & {0.19} & {0.17} & {0.15} \ \end{array}[/tex]
Required
The expected number of offspring
This implies that we calculate the expected value of the function.
So, we have:
[tex]E(x) = \sum x * P(x)[/tex]
Substitute known values
[tex]E(x) = 0 * 0.24 + 1 * 0.25 + 2 * 0.19+ 3 * 0.17 + 4 * 0.15[/tex]
Using a calculator, we have:
[tex]E(x) = 1.74[/tex]
[tex]E(x) = 2[/tex] --- approximated
A line passes through the point (-2,4) and has a slope of 7. Write an equation for this line
Answer: y = 7x + 18
Step-by-step explanation:
y = mx + b, (-2,4), m = 7
4 = 7(-2) + b
4 = -14 + b
b = 18
y = 7x + 18
If f(×)=16×-30 and g(×)=14×-6, for which value of x does (f-g)(x)=0
Answer: [tex]x=12[/tex]
Step-by-step explanation:
[tex]f(x)=16x-30\\g(x)=14x-6[/tex] are the equations that you've given us.
Now if we plot these two equations on the graph we notice there's an intersection at (12,162). Therefore meaning that [tex]x=12[/tex].
We can prove that by doing the following calculations to prove that both sides are equal to each other.
The left side of the equal sign:
Step 1: Write the equation down:
[tex]16x-30[/tex]
Step 2: Substitute x for the numerical value we found.
[tex]16(12)-30[/tex]
Step 3: We will multiply [tex]16*20[/tex] first, giving us 192.
[tex]192-30[/tex]
Step 4: Subtract 192 from 30. Which gives us 162.
[tex]162[/tex]
The right side of the equal sign:
Step 1: Write the equation down:
[tex]14x-6[/tex]
Step 2: Substitute x for the numerical value we found.
[tex]14(12)-6[/tex]
Step 3: We will multiply [tex]14*12[/tex] first, giving us 168.
[tex]168-6[/tex]
Step 4: Subtract 168 from 6. Which gives us 162.
[tex]162[/tex]
We know that [tex]x=12[/tex] because when substituting x with 12, we get 162 on both sides. Therefore making this statement true and valid.
[tex]162=162[/tex]
IF A= -35 , B = 10 , C= -5 verify that:-
a x (b+c) = a x b + a x c
Plz tell
Answer:
see below
Step-by-step explanation:
a x (b+c) = a x b + a x c
Let A= -35 , B = 10 , C= -5
-35 * ( 10 -5) = -35 *10 + -35 * -5
-35 *(5) = -350 + 175
-175 = -175
Convert 653 in base 7 to base 10
An advertiser goes to a printer and is charged $36 for 80 copies of one flyer and $46 for 242 copies of another flyer. The printer charges a fixed setup cost plus a charge for every copy of single-page flyers. Find a function that describes the cost of a printing job, if xx is the number of copies made.
Answer:
ytre
Step-by-step explanation:
P is inversely proportional DY. IF P=1.2=when y=100, calculate
a the value of p when y=4
b the value of y when p=3
Answer:
a. P = 30
b. Y = 40
Step-by-step explanation:
Given the following data;
P = 1.2
Y = 100
First of all, we would have to determine the constant of proportionality;
P = k/Y (inverse proportion or relationship)
1.2 = k/100
k = 1.2 * 100
k = 120
a. To find the value of p when y = 4;
P = k/Y
P = 120/4
P = 30
b. To find the value of y when p = 3;
P = k/Y
Y = k/P
Y = 120/3
Y = 40
Air is being pumped into a spherical balloon at a rate of 5 cm^3/min. Determine the rate at which the radius of the balloon is increasing when the diameter of the balloon is 20 cm
0.08 cm/min
Step-by-step explanation:
Given:
[tex]\dfrac{dV}{dt}=5\:\text{cm}^3\text{/min}[/tex]
Find [tex]\frac{dr}{dt}[/tex] when diameter D = 20 cm.
We know that the volume of a sphere is given by
[tex]V = \dfrac{4\pi}{3}r^3[/tex]
Taking the time derivative of V, we get
[tex]\dfrac{dV}{dt} = 4\pi r^2\dfrac{dr}{dt} = 4\pi\left(\dfrac{D}{2}\right)^2\dfrac{dr}{dt} = \pi D^2\dfrac{dr}{dt}[/tex]
Solving for [tex]\frac{dr}{dt}[/tex], we get
[tex]\dfrac{dr}{dt} = \left(\dfrac{1}{\pi D^2}\right)\dfrac{dV}{dt} = \dfrac{1}{\pi(20\:\text{cm}^2)}(5\:\text{cm}^3\text{/min})[/tex]
[tex]\:\:\:\:\:\:\:= 0.08\:\text{cm/min}[/tex]
Surface area of the below shape
Solve all of the equations below and add all of the solutions to those equations to get your answer.
10x4x2=
8x4x2=
10x8=
(10x8)-(7x6)=
7x2x2=
6x2x2=
7x6=
help me please i’ll give brainliest the
Answer:
y=-1/2x+-1
Step-by-step explanation:
try desmos with this equation.
y=mx+b
m=the slope which is -1/2. It goes down 1 it is negative because it is going down, and to the right 2.
b=y-intercept meaning the point which the line crosses the line y .-1
Jacob bought a magazine for $2.80 and three candy bars. Write an expression for how much Jacob paid.
Answer:
total = 2.8 + 3x
x is the price of the candy bars
Yooooo HELPPP
with this question plz
Answer:
Step-by-step explanation:
(x-2)(x+4)=x^2+4x-2x-8=0=> x =2, x=0
Answer:
A
Step-by-step explanation:
There is 3m wide path around a circular cricket ground having the diameter of 137 m. Find the area of the path.
Answer:
1320 m^2
Step-by-step explanation:
area of ground = π r ^2
= (22/7) × (137/2)^2
= 14,747.0714286 m^2
area of ground and path
=( 22/7)(143/2)^2
= 16,067.0714286 m^2
area of path
=16,067.0714286 -14,747.0714286
= 1320 m^2
note :
r = radius = diameter /2
area of a circle = π r^2
diameter of circle created with path and ground = 137 + 2 × width of path
= 137 + 2× 3 = 143 m
A certain standardized test measures students’ knowledge in English and math. The English and math scores for 10 randomly selected students are given in the table.Using technology, what is the correlation coefficient?
0.68
0.83
0.91
0.95
Answer:
The answer is C
.91
ED2021
300-20+100 divided by 4=
Answer:
95
Step-by-step explanation:
300-20=280
280+100=380
380÷4=95
There you go...
Probability that a person is chosen at random
Answer:
152 / 370
Step-by-step explanation:
Total number of people
152+218 = 370
P( own a dog) = people said yes / total
= 152 / 370
Not sure how to do this
a. 1140
b. 1130
c. 1120
d. 115
Answer:
1130
Step-by-step explanation:
1109+7 = 1116
1116+7 = 1123
Adding 7 each time
1123+7 = 1130
find the angle and area of shaded region
Area of shaded region = 1/2(πr²)
= 1/2(22/7×3×3)
= 99/7
= 99/7×2
= 198/7 cm^2
Thats the total area of the shaded region
Must click thanks and mark brainliest
HELP WITH 16 What is the value of X
Answer:
C - 136
(115+157)/2
Step-by-step explanation:
A certain marathon has had a wheelchair division since 1977. An interested fan wondered who is faster: the men's marathon winner or the women's wheelchair marathon winner, on average. A paired t-test was performed on data from a random selection of 15 of the marathons to determine if there was evidence to indicate that the women's winning wheelchair time is faster than the men's winning running time, on average. What must be true about the population of differences in the women's wheelchair winning times and men's winning times at this marathon for conclusions from the paired t-test to be valid? Choose the correct answer below. A. The distribution of sample means of the differences will be approximately normal if there are at least 30 years of data in the sample and/or if the population of differences in winning times for all years is normal. B. Because there were at least 5 years of observations, the distribution of sample means of the differences will be approximately normal by the Central Limit Theorem. C. Because the sample size is large enough, the distribution of differences for all years will be normal. D. Because of the small sample size of differences in winning times between the women's wheelchair winner and the men's running winner, the distribution of sample means of the differences cannot be normal.
Answer:
A. The distribution of sample means of the differences will be approximately normal if there are at least 30 years of data in the sample and/or if the population of differences in winning times for all years is normal.
Step-by-step explanation:
In other to perform a valid paired test, one of the conditions required is that, data for both groups must be approximately normal. To attain normality, the population distribution for the groups must be normal or based on the central limit theorem, the sample size must be large enough, usually n > 30. Hence, once either of the two conditions are met, the paired sample will be valid.
What's an equivalent fraction of 3/4 that has a denominator of 32
Answer:
24/32
Step-by-step explanation:
[tex]\frac{3}{4} = \frac{x}{32}[/tex]
To get from 4 to 32, you multiply by 8
so to get from 3 to x, multiply by 8
The answer for this would be 24/32
The answer to this question please.
Answer:
Part A) y=1,100x + 4,500
Part B) 14,400
Step-by-step explanation:
Part A)
There is a base fee of $4,500, meaning that the line begins at y=4500 (i.e. The y-intercept is [0,4500], so 'b' in y=mx+b is 4,500). There is a $1,100 hourly rate, which is proportional to the value of x, the amount of hours filmed. Therefore, 'm' in y=mx+b is $1,100.
Thus, the final equation looks like:
y= 1,100x + 4,500
Part B)
x=9
y=1,100x+4,500
y=1,100(9)+4,500
y=9,900+4,500
y=14,400
I will give brainliest if you answer properly.
Answer:
See below
Step-by-step explanation:
a)
[tex]2\sin(x) +\sqrt{3} =0 \implies 2\sin(x)=-\sqrt{3} \implies \boxed{\sin(x)=-\dfrac{\sqrt{3}}{2} }[/tex]
[tex]\therefore x=\dfrac{4\pi }{3}[/tex]
But note, as sine does represent the [tex]y[/tex] value, [tex]\dfrac{5\pi }{3}[/tex] is also solution
Therefore,
[tex]x=\dfrac{4\pi }{3} \text{ and } x=\dfrac{5\pi }{3}[/tex]
This is the solution for [tex]x\in[0, 2\pi ][/tex], recall the unit circle.
Note: [tex]\sin(x)=-\dfrac{\sqrt{3}}{2} \implies \sin(x)=\sin \left(\pi +\dfrac{\pi }{3} \right)[/tex]
b)
[tex]\sqrt{3} \tan(x) + 1 =0 \implies \tan(x) = -\dfrac{1}{\sqrt{3} } \implies \boxed{ \tan(x) = -\dfrac{\sqrt{3} }{3} }[/tex]
Once
[tex]\tan(x) = -\dfrac{\sqrt{3} }{3} \implies \sin(x) = -\dfrac{1}{2} \text{ and } \cos(x) = \dfrac{\sqrt{3} }{2}[/tex]
As [tex]\tan(x) = \dfrac{\sin(x)}{\cos(x)}[/tex]
[tex]\therefore x=-\dfrac{\pi }{6}[/tex]
c)
[tex]4\sin^2(x) - 1 = 0 \implies \sin^2(x) = \dfrac{1}{4} \implies \boxed{\sin(x) = \pm \dfrac{\sqrt{1} }{\sqrt{4} } = \pm \dfrac{1}{2}}[/tex]
Therefore,
[tex]\sin(x)=\dfrac{1}{2} \implies x=\dfrac{\pi }{6} \text{ and } x=\dfrac{5\pi }{6}[/tex]
[tex]\sin(x)=-\dfrac{1}{2} \implies x=\dfrac{7\pi }{6} \text{ and } x=\dfrac{11\pi }{6}[/tex]
The solutions are
[tex]x=\dfrac{\pi }{6} \text{ and } x=\dfrac{5\pi }{6} \text{ and }x=\dfrac{7\pi }{6} \text{ and } x=\dfrac{11\pi }{6}[/tex]
Which statement is sufficient to prove that quadrilateral ABCD is a parallelogram?
A) m∠A ≅ m∠C, m∠B ≅ m∠D
B) AB ≅ CD
C) AC ≅ BD
D) BC // AD
Answer:
A) m∠A ≅ m∠C, m∠B ≅ m∠D
Step-by-step explanation:
If both pairs of opposite angles are congruent, then the figure is a parallelogram.
PLEASE HELP
Identify the first five terms of the sequence in which a, = 3n2 - 1.
Step-by-step explanation:
you cannot just put the actual numbers in and calculate ?
and you can't provide the correct problem statement, as it seems.
I assume you mean
an = 3n² - 1
a sequence starts with a1, so, n>=1
a1 = 3×1² - 1 = 3-1 = 2
a2 = 3×2² -1 = 3×4 - 1 = 12 - 1 = 11
a3 = 3×3² - 1 = 3×9 - 1 = 27 - 1 = 26
a4 = 3×4² - 1 = 3×16 - 1 = 48 - 1 = 47
a5 = 3×5² - 1 = 3×25 - 1 = 75 - 1 = 74
there, that is all there is to it. you really needed help with that ?
A store surveyed their customers to find out their ages. The bar graph below shows the number of customers in each age group. What percent of customers surveyed were over 50%? Round your answer to 1 decimal place.
Bar graphs are used to represent data, where the vertical axis represents the frequency and the horizontal axis.
The percentage that is over 50 is 15.6%:
The data on the bar graph can be represented as:
Under 17 [tex]\to[/tex] 25
18 - 24 [tex]\to[/tex] 35
25 - 34 [tex]\to[/tex] 40
35 - 50 [tex]\to[/tex] 35
Over 50 [tex]\to[/tex] 25
So, the total customer surveyed are:
[tex]Total = 25 + 35 + 40 + 35 + 25[/tex]
[tex]Total = 160[/tex]
The percentage over 50 are:
[tex]\%Over\ 50 = \frac{Over\ 50}{Total } * 100\%[/tex]
[tex]\%Over\ 50 = \frac{25}{160} * 100\%[/tex]
[tex]\%Over\ 50 = 0.15625* 100\%[/tex]
[tex]\%Over\ 50 = 15.625\%[/tex]
Approximate
[tex]\%Over\ 50 = 15.6\%[/tex]
Read more at:
https://brainly.com/question/10440833
MY NOTES Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. (Enter your answers as a comma-separated list.) f(x) = 2x2 − 4x + 3, [−1, 3
Answer:
b) [tex]c=1[/tex]
Step-by-step explanation:
From the question, we are told that:
Function
[tex]F(x)=2x^2-4x+9[/tex]
Given
Rolle's theorem states that if a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b) such that f(a) = f(b), then f′(x) = 0 for some x with a ≤ x ≤ b.
Generally, the Function above is a polynomial that can be Differentiated and it is continuous
Where
-F(x) is continuous at (-1,3)
-F(x) Can be differentiated at (-1.3)
-And F(-1)=F(3)
Therefore
F(x) has Satisfied all the Requirements for Rolle's Theorem
Differentiating F(x) we have
[tex]F'(x)=4x-4[/tex]
Equating F(c) we have
[tex]F'(c)=0[/tex]
[tex]4(c)-4=0[/tex]
Therefore
[tex]c=1[/tex]
