calculate the volume under the elliptic paraboloid z=4x2 7y2 and over the rectangle r=[−4,4]×[−1,1]\

Answers

Answer 1

The volume under the elliptic paraboloid and over the given rectangle is (3584/9) cubic units.

To find the volume under the elliptic paraboloid and over the given rectangle, we need to evaluate the double integral:

[tex]∬R 4x^2 + 7y^2 dA[/tex]

where R is the rectangle [−4,4]×[−1,1].

Using iterated integrals, we first integrate with respect to y and then with respect to x:

[tex]∫ from -4 to 4 [ ∫ from -1 to 1 (4x^2 + 7y^2) dy ] dx[/tex]

Integrating with respect to y, we get:

[tex]∫ from -4 to 4 [ (4x^2)y + (7/2)y^3 ][/tex]evaluated from -1 to 1 dx

Simplifying, we get:

[tex]∫ from -4 to 4 (56x^2/3) dx[/tex]

Integrating with respect to x, we get:

[tex](56/9) [ x^3 ] evaluated from -4 to 4[/tex]

= (56/9) [ 64 - (-64) ]

= (3584/9)

Therefore, the volume under the elliptic paraboloid and over the given rectangle is (3584/9) cubic units.

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Related Questions

The weight of football players is normally distributed with a mean of 180 pounds and a standard deviation of 20 pounds. what is the probability of a player weighing less than 215 pounds?

Answers

Answer:

Given:

mu = 200 lb, the mean sigma = 25 the standard deviation

For the random variable x = 250 lb, the

z-score is z = (x - mu) / sigma = (250 - 200) / 25 = 2

From standard tables for the normal distribution, obtain

P(x < 250) = 0.977

Answer: 0.977

In ΔPQR, find the measure of ∡P. Hypotenuse is 57.6 and the opposite side is 33.8.

Answers

Step-by-step explanation:

pythogoras theorem = Q²=P²+R²

P=P

Q= 57.6

R=33.8 =

(57.8)²=(P)²+(33.8)²

=3,340.84=(P)²+1142.44

=3340.84-1142.44=P²

=2,198.4=P²

[tex] = \sqrt{2198.4} = p \\ = 46.8 = p[/tex]

B=(2x+3)(4x^2-6x+9)-2(4^3-1)

Answers

B = (2x+3)(4x^2-6x+9)-2(4^3-1)
B = 8x^3-99

Hope it helps : )

The points (-3,2) (5,2) and (5,1) are three vertices of a rectangle what is the fourth vortex?

Answers

Answer is ( -3, 1 )
Reason
See attached graph
( 5, 2 ) and ( 5, 1 ) are both in quadrant 1, making up two end points.
The third given is in the 2nd quadrant and must match the other two to make a rectangle. So ( -3, 2 ) will match with ( -3, 1 )

Levi rented a movie for $3.20 and bought a package of candy for $2.55. How much money did Levi spend in total?

$5.25
$5.50
$5.75
$6.00

Answers

The total amount of money Levi spent on renting movie and buying candy is $5.75

Equation

Amount Levi rented movie = $3.20A package of candy = $2.55

Total = Amount Levi rented movie + A package of candy

= $3.20 + $2.55

= $5.75

Therefore, the total money spent by Levi is $5.75

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The local high school is hosting the last soccer game. They charged adults, x, 5 dollars to enter, and 3 dollars for students, y. It cost the school $300 to pay the referees for the game. The school wants to make a profit on the game, and 75 people attended. This is represented by the system:
5x + 3y > 300
x + y = 75

Which of the following points is a solution to the system?
(20, 15)
(25, 70)
(30, 45)
(40, 35)

IVE HEARD (30, 45) AND (40, 35). PLEASE HELP.

Answers

The correct answer is (40, 35) because by plugging in,  40 +35 = 75 and

(40 x 5) + (35 x 3) > 300

How to solve Word Problem ?

Word problem can be solved by interpreting the problem into its best fit equation. The equation may be linear, quadratic or simultaneous equations.

Given that

5x + 3y > 300

x + y = 75

Let us first assume that 5x + 3y = 300. That is,

5x + 3y = 300

x + y = 75

Eliminate y by multiplying equation 2 by 3

5x + 3y = 300

3x + 3y = 225

2x = 75

x = 75/2

x = 37.5

Substitute x in equation 2

37.5 + y = 75

y = 75 - 37.5

y = 37.5

The correct answer is (40, 35) because 40 +35 = 75 and

(40 x 5) + (35 x 3) > 300

Therefore,  the solution to the system is (40, 35)

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Please help me
better be worth my 57 points

Answers

Answer: a

Step-by-step explanation:

The slope is the rate at which a line goes up or down (i.e., how steep it is). It is measured by the slope formula, which is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where (x1, y1) and (x2, y2) are two points on the line.

Below, (x1, y1) are (c, d) and (x2, y2) are (a, b).

When all variables are plugged in, the slope is

[tex]\frac{b-d}{a-c}[/tex]

Solve the system of equations 4x+5y=-1 and -5x-8y=10 by combining the equations.

Answers

The solutions to the given system of equations are x = 6 and y = -5

Simultaneous linear equations

From the question, we are to solve the given system of equations

The given system of equation is

4x+5y=-1

-5x-8y=10

Multiply the first equation by 5 and the second equation by 4

5× (4x+5y=-1)

4× (-5x-8y=10)

20x + 25y = -5

-20x - 32y = 40

------------------------

0x + (-7y) = 35

-7y = 35

y = 35/-7

y = -5

Substitute the value of y into the first equation to find x

4x + 5y = -1

4x + 5(-5) = -1

4x -25 = -1

4x = -1 +25

4x = 24

x = 24/4

x = 6

Hence, the solutions to the given system of equations are x = 6 and y = -5

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The inverse variation equation shows the relationship between wavelength in meters, x, and frequency, y. y = startfraction 3 x 10 superscript 8 baseline over x endfraction what are the wavelengths for x-rays with frequency 3 × 1018?

Answers

The wavelength of X-rays for the given frequency is [tex]$1 \times 10^{-10} \mathrm{~m}$[/tex].

What is the wavelength of light ?

The distance between the two crests or troughs of the light wave is known as the wavelength of light.

The color of light is determined by its wavelength, and the pitch of sound is determined by its wavelength. The visible spectrum of light has wavelengths between around 700 nm (red) to 400 nm (violet). The range of audible sound wavelengths is roughly 17 mm to 17 m.

To calculate the wavelength of light, we use the equation:

[tex]$\lambda=\frac{c}{\nu}$[/tex]

where,

λ = wavelength of the light  

c = speed of light = [tex]$3 \times 10^{8} \mathrm{~m} / \mathrm{s}$[/tex]

ν= frequency of light = [tex]$3 \times 10^{18} s^{-1}$[/tex]

Putting the above value in equation,

[tex]$\lambda=\frac{3 \times 10^{8} \mathrm{~m} / \mathrm{s}}{3 \times 10^{19} \mathrm{~s}-1}=1 \times 10^{-10} \mathrm{~m}$[/tex]

Hence, the wavelength of X-rays for the given frequency is [tex]$1 \times 10^{-10} \mathrm{~m}$[/tex].

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suppose cos(A) = 4/5. use the trig identity sin^2(A)+cos^2(A)=1 to find sin(A) in quadrant IV. round to the ten-thousandth.

a. -0.3954
b. -0.6000
c. 0.6485
d. 0.4500

Answers

In quadrant IV, [tex]\sin(A)[/tex] is negative. So

[tex]\sin^2(A) + \cos^2(A) = 1 \implies \sin(A) = -\sqrt{1-\cos^2(A)} = -\dfrac35 = \boxed{-0.6000}[/tex]

Given the graph of the function, f(x) , what is the value of f (-2)?

Answers

The value of f(-2) is 0

How to evaluate the function?

The graph of the function is added as an attachment

The graph is given as:

y = f(x)

When x =-2. we have

y = f(-2)

From the graph, we have:

x = -2 and y = 0

So, we have

f(-2) = 0

Hence, the value of f(-2) is 0

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what should be added to 3x³-5x²+7x-4 to get 7x³+2x²-3x+9​

Answers

Answer:

Let the number be a.

==: a + (5x³-2x²+3x+7) = (7x³+7x-5)

==: a = (7x³+7x-5) - (5x³-2x²+3x+7)

==: a = 7x³ + 7x - 5 - 5x³+ 2x² - 3x - 7

==: a = 2x³ + 2x² + 4x - 12

i guess this is the process if you don't understand i can explain more

Find the surface area of the composite figure. Round to the nearest tenth if necessary.

Answers

The surface area of the composite figure is equal to 233.6 square centimeters.

How to determine the surface area of a solid

The surface area is the area of all faces of a solid. Since the surface area of the figure is a combination of triangles and quadrilaterals, we must sum all the areas to determine the surface area of the figure. Now we proceed to determine this:

A = 4 · (1/2) · (3 cm) · (2 cm) + 2 · (6 cm) · (3 cm) + 2 · (8 cm) · (6 cm) + 2 · (8 cm) · (2 cm) + 2 · (8 cm) · (3.6 cm)

A = 233.6 cm²

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Express tan D as a fraction in simplest terms. 40 B 24 32 C​

Answers

Answer:

[tex]\sf Tan \ D = \dfrac{4}{3}[/tex]

Step-by-step explanation:

Trigonometry ratios:

       [tex]\sf \boxed{\bf \tan \ D =\dfrac{opposite \ side \ of \ \angle \ D}{adjacent \ side \ of \ \angle D}}[/tex]

                   [tex]\sf =\dfrac{BC}{DC}\\\\ =\dfrac{32}{24}\\\\=\dfrac{4}{3}[/tex]

Which of the measurements of triangleBAC are correct

Answers

Answer:

yes

no

yes

Step-by-step explanation:

sin C = opp/hyp = 9/15 yes

tan B = opp/adj = 12/9 no

tan B = 12/9; B = tan^-1 12/9 = 53.13°

A company makes rubber rafts. 12% of them develop cracks within the first month of operation. 27 new rafts are randomly sampled and tested, by being used for one month, under standardized conditions that mimic typical operating conditions. Calculate the probability that the number of tested rafts that develop cracks is no more than 3. Round your answer to four decimal places.

Answers

The probability that the number of tested rafts that develop cracks is no more than 3 is .00006.

The true proportion, p for the population is given to 0.12.

Thus, the mean, μ, for the sample = np = 27*0.12 = 3.24.

The sample size, n, given to us is 27.

Thus, the standard deviation, s, for the sample can be calculated using the formula, s = √{p(1 - p)}/n.

s = √{0.12(1 - 0.12)}/27 = √0.003911 = 0.0625389.

We are asked to calculate the probability that the number of tested rafts that develop cracks is no more than 3, that is, we need to calculate P(X ≤3).

P(X ≤ 3)

= P(Z ≤ {(3 - 3.24)/0.0625389) {Using the formula z = (x - μ)/s}

= P(Z ≤ -3.8376114706)

= .00006 {From table}.

Thus, the probability that the number of tested rafts that develop cracks is no more than 3 is .00006.

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Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 2 more than 5 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 110

Answers

Mark and Don have 18  and 92 marbles respectively.

What is the solution of the equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.

Let the number of marbles Mark has be x.

According to the question,

Don has (5x+2) marbles.

Total number of marbles=110

Thus, the required equation is:

x+5x+2=110

6x=108

x=108/6

x=18

Mark has 18 marbles.

Don has (5*18+2)=92 marbles.

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In the 30-60-90 triangle below, side s has a length of
length of
30
90°
S
60
OA. 16√3, 5
B. 4√2, 4√2
OC. 4, 4√3
OD. 8.5, 16
OE. 16√3, 16√3
OF. 4, 8√3
and side q has a

Answers

Answer:

4, 4√3

Step-by-step explanation:

In a 30-60-90 triangle:

The leg opposite of the 30-degree angle is 1/2 of the hypotenuse: 8/2 = 4

The longer leg is √3 times the shorter leg: 4*√3 = 4√3

Check work: 4^2+(4√3)^2 = 8^2 --> 16+48 = 64 --> 64 = 64

Nani needs to buy 8 cups of fresh pineapple for a fruit cocktail. the table shows the unit prices of pineapple at different stores. if nani only has $4, from which stores could she purchase her pineapple?

Answers

Nani could purchase her pineapple from stores A, D, and E.

Given Information

It is given that Nani needs to purchase  8 cups of pineapple.

The unit prices of pineapple at each store is as follows,

Store A : 0.49

Store B : 0.51

Store C : 0.55

Store D : 0.48

Store E : 0.45

Amount that Nani has = $4

Reason Behind Purchasing From Either A, D, or E

Since Nani has amount of $4, she can purchase pineapple only from the stores where the total cost of 8 pineapple cups adds up to less than $4. The purchase of 8 pineapple cups at each store would be given as,

Store A : 0.49(8) = $3.92

Store B : 0.51(8) = $4.08

Store C : 0.55(8) = $4.40

Store D : 0.48(8) = $3.84

Store E : 0.45(8) = $3.60

As it can be seen, Nani can purchase from the store A, D, and E as it falls within her budget of $4.

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A polypay sheep produces an average $9.9$ pounds of wool annually. This wool is cleaned, spun into yarn and then packaged into skeins of $175$ yards of yarn each. One pound of wool makes $10.95$ miles of yarn. If farmer Bill has a flock of $200$ polypay sheep, to the nearest thousand skeins, how many skeins of yarn is his flock expected to produce in one year

Answers

Answer:

218,048. skeins

Step-by-step explanation:

Break down the process into proper order.

This question is built to throw you off by not telling you about the information in order.

First, the polypay sheep produces 9.9 pounds of wool.

Then, each pound produces 10.95 miles of yarn.

And finally, the yarn is packaged into skeins that are 175 yards each.

Step 1: Outline the work

Each polypay sheep is 9.9 pounds. And we will use that total weight to find the amount of yarn in miles.
Then we will split up that yarn into equal pieces to make skeins.

BUT, the pieces are measured in yards, so we will have to convert the miles of yarn into an equivalent amount in yards as well. (Unmatched units of measurements don't mix well).

So, our equation will look like this:

(#of sheep) [tex]\times[/tex] (9.9 pounds per sheep) [tex]\times[/tex] (10.95 miles per yarn) [tex]\times[/tex] (1760 yards per mile) [tex]\div[/tex] (175 skeins per yard)

Step 2: Plug and Ch

The number of sheep Bill has is 200.

So, we plug that into the number model we made.

[tex]200\times9.9\times10.95\times1760\div175[/tex]

We end up with:

218,048.914

The decimal indicates that there is a remaining amount of yarn that couldn't be properly packaged into a skein.

Since, that remainder is not a complete skein, we must ignore its existence.

So the number of skeins expected is:

218,048

The number of skeins of yarn is Bill's flock expected to produce in one year is 1819.

What is the unitary method?

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, a polypay sheep produces an average 9.9 pounds of wool annually.

Farmer Bill has a flock of 200 polypay sheeps

So, total weight of wool is 9.9×200

= 1980 pounds

One pound of wool makes 10.95 miles of yarn.

So, the number of yarns = 1980/10.95

= 180.82 miles of yarn

We know that, 1 mile =1760 yards

Then, 180.82 miles

= 318243.2 yards

This wool is cleaned, spun into yarn and then packaged into skeins of 175 yards of yarn each.

Number of skeins = 318243.2/175

= 1819

Therefore, the number of skeins of yarn Bill's flock expected to produce in one year is 1819.

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The slope-intercept form of the equation of a line that passes through point (-3, 8) is y = -2x + 6. What is the
point-slope form of the equation for this line?
O y-3=-%(x + 8)
y+3=-2(x-8)
y+8=-%(x-3)
D y-8 = -2(x + 3)

Answers

Answer: [tex]y-8=-2(x+3)[/tex]

Step-by-step explanation:

See attached image, it's direct formula substitution.

Select the correct answer from each drop-down menu.
Consider the function represented by this graph.

As the value of x increases, the value of f (x)........ increases or decreases

The x-intercept is the point......

Answers

As the value of x increases and the function of f(x) also increases since it is moving in the upward direction. The x-intercept is (-3,0)

What is the function?

A function is a set of input values into a program that produces the desired output. In mathematical terms, we can say a function is a set of x values that maps to a set of y values.

Functions can also be represented on the graph called graphical representation.

From the given graphical information, as the value of x increases, the function of f(x) also increases since it is moving in the upward direction.

The x-intercept is the value where the line cuts the horizontal x-axis when y is zero, therefore the x-intercept is (-3,0)

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Rewrite each equation without absolute value for the given conditions.

[tex]y=/x-5/+/x+5/ if -5\ \textless \ x\ \textless \ 5[/tex]

Answers

Answer: 10

Step-by-step explanation:

If [tex]-5 < x < 5[/tex], then [tex]|x-5|=5-x[/tex] and [tex]|x+5|=x+5[/tex].

So, the expression is equal to 10.

help me please 10 points

Answers

Answer:160ft^3

Step-by-step explanation:

Volume=(bh/2)h

V=(5ftx8ft/2)8ft

V=20x8=160

Volume=160ft^3

HOPE YOU GET IT RIGHT:)!

Use trig to find the height of the hot air balloon. Write an equation and show work. Round answer to the nearest tenth

Answers

Answer:

x = 753.6 ft

Step-by-step explanation:

One leg is x.

The other leg is given.

The trig function that relates the two legs of a right triangle is the tangent.

tan A = opp/adj

tan 37° = x/1000ft

x = 1000 ft × tan 37°

x = 753.6 ft

Answer: 753.6 feet

Step-by-step explanation:

The angle, theta, is 37 degrees. However, we're not given the length of the hypotenuse in this case. So sine would be x by the hypotenuse and cosine would be 1,000 by the hypotenuse. In this case, we can use tangent, which is sine/cosine. In this case, tan 37 = x/1,000.

Hence,

tan 37 = x/1,000

x = tan 37 * 1000

x is approximately 753.6, rounded to the nearest tenth.

The vertex of a parabola is (0,0)and the focus is (1/8, 0) . What is the equation of the parabola?

Answers

The equation of a parabola whose vertex is (0, 0) and focus is (1 / 8, 0) is equal to x = 2 · y².

How to derive the equation of the parabola from the locations of the vertex and focus

Herein we have the case of a parabola whose axis of symmetry is parallel to the x-axis. The standard form of the equation of this parabola is shown below:

(x - h) = [1 / (4 · p)] · (y - k)²     (1)

Where:

(h, k) - Coordinates of the vertex.p - Distance from the vertex to the focus.

The distance from the vertex to the focus is 1 / 8. If we know that the location of the vertex is (0, 0), then the standard form of the equation of the parabola is:

x = 2 · y²     (1)

The equation of a parabola whose vertex is (0, 0) and focus is (1 / 8, 0) is equal to x = 2 · y².

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ok more of a question not like a equation or anything but when do you know when there is a extraneous answer and how do you solve it (please provide an example equation)

Answers

One can know if an equation is extraneous if after plugging it in the original equation, it shows a false meaning or the value is undefined.

What is an extraneous equation?

It should be noted that an extraneous equation means a root of a transformed equation that isn't the root of the original equation due to the fact that it's excluded from the domain of the original equation.

In this case, one can know if an equation is extraneous if after plugging it in the original equation, it shows a false meaning or the value is undefined.

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Explain why the following form linearly dependent sets of vectors. (solve this problem by inspection.)

u1 = (3, -l), u2 = (4, 5), u3 = (-4, 7) in r2

Answers

A set of vectors {v1,v2,...,vk} is linearly independent if the vector equation x1v1 + x2v2 + .......... + xkvk = 0 has only the trivial solution

x1 = x2 = .... = xk =0. Then the set  {v1,v2,...,vk} is linearly dependent otherwise.

So putting in the formula we get

x1u1 + x2u2 + x3u3 = 0

x1u1 + x2u2 = -x3u3

au1 + bu2 = u3               ∵ (-x1/x3 = a & -x2/x3 = b)

On putting in the values

a(3,-1) + b(4,5) = (-4,7)

(3a+4b,-a+5b) = (-4,7)

On comparing we get

3a + 4b = -4 -(1)

-a + 5b = 7  -(2)

on solving these equations we get

b = 17/19 and a= -48/19

which is non trivial.

Thus the following form linearly dependent sets of vectors.

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When figuring out the sign of a fraction as a
whole, you use the rules for dividing negatives.

Answers

Yes that is correct ,

In a right triangle the length of the hypotenuse is a and the measurement of one of the
acute angle is a. Find the measurement of the other acute angle and the lengths of the
legs.

Answers

Answer:

The measure of the acute angle = 90 - a

Leg 1 = a cos(a)

Leg 2 = a sin(a)

Step-by-step explanation:

In a right triangle ,the two acute angles are complementary

We are given that the measure of one of the acute angles is ‘a’

Then

The measure of the other one is ‘90 - a’

Now, we use the law of sine to determine the length of the legs :

Let x and y be respectively the length of the two legs.

[tex]\frac{x}{\sin \left( 90-a\right) } =\frac{a}{\sin \left( 90\right) }[/tex]

[tex]\Longleftrightarrow \frac{x}{\sin \left( 90-a\right) } =a[/tex]

[tex]\Longleftrightarrow x = a \times\sin \left( 90-a\right)[/tex]

[tex]\Longleftrightarrow x = a \times\cos \left( a\right)[/tex]

On the other hand,

[tex]\frac{y}{\sin \left( a\right) } =\frac{a}{\sin \left( 90\right) }=a[/tex]

Then

[tex]y = a \times \sin(a)[/tex]

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