I need help with this badly.

Answer:

?

Step-by-step explanation:

Answer:

3 feet

Step-by-step explanation:

Let x represent the length of the shortest board.

Since the other is two times as long, its length can be represented by 2x.

Create an equation to represent the situation, and solve for x:

x + 2x = 9

3x = 9

x = 3

So, the shortest board is 3 feet long

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]

Answer:

5/y^3

Step-by-step explanation:

which expression is equivalent to 5y^-3

for example a^-1 = 1/a

5y^-3 = 5/y^3

Answer:

Using 3.14   for pi  A = 113.0  ft^2

Using the pi button A = 113.1 ft^2

Step-by-step explanation:

The area of a circle is given by

A = pi r^2

A = pi ( 6)^2

A = 36 pi

Using 3.14 for an approximation for pi

A = 36(3.14) = 113.04

To 1 decimal

113.0

Using the pi button

A = 113.0973355

A = 113.1

Correct options are -10 and 10

-7 + (-10² - 19)³/⁴ = 20

-7 + (100 - 19)^3/4 = 20

-7 + (81)^3/4 = 20

-7 + 27 = 20

20 = 20

RHS = LHS

-7 + (10² - 19)^3/4 = 20

-7 + (100 - 19)^3/4 = 20

-7 + (81)^3/4 = 20

-7 + 27 = 20

20 = 20

RHS = LHS

Rest options are incorrect

Answered by Gauthmath must click thanks and mark brainliest

Answer:

B and C, so 10 and -10

Step-by-step explanation:

Answer:

B. 18 sq in.

Step-by-step explanation:

Surface area of the triangular pyramid excluding the base = area of the three triangular faces = 3(½ × base × height)

Where,

base = 3 inches

height = ED = 4 inches

Plug in the known values into the equation

Surface area of the triangular pyramid excluding the base = 3(½ × 3 × 4)

= 3(3 × 2)

= 3(6)

= 18 sq in.

Answer:

Paired t test

H0 : μd = 0

H1 : μd > 0

Critical value = 3.499

Test statistic = 2.230

Reject H0 if test statistic > Critical value

Kindly check explanation.

Step-by-step explanation:

Given the data :

110 90 120 98 100 100 90 110

124 100 102 120 110 110 123 120

The hypothesis :

H0 : μd = 0

H1 : μd > 0

Tcritical value, df = n - 1 = 8 - 1 = 7

Tcritical(0.01, 7) = 3.499

The difference, d = (-14,-10,18,-22,-10,-10,-33,-10)

The test statistic :

Xdbar / Sd/√n

The mean difference, Xdbar = Σx / n = - 11.375

The standard deviation of difference, Sd = 14.431

The test statistic :

-11.375 / (14.431/√8) ;

-11.375 / 5.102

= 2.230

Decison :

Reject H0 if test statistic > Critical value

Since ; 2.230 <3.499 ;

We fail to reject the null

Answer:

No, they are not.

Step-by-step explanation:

If you distributed 12(x - 4y), you would get 12x - 48y. If you distributed 3(3x-y), you would get 9x- 3y. 12x - 48y and 9x - 3y are not equivalent. Hope this helped!

Answer:

y=-2/3x+6

Step-by-step explanation:

Graph it

Answer:

y= -2/3 x + 6

Step-by-step explanation:

1. In the graph, you can see the points (0,6) and (6,2)

2. Since you have all the available options, you can input both points into all equations.

3. In this case, the correct answer is y= -2/3 x + 6

Answer:

the domain is all real numbers except  x=3

Step-by-step explanation:

The domain is the values that x can take

X can be all real number except when the denominators equal zero

x-3 ≠ 0

x≠3

the domain is all real numbers except 3

Solve for  x  by simplifying both sides of the equation, then isolating the variable.

x  ≈  0.13893498

Answer:

25x + 100 = 11300

25x = 11200

448 = x

Step-by-step explanation:

the certain number is 448

Answer: [tex]y=-\frac{2}{5}x+12[/tex]

y = mx + b

m = slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{18-8}{-15-10}=\frac{10}{-25}=\frac{2(5)}{-5(5)}=-\frac{2}{5}[/tex]

The y-intercept(b) can be found by substituting a point into the function.

[tex]y = -\frac{2}{5}x + b \\\\8=-\frac{2}{5}(10) + b\\\\8=-4+b\\\\b=8+4=12[/tex]

Therefore, the function is:

[tex]y=-\frac{2}{5}x+12[/tex]

Answer: 2

Step-by-step explanation:

We know by different of squares, (x-y)(x+y)=74. Since we need to find the smallest possible answer for x+y, we let x+y=2, where both x and y = 1.

Answer:

Step-by-step explanation:

Answer:

D NO IS THE WRITE ANSWER .

Answer:

D)

Step-by-step explanation:

Answer:

Mr. Abernathy purchased 10 of $1.50 wrenches, 10 of $2.50 wrenches, 5 of $4 wrenches and 6 of $3 wrenches.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Number of attendees the first day = x.

Solve the following equation for x:

Answer:

9

Step-by-step explanation:

First multiple of 8 in that range is 8(2)=16.

The last multiple of 8 in that range is 8(10)=80.

So we just need to find how many numbers there are between 2 and 10. inclusive.

10-2+1=9

It's also not that long to write out and count.

1-2

2-3

3-4

4-5

5-6

6-7

7-8

8-9

9-10

9 numbers there are

Multiply those 9 numbers by i you will have all multiples of 8 btw 15 and 85.

8(2)=16

8(3)=24

8(4)=32

8(5)=40

8(6)=48

8(7)=56

8(8)=64

8(9)=72

8(10)=80

Answer:

true

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

A

[tex]\frac{12}{2\pi }[/tex]  ≈ 1.91 < 2

B

8 - π 8 - 3.14 = 4.86 < 5

C

10π ≈ 31.42 > 30 ← True

D

π + 4 = 3.14 + 4 = 7.14 > 7

Option C is a true inequality

If you're familiar with surface integrals, start by parameterizing the surface by the vector-valued function,

r(u, v) = 3 cos(u) sin(v) i + 3 sin(u) sin(v) j + 3 cos(v) k

with 0 ≤ u ≤ 2π and 0 ≤ v ≤ arccos(1/√8).

Then the area of the surface (I denote it by S) is

[tex]\displaystyle\iint_S\mathrm dA = \int_0^{2\pi}\int_0^{\arccos\left(1/\sqrt8\right)}\left\|\dfrac{\partial\mathbf r}{\partial u}\times\frac{\partial\mathbf r}{\partial v}\right\|\,\mathrm dv\,\mathrm du \\\\ = \int_0^{2\pi}\int_0^{\arccos\left(1/\sqrt8\right)}9\sin(v)\,\mathrm dv\,\mathrm du \\\\ =18\pi \int_0^{\arccos\left(1/\sqrt8\right)}\sin(v)\,\mathrm dv = \boxed{\frac{9(4-\sqrt2)\pi}2}[/tex]

Answer:

11/20

Step-by-step explanation:

Answer:

-12

Step-by-step explanation:

that is b

PMA = 37

CMT =  101 - 54 =47

Total = 37 + 47 = 84

Answer: A. 84

9514 1404 393

Answer:

  20

Step-by-step explanation:

A whole can be divided into two pieces that are each 1/2 of the whole.

 (10 wholes) × (2 pieces per whole) = 20 pieces

Answer:

12

Step-by-step explanation:

120 divided by 100 =1.2 x 10

Answer:

− 8 a ^7

Step-by-step explanation:

See picture for steps :)

9514 1404 393

Answer:

  roots are between -5 and -4, and between -1 and -2.

Step-by-step explanation:

The graph shows the roots are approximately ...

  -4.2 — between -5 and -4

  -1.8 — between -2 and -1

Answer:

a. In first study, the treatment is not imposed on the subjects, whereas in the second study the treatment is imposed on subjects.

Step-by-step explanation:

In the first study, observation are made on 300 adults who eat 3 servings of vegetables a day on average. The second study has further intensified the research which imposed treatment on the subjects. The random samples of adults are observed in both studies.