The shaded region R in diagram below is enclosed by y-axis, y = x^2 - 1 and y = 3.
Determine the volume of the solid generated when the shaded region R is revolved
about x = -1 by using Disk method.

Answer:

a. -3

Step-by-step explanation:

-2 turns into 6 by multiplying it by -3.

the same from 6 to -18, from -18 to 54, ...

so, an/an+1 = -3

Answer:

B. 9

Step-by-step explanation:

We are given that y varies inversely with x. Recall that inverse variation has the form:

[tex]\displaystyle y=\frac{k}{x}[/tex]

Where k is the constant of variation.

We are given that y = 18 when x = 12. Hence:

[tex]\displaystyle (18)=\frac{k}{(12)}[/tex]

Solve for k. Multiply both sides by 12:

[tex]k=12(18)=216[/tex]

Thus, our equation is:

[tex]\displaystyle y=\frac{216}{x}[/tex]

We want to find x when y = 24. Substitute:

[tex]\displaystyle \frac{24}{1}=\frac{216}{x}[/tex]

Cross-multiply:

[tex]24x=216[/tex]

Divide both sides by 24. Hence:

[tex]x=9[/tex]

Our answer is B.

Answer:

B

Step-by-step explanation:

Given that y varies inversely with x then the equation relating them is

y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation

To find k use the condition y = 18 when x = 12 , then

18 = [tex]\frac{k}{12}[/tex] ( multiply both sides by 12 )

216 = k

y = [tex]\frac{216}{x}[/tex] ← equation of variation

When y = 24 , then

24 = [tex]\frac{216}{x}[/tex] ( multiply both sides by x )

24x = 216 ( divide both sides by 24 )

x = 9

Answer:

The system is inconsistent

Step-by-step explanation:

Given the matrix system solutions in the attachment, we can see that the coefficient of the matrix rank has become zero. This shows that it has no solution.

Answer:

Y' = - 1

Step-by-step explanation:

Y' = - 2x +3

So y' (2,2) =-2*2 +3= - 1

Answer:

A

Step-by-step explanation:

since it's negative so it will get smaller

Answer:

98.93

Step-by-step explanation:

we're looking for

4 ft 9 <x<6 ft 4

Let's convert this into inches

4 ft 9 = 57 in

6 ft 4= 76

so we're looking for

57<x<76

which is equal to

p(76)-p(57)

let's start by p(76)

(76-62.3)/2.3= 5.946521 which on a ztable is equal to 1

p(57)=

(57-62.3)/2.3= -2.3

which is equal to 1-.9893= .0107

Finally,

1-.0107= .9893 = 98.93%

Answer:

[tex]9 + 7i[/tex]

Step-by-step explanation:

[tex]7i^5+9i^8[/tex]

[tex]i^5 = i\\ i^8 = 1[/tex]

Answer:

hgfyjtdjtrxgfyfguktfkgh

Step-by-step explanation:

hgfytrdutrc

Given:

The graph of a line.

To find:

The equation for the given line.

Solution:

From the given graph, it is clear that the line passes through the points (0,-5) and (5,0). So, the equation of the line is:

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

[tex]y-(-5)=\dfrac{0-(-5)}{5-0}(x-0)[/tex]

[tex]y+5=\dfrac{5}{5}(x)[/tex]

[tex]y+5=x[/tex]

Subtract 5 from both sides.

[tex]y+5-5=x-5[/tex]

[tex]y=x-5[/tex]

Therefore, the equation of the given line is [tex]y=x-5[/tex].

Answer:$36 depending on what question is i just assuming how much she has to pay

Step-by-step explanation:

48 divded by 4 is 12. $48-$12 is $36. The $12 is the 1/4 discount.

Answer:

0.9898 = 98.98% probability that there will not be more than one failure during a particular week.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

3 failures every twenty weeks

This means that for 1 week, [tex]\mu = \frac{3}{20} = 0.15[/tex]

Calculate the probability that there will not be more than one failure during a particular week.

Probability of at most one failure, so:

[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]

Then

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-0.15}*0.15^{0}}{(0)!} = 0.8607[/tex]

[tex]P(X = 1) = \frac{e^{-0.15}*0.15^{1}}{(1)!} = 0.1291[/tex]

Then

[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.8607 + 0.1291 = 0.9898[/tex]

0.9898 = 98.98% probability that there will not be more than one failure during a particular week.

Step-by-step explanation:

Answer:

[tex]x<41[/tex]

Step-by-step explanation:

[tex](x)+(x+1)<83[/tex]

simplify both sides

[tex]2x+1<83[/tex]

subtract one from the both sides to isolate the variable

[tex]2x<82[/tex]

divide both sides by 2 to isolate the variable

[tex]x<41[/tex]

Answer:

Area of ellipse=[tex]\pi ab[/tex]

Step-by-step explanation:

We are given that

[tex]x=acos\theta[/tex]

[tex]y=bsin\theta[/tex]

[tex]0\leq\theta\leq 2\pi[/tex]

We have to find the area enclose by it.

[tex]x/a=cos\theta, y/b=sin\theta[/tex]

[tex]sin^2\theta+cos^2\theta=x^2/a^2+y^2/b^2[/tex]

Using the formula

[tex]sin^2x+cos^2x=1[/tex]

[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]

This is the equation of ellipse.

Area of ellipse

=[tex]4\int_{0}^{a}\frac{b}{a}\sqrt{a^2-x^2}dx[/tex]

When x=0,[tex]\theta=\pi/2[/tex]

When x=a, [tex]\theta=0[/tex]

Using the formula

Area of ellipse

=[tex]\frac{4b}{a}\int_{\pi/2}^{0}\sqrt{a^2-a^2cos^2\theta}(-asin\theta)d\theta[/tex]

Area of ellipse=[tex]-4ba\int_{\pi/2}^{0}\sqrt{1-cos^2\theta}(sin\theta)d\theta[/tex]

Area of ellipse=[tex]-4ba\int_{\pi/2}^{0} sin^2\theta d\theta[/tex]

Area of ellipse=[tex]-2ba\int_{\pi/2}^{0}(2sin^2\theta)d\theta[/tex]

Area of ellipse=[tex]-2ba\int_{\pi/2}^{0}(1-cos2\theta)d\theta[/tex]

Using the formula

[tex]1-cos2\theta=2sin^2\theta[/tex]

Area of ellipse=[tex]-2ba[\theta-1/2sin(2\theta)]^{0}_{\pi/2}[/tex]

Area of ellipse[tex]=-2ba(-\pi/2-0)[/tex]

Area of ellipse=[tex]\pi ab[/tex]

Answer: Hello attached below is the well written complete question

answer:

T = 40 + 30e^-0.0288t

Step-by-step explanation:

To( outside temperature ) = 40°F

T  = ?

k( thermal conductivity ) = constant

A( area of heat transfer) = constant

Hence Differential equation for the temperature of the house

T = 40 + 30e^-0.0288t

Attached below is the detailed solution of the problem

Answer with Step-by-step explanation:

We are given that

Side of cube, x=30 cm

Error in measurement of edge,[tex]\delta x=0.5[/tex] cm

(a)

Volume of cube, [tex]V=x^3[/tex]

Using differential

[tex]dV=3x^2dx[/tex]

Substitute the values

[tex]dV=3(30)^2(0.5)[/tex]

[tex]dV=1350 cm^3[/tex]

Hence,  the maximum possible error in computing the volume of the cube

=[tex]1350 cm^3[/tex]

Volume of cube, [tex]V=(30)^3=27000 cm^3[/tex]

Relative error=[tex]\frac{dV}{V}=\frac{1350}{2700}[/tex]

Relative error=0.05

Percentage  error=[tex]0.05\times 100=5[/tex]%

Hence, relative error in computing the volume of the cube=0.05  and

percentage error in computing the volume of the cube=5%

(b)

Surface area of cube,[tex]A=6x^2[/tex]

[tex]dA=12xdx[/tex]

[tex]dA=12(30)(0.5)[/tex]

[tex]dA=180cm^2[/tex]

The maximum possible error in computing the volume of the cube=[tex]180cm^2[/tex]

[tex]A=6(30)^2=5400cm^2[/tex]

Relative error=[tex]\frac{dA}{A}=\frac{180}{5400}[/tex]

Relative error  in computing the volume of the cube=0.033

The percentage error in computing the volume of the cube=[tex]0.033\times 100=3.3[/tex]%

Answer:

A. (-2, -5), (0, -7), (1, -4)

Step-by-step explanation:

The following transformation is applied:

[tex](x,y) \rightarrow (y + 2, -x - 4)[/tex]

To find the range:

We apply the transformation to the points in the domain. Thus:

[tex](1,-4) \rightarrow (-4 + 2, -1 - 4) = (-2, -5)[/tex]

[tex](3,-2) \rightarrow (-2 + 2, -3 - 4) = (0, -7)[/tex]

[tex](0,-1) \rightarrow (-1 + 2, 0 - 4) = (1, -4)[/tex]

Thus the correct answer is given by option a.

Answer:

[tex]x=\frac{1}{2}[/tex]

Step-by-step explanation:

By definition, we have [tex]\log_a b=c\implies c^a=b[/tex].

Therefore, given [tex]\log_e \sqrt{e}=x[/tex], we have:

[tex]e^x=\sqrt{x}[/tex]

Solving, we have:

[tex]x=\boxed{\frac{1}{2}}[/tex]

(Recall that [tex]a^{(\frac{b}{c})}=\sqrt[c]{a^b}[/tex]).

Answer:

1/2

Step-by-step explanation:

Given :-

Answer:

Step-by-step explanation:

P(4,3), Q(4,1), S(-1,3), R(-1,1)

[tex]Distance =\sqrt{(x_{2}-x_{1})^{2}+(y_{2} -y_{1})^{2}}\\\\PQ= \sqrt{(4-4)^{2}+(1-3)^{2}}\\\\=\sqrt{(-2)^{2}}\\\\\=\sqrt{4}\\\\=2 \ units\\\\\\QS=\sqrt{(-1-4)^{2}+(3-1)^{2}}\\\\=\sqrt{(-5)^{2}+(2)^{2}}\\\\=\sqrt{25+4}\\\\=\sqrt{29}\ units\\\\\\SR =\sqrt{(-1-[-1])^{2}+(1-3)^{2}}\\\\=\sqrt{(-1+1)^{2}+(-2)^{2}}\\\\=\sqrt{0+4}\\\\= \sqrt{4}\\\\= 2 \\\\\\PR = \sqrt{(-1-4)^{2}+(1-3)^{2}}\\\\=\sqrt{(-5)^{2}+(-2)^{2}}\\\\=\sqrt{25+4}\\\\=\sqrt{29}\\\\[/tex]

PQRS is a rectangle

Area= length *breadth

       = 2 * √29

       = 2√29 sq.units

Answer:

5 905 272

Step-by-step explanation:

you can refer to this lattice multiplication or u can search you tube for the examples of lattice multiplication

Answer:

I think no. D is the answer

[tex]option(c) \: cylinder[/tex]

Step-by-step explanation:

You can see that in the figure, this is rectangle. Here, ABCD is rotated around the vertical line through A and D. So, you will get Cylinder shape as you rotate it.

Answer:

[tex]\text{Perimeter: }48\:\mathrm{m},\\\text{Area: }84\:\mathrm{m^2}[/tex]

Step-by-step explanation:

The area of a triangle with side lengths [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex] is given by:

[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex], where [tex]s=\frac{a+b+c}{2}[/tex]

Substituting [tex]a=21, b=17, c=10[/tex], we have:

[tex]A=\sqrt{24(24-21)(24-17)(24-10)},\\A=\sqrt{24(3)(7)(14)},\\A=\sqrt{7,084},\\A=\boxed{84\:\mathrm{m^2}}[/tex]

The perimeter of a polygon is given by the sum of its sides. Since the triangle has sides 10, 17, and 21, its perimeter is [tex]10+17+21=\boxed{48\:\mathrm{m}}[/tex].

Answer:

338

Step-by-step explanation:

1×2=2 2+6+10+14+18+22+26+30

3×2=6 +34+36+38+42+46+50=338

5×2=10

7×2=14

9×2=18

11×2=22

13×2=26

15×2=30

17×2=34

19×2=38

21×2=42

23×2=46

25×2=50

The requirement is fulfilled when 10 bananas and 2 apples are kept in the basket.

The equation can be given as

10y + 2x = 80

Here,

y means 7 ounces (weight of banasas)

x means 5 ounces (weight of apples)

Answer:

Hence the value of p is 0.04746.

Step-by-step explanation:

The test statistic is

[tex]Z=(\bar x-\mu)/(s/vn)\\\\=(355-390)/(115/ \sqrt(30))\\\\=-1.667[/tex]

The p-value= P(Z<-1.67) =0.04746. (from standard distribution table)

Therefore p-value =0.04746.

Answer:

distinctly over here I think so