solve for X

























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The volume of the solid obtained by rotating the region bounded by the given curves about [tex]y = 1[/tex] is [tex]\frac{11\pi}{30} [/tex] cubic units.

Let [tex]f(x) = 1[/tex], [tex]g(x) = x^{1/2}[/tex] and [tex]h(x) = x^{2}[/tex], both [tex]g(x) [/tex] and [tex]h(x)[/tex] have the following intersection points: [tex](x_{1}, y_{1}) = (0, 0)[/tex] and [tex](x_{2}, y_{2}) = (1,1)[/tex]. This means that the interval of x-coordinates for the solid of revolution is [tex]x \in [0, 1][/tex].

The integral formula for the volume of the solid of revolution ([tex]V[/tex]), in cubic units, is:

[tex]V = \pi \int\limits^{1}_{0} {[h(x)-f(x)]^{2}} \, dx - \pi \int\limits^{1}_{0} {[g(x)-f(x)]^{2}} \, dx [/tex] (1)

After substituting on each function and simplifying terms we get the following integral:

[tex]V = \pi \int\limits^{1}_{0} {(x^{2}-1)^{2}} \, dx - \pi \int\limits^{1}_{0} {(x^{1/2}-1)^{2}} \, dx [/tex]

[tex]V = \pi\left[\int\limits^{1}_{0} {x^{4}} \, dx - 2\int\limits^{1}_{0} {x^{2}} \, dx -\int\limits^{1}_{0} {x} \, dx + 2\int\limits^{1}_{0} {x^{1/2}} \, dx \right][/tex]

And the volume of the solid of revolution is:

[tex]V = \pi \cdot \left(\frac{1}{5}-\frac{2}{3} -\frac{1}{2}+\frac{4}{3} \right)[/tex]

[tex]V = \frac{11\pi}{30} [/tex]

The volume of the solid obtained by rotating the region bounded by the given curves about [tex]y = 1[/tex] is [tex]\frac{11\pi}{30} [/tex] cubic units. [tex]\blacksquare[/tex]

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40/20=2

So an opossum is 2 times as long as a bat

4.5 g 56.25 g Since the only type of measurement mentioned in this question is weight or mass, I'll assume that the percentage concentration is % m/m (mass/mass). For that type of concentration measurement, simply multiple the percentage by the total mass to get the mass of the desired substance. So 150 g * 3% = 150 g * 0.03 = 4.5g For the amount of 8% solution with the same amount of dry substance, there's 2 ways of calculating the mass of solution. First, use the ratio of percentages, multiplied by the mass of the original solution to get the desired amount of new solution: 3/8 * 150 g = 56.35 g Or calculate it from scratch, like 4.5/X = 8/100 450/X = 8 450 = 8X 56.25 = X In both cases, the result is that you desire 56.25 grams of 8% solution.

Answer:

y = -2x-1

Step-by-step explanation:

The formula for a line is [tex]y-y_{1} = m(x-x_{1})[/tex].

Plug in the information given in the problem: y-(-7) = -2(x-3)

So you get y+7 = -2x+6.

The final form you want needs to be equal to y (that means you want y by itself on the left side of the equals), so subtract 7 from both sides.  

You get y = -2x-1

[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{-7})~\hspace{10em} m = -2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-7)}=\stackrel{m}{-2}(x-\stackrel{x_1}{3}) \\\\\\ y+7=-2x+6\implies \blacktriangleright y=-2x-1 \blacktriangleleft[/tex]

Answer:

61

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Answer: the test doesn't explain the order it was taken or dates. So it can be misleading

Step-by-step explanation:

Answer:

4 1/4 is the answer u want

30% × 390 = 117

= 390 - 117

= 507 kw/h

mx + 5 = (x - 5) / m

mx + 5 = x/m - 5/mAnswer:

Step-by-step explanation:

first find the inverse equation

y = mx + 5

y - 5 = mx

(y - 5) / m = x

(x - 5) / m = f⁻ˣ(x)

The original function is a line with slope m and y intercept of 5

The inverse function is a line with a slope 1/m and x intercept of 5

so the common line is where m = 1/m

m = 1/m

m² = 1

m = ± 1

The only line with a common slope between these two options is when

m = -1 and y intercept is 5

Answer:

Step-by-step explanation:

Answer:

B) 2x + 3 = 2x + 4 - 1

Step-by-step explanation:

A) 3x + 4 = 5x - 1

2x = 5

x = 2/5

B) 2x + 3 = 2x + 3

True

C) 5x = 10

x = 2

D) -3x + 1 = -3x - 5

False

Hi there!

We can begin by writing an equation for each company.

Let x = number of hours

Company A:

y = 250 + 50x (hourly rate is $50)

Company B:

y = 150 + 75x (hourly rate is $75)

We can set the two equations equal to each other to find their intersection point:

250 + 50x = 150 + 75x

Solve for x:

250 - 150 = 75x - 50x

100 = 25x

x = 4

Solve for y by plugging x into an equation:

y = 150 + 75(4) = 150 + 300 = 450

Thus, the lines intersect at (4, 450)

4 hours ⇒ $450 dollars

Answer:

3m-8/7m+14

Step-by-step explanation:

Answer: hi , b other one b too

Answer:

19) b

20) b

Step-by-step explanation:

Answer:

5/2

Step-by-step explanation:

c (constant of proportionality) = y/x = 5/2 in this case

Answer:

tag archives and records and counting the days

Answer:

1st number is 6

2nd number is 30

3rd number is 33

Step-by-step explanation:

Let x be the first number.

The second of three numbers is 5 times the first = 5x

The third number is 3 more than the second = 5x + 3

If the second is decreased by twice the third, the result is -21.

Multiply the third number by 2.

2(5x + 3)

= 10x + 6

Subtract the second number to it.

(5x)-(10x + 6) = -21

-5x - 6 = -21

Use APE or Addition Property of Equality

-5x = -21 + 6

-5x = -15

Use DPE or Division Property of Equality to get the value of x

[tex]\frac{-5x}{-5} = \frac{-15}{-5}[/tex]

x = 3

Now put the value of x in the equation

first number(x) = 6

second number(5x) = 5(6) = 30

third number(5x + 3)

5(6) + 3

30 + 3 = 33

Answer:

1. M

2. H

3. A

4. K

5. B

6. C

7. G

8. E

and so on

Step-by-step explanation:

definitions to know:

same side interior/exterior angles

vertical angles

alternate interior/exterior angles

corresponding angles

The numbers less or equal to 300 that are divisible by 3, 4, or both, but not by 9 are 142.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have a 3 - digit number as 300.

Assume that the numbers less or equal to 300 that are divisible by 3, 4, or both, but not by 9 are [x].

Sequence of numbers divisible by 3 -

3, 6, 9, 12, ...., 300

300 = 3 + (n - 1)3

297 = 3n - 3

n(3) = 100

Sequence of numbers divisible by 4 -

4, 8, 12, ..., 300

300 = 4 + (n - 1)4

296 = 4n - 4

n(4) = 75

Sequence representing numbers less than 300, divisible by 9 -

9, 18, 27, ..., 297

297 = 9 + (n - 1)9

n(9) = 33

So, the numbers less or equal to 300 that are divisible by 3, 4, or both, but not by 9 are -

[x] = n(4) + n(3) - n(9)

100 + 75 - 33

175 - 33

142

Therefore, the numbers less or equal to 300 that are divisible by 3, 4, or both, but not by 9 are 142.

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Answer:

404 & 408

Step-by-step explanation:

Answer:

A'(5,1)

B'(6,-3)

C'(2,3)

Step-by-step explanation:

assuming the translation is right 3, just add 3 to each x value

Answer:

x=34 because you simplify it and then take 45 and at it to it

Answer:

8

Step-by-step explanation:

11-3=8

11-3=8 must subtract for anser

The first roles of the image of the triangle are (-13, 2), (-7, 2), and (-7, -6).

Given the coordinates of the vertices (1,4),(1,1), and (-3,1), if the coordinate is dilated by a factor of 2, the resulting coordinates will be gotten by multiplying each coordinate by "2" to have (2, 8),(2,2), and (-6,2).

If it is translated five units up, the resulting coordinate will be gotten by adding 5 to the y-coordinates to have  (2, 13),(2, 7), and (-6,7).

If the resulting coordinate is then rotated 90° counterclockwise about the origin, the final position of the vertices will be at (-13, 2), (-7, 2), and (-7, -6).

Learn more here: https://brainly.com/question/14191421

The stream gradient of a stream that drops 30 feet in elevation over a horizontal distance of 2640 feet is 0.01136363636.  

Stream gradient is the ratio of drop in elevation of a stream per units horizontal distance. Therefore,

stream gradient = vertical change in elevation / horizontal distance

where

vertical change in elevation = 30 feet

horizontal distance = 2640 feet

stream gradient = 30 / 2640

stream gradient  = 0.01136363636

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Answer:

The area of a rectangle is A=l x w.

So, 200=10 x w

Divide both sides by 10.

20 = w

The width of the rectangle is 20 m.

:)

We want to find different ways of selecting and ordering elements. The answers are:

A) C = 395

B) combinations = 479,001,600

C) combinations = 239,500,800

First, we know that Rebecca has 12 photos.

A) She wants to choose 8 of these 12 photos, we want to see in how many ways she can choose these 8 photos.

Remember that for a set of N elements, the number of different combinations of K elements (such that K is smaller than N) is given by:

[tex]C(N, K) = \frac{N!}{(N - K)!*K!}[/tex]

Here we have N = 12 and K = 8, then:

[tex]C(12, 8) = \frac{12!}{(12 - 8)!*8!} = \frac{12!}{4!*8!} = \frac{12*11*10*9}{4*3*2*1} = 495[/tex]

So there are 495 different ways of choosing 8 photos out of the 12.

B) Now we want to see in how many ways she can arrange all 12 photos.

The total number of combinations is just the product between the numbers of options, we got:

[tex]combinations = 12*11*10*9*8*7*6*5*4*3*2*1 = 479,001,600[/tex]

C) Now we must combine the two things we did before, first, we select 10 out of the 12 photos, and then we want to find in how many ways we can arrange these 10 photos.

[tex]C(12, 10) = \frac{12!}{(12 - 10)°*10°} = \frac{12*11}{2} = 66[/tex]

And we multiply this by the total number of arrangements of these 10 photos, that is just given by 10!, so we get:

[tex]c = 66*10! = 66*(10*9*8*7*6*5*4*3*2*1) = 239,500,800[/tex]

If you want to learn more, you can read:

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[tex]n^{th}\textit{ term of a geometric sequence} \\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} a_7=\stackrel{7^{th}\ term}{192}\\ 7=\textit{term position}\\ a_1=\textit{first term}\\ r=\stackrel{\textit{common ratio}}{2} \end{cases} \qquad \qquad a_7=a_1\cdot 2^{7-1} \\\\\\ 192=a_1\cdot 2^6 \implies 192=64a_1\implies \cfrac{192}{64}=a_1\implies \boxed{3=a_1}[/tex]

we have (7 x 10^-6)(7 x 10^-6) = (7 x 10^-6)^2 = 49 x 10^-3 = 0.049

ok done. Thank to me :>

Answer:

The answer is 3 hours

Step-by-step explanation:

Answer is A. 101°

Step-by-step explanation: