1.
A. SSS
B.T SAS
C. ASA
D. AAS
E. HL
F.. Not

===========================================================

Explanation:

Check out figure 1 in the attached images below. In this figure, I've plotted the function y = 6/(2x-3) on a 2D grid system. The function curve is in blue. Then I've plotted (2,0) and (3,0) on the x axis. Point A is somewhere between those endpoints. Point A is also on the x axis. Directly above A is point B such that B is on the blue function curve.

The distance from A to B is found by subtracting the y values of each point.

The y coordinate of A is y = 0. The y coordinate of B is y = 6/(2x-3)

Therefore, the distance from A to B is 6/(2x-3) units. This will form the radius of each cylindrical slice as figure 2 shows. Note the color coding to help see how the 2D view corresponds to the 3D view. The xy plane has been laid flat on the floor. So we're viewing the function curve at a downward angle now. Each of those gray cylinders combine to form an approximate 3D volume. The more cylinders we have, and the finer the cuts, the more accurate the total volume.

So it comes down to finding the volume of each cylindrical slice and adding up the volumes. This is effectively what integral calculus is all about.

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

Since the radius of each cylinder is y = 6/(2x-3), this means r = 6/(2x-3) is plugged into the formula

V = pi*r^2*h

which is the volume of a cylinder formula

The height of each cylinder is delta x, which we'll use dx for short. So this is where the dx comes from in integrals.

This is what the integral will look like

[tex]\displaystyle V = \int_{2}^{3} \pi*\left(\frac{6}{2x-3}\right)^2dx[/tex]

which turns into

[tex]\displaystyle V = 36\pi\int_{2}^{3}\frac{1}{(2x-3)^2}dx[/tex]

after a bit of algebra. We're able to factor the 36pi out because it's a constant

From here we use u-substitution. Let u = 2x-3

This leads to du/dx = 2 which can be solved to dx = du/2

Since u = 2x-3, the lower endpoint x = 2 leads to

u = 2x-3 = 2*2-3 = 1

and x = 3 leads to

u = 2x-3 = 2*3-3 = 3

So the interval 2 < x < 3 turns into 1 < u < 3

After using u-sub, making the proper replacements, and integrating, we get

[tex]\displaystyle V = 36\pi\int_{2}^{3}\frac{1}{(2x-3)^2}dx\\\\\\\displaystyle V = 36\pi\int_{1}^{3}\frac{1}{u^2}\frac{du}{2}\\\\\\\displaystyle V = 36\pi*\frac{1}{2}\int_{1}^{3}\frac{1}{u^2}du\\\\\\\displaystyle V = 18\pi\int_{1}^{3}u^{-2}du\\\\\\\displaystyle V = 18\pi\left[-u^{-1}+C\right]_{1}^{3}\\\\\\\displaystyle V = 18\pi\left[-\frac{1}{u}+C\right]_{1}^{3}\\\\\\[/tex]

Let's evaluate that to get the following

[tex]\displaystyle V = 18\pi\left[-\frac{1}{u}+C\right]_{1}^{3}\\\\\\\displaystyle V = 18\pi\left[\left(-\frac{1}{3}+C\right)-\left(-\frac{1}{1}+C\right)\right]\\\\\\\displaystyle V = 18\pi\left(-\frac{1}{3}+1\right)\\\\\\\displaystyle V = 18\pi\left(\frac{2}{3}\right)\\\\\\\displaystyle V = 12\pi\\\\\\[/tex]

So the 3D volume formed by rotating that region (under the curve from x = 2 to x = 3) is exactly 12pi cubic units

Answer:

3x-8y=32

Step-by-step explanation:

Answer: 9

Step-by-step explanation:

Answer: well it's correct-

Step-by-step explanation: it shows that e equals to 6-x, x would be 3 so then the problem would still be correct (3=|3|) and |3| just equals, well, 3.

Answer:

the answer is 0.3%

Step-by-step explanation:

12 divided by 40 is 0.3

Answer:

30%

Step-by-step explanation:

Write a proportion.

12 / 40 = x / 100

Cross multiply.

40x = 1200

Solve for x.

x = 30

She ate 30% of the chips.

Answer:

rage we are not doing ur homework

Step-by-step explanation:

14236.53

Step-by-step explanation:

I lookedd it up I'm not smart. ;)

Try using the pythagorean theorem i think?

Answer:

The Base is Greater than the height

Step-by-step explanation:

So the answer has to be greater than eight.

Answer: 224

Step-by-step explanation:

Answer: It is point B

Step-by-step explanation:

Answer: point b

Step-by-step explanation:

Answer:

565

Step-by-step explanation:

77

Answer:

The expression for the area of the given triangle is 5x^4+4x^3units

Step-by-step explanation:

Answer:

1.5

Step-by-step explanation:

6 * 1.5 = 9

Answer:

1.3

Step-by-step explanation:

[tex]\sqrt[6]{9}[/tex]  = 9 divided by 6, 6 goes into 9, 1 time. Remainder of 3, 1.3 is the answer.

Answer:

What two consecutive odd integers have a sum of 88? x + x + 2 = 88 • 2x + 2 = 88 • 2x = 86 • x = 43, x + 2 = 45 • 43 + 45 = 88 • Ans: 43, 45 • They equal 88 and are both odd.

Answer:

C

Step-by-step explanation:

Answer :need the options you choose frome

Step-by-step explanation:

Answer:

30km/hr

Step-by-step explanation:

18km/hr +12km/hr

The man rides 86.4 km distance.

Speed tells us how slow or fast an object moves. It describes the distance travelled divided by the time taken to cover the distance.

Speed is directly Proportional to Distance and inversely proportional to Time.

Speed = Distance/Time

Given,

Speed of man way to the village = 18km/hour

Speed of man when returns from the village = 12km/hour

Time for double journey = 6 hour

Let going time is x and returning time is y

x + y = 6   -------(a)

⇒ x = 6 - y

Distance for going = distance for returning

18x = 12y

Putting value of x in terms of y

18(6 - y) = 12y

108 - 18y = 12y

30y = 108

y = 108/30

y = 3.6 hours

Putting value of y in equation (a)

x + 3.6 = 6

x = 6 - 3.6

x = 2.4

Returning time = 3.6 hours

Returning distance = returning time × returning speed = 3.6 × 12

Returning distance = 43.2 km

Going distance = Returning distance = 43.2

Total ride distance = 43.2 + 43.2 = 86.4 km

Hence, 86.4 km is the distance of ride by the man.

Learn more about speed here:

https://brainly.com/question/28224010

#SPJ2

Answer:

B) 35 divided by 7 = 5

Step-by-step explanation:

You have 35 blocks, you are devideding them in groups of 7, how many groups do you have?

Answer:

Its d i took the class

Step-by-step explanation:

Answer:500

Step-by-step explanation:500 +7++U+U++UU+

Answer:

1/2

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

since her test average for the first 8 tests is 80, the sum of all the scores for the first 8 tests is 640. Since her 9th test is 71, we do 640+71=711. To find the average of all 9 tests, we do 711/9 = 79

D

Answer:

5 letters

Step-by-step explanation:

Let x = the number of letters engraved.

For the first store, the cost can be written as (18.50 + 0.15x).

For the second store, the cost can be written as (18 + 0.25x).

For the cost and value of x to be the same, let them equal eachother and evaluate x:

18.5 + 0.15x = 18 + 0.25

0.1x = 0.5

∴x=5

Answer:

7/2

Step-by-step explanation:

Answer:

101.76

Step-by-step explanation:

Answer:

(12.9 - 3.1) i'm in middle school so if i can do it you can

Step-by-step explanation:

Answer:

[tex]\log _b\left(\sqrt{\frac{57}{74}}\right)[/tex] is equivalent to  [tex]\frac{1}{2}\left(\log \:_b\left(57\right)-\log \:_b\left(74\right)\right)[/tex].

Hence, option 'c' is true.

Step-by-step explanation:

Given the expression

[tex]\log _b\left(\sqrt{\frac{57}{74}}\right)[/tex]

Rewrite as

[tex]=\log _b\left(\left(\frac{57}{74}\right)^{\frac{1}{2}}\right)[/tex]

[tex]\mathrm{Apply\:log\:rule\:}\log _a\left(x^b\right)=b\cdot \log _a\left(x\right),\:\quad \mathrm{\:assuming\:}x\:\ge \:0[/tex]

[tex]=\frac{1}{2}\log _b\left(\frac{57}{74}\right)[/tex]

[tex]\mathrm{Apply\:log\:rule}:\quad \log _c\left(\frac{a}{b}\right)=\log _c\left(a\right)-\log _c\left(b\right)[/tex]

[tex]=\frac{1}{2}\left(\log _b\left(57\right)-\log _b\left(74\right)\right)[/tex]     ∵ [tex]\log _b\left(\frac{57}{74}\right)=\log _b\left(57\right)-\log _b\left(74\right)[/tex]

Therefore,

[tex]\log _b\left(\sqrt{\frac{57}{74}}\right)[/tex] is equivalent to  [tex]\frac{1}{2}\left(\log \:_b\left(57\right)-\log \:_b\left(74\right)\right)[/tex].

Hence, option 'c' is true.

Answer:

The longest side length b is approximately 13.172 cm

Step-by-step explanation:

The given parameters are;

The area of the triangle = 22.4 cm²

The given angles of the triangle = ∠97°

The given side of the triangle = 3.7 cm

The formula for the area of a triangle, A = 1/2 × a × b × sin(C)

Where;

a, and b are the side legs forming the angle C

Therefore,  we have;

A = 22.4 = 1/2 × 3.7 × a × sin(97°)

a =  22.4/(1/2 × 3.7 × sin(97°)) ≈ 12.199

a ≈ 12.199 cm

Therefore, by cosine rule, we have;

b² = a² + c² - 2 × a × c × Cos(B)

Substituting the values, gives;

b² = 12.199² + 3.7² - 2 × 12.199 × 3.7 × Cos(97°)

b² ≈ 173.507

∴ b ≈ √173.507 ≈ 13.172

b ≈ 13.172 cm

Answer:

I think that it is y= -2x +9

Step-by-step explanation:

I am sure about the slope but the y-intercept (9) might be wrong.