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3 years ago

What is the slope of the line passing through (1, 2) and (3, 8)?

Mathematics

2 answers:

saveliy_v [14]3 years ago

6 0

Answer:

Option C is correct.

Step-by-step explanation:

Points given are

(1,2) and (3,8)

The formula used for slope is:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

x₁ = 1, x₂=3, y₁=2 and y₂=8

$m=\frac{8-2}{3-1}\\m=\frac{6}{2}\\m=3$

So, slope =3

Option C is correct.

kipiarov [429]3 years ago

5 0

Answer:

The slope of the line passing through (1,2) and (3,8) is 3.

Step-by-step explanation:

Slope formula is y2-y1/x2-x1

y2=8

y1=2

x2=3

x1=1

8-2/3-1

8-2=6

3-1=2

6/2=3

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Find the surface area of the solid generated by revolving the region bounded by the graphs of y = x2, y = 0, x = 0, and x = 2 ab

Nikitich [7]

Answer:

See explanation

Step-by-step explanation:

The surface area of the solid generated by revolving the region bounded by the graphs can be calculated using formula

$SA=2\pi \int\limits^a_b f(x)\sqrt{1+f'^2(x)} \, dx$

If $f(x)=x^2,$ then

$f'(x)=2x$

and

$b=0\\ \\a=2$

Therefore,

$SA=2\pi \int\limits^2_0 x^2\sqrt{1+(2x)^2} \, dx=2\pi \int\limits^2_0 x^2\sqrt{1+4x^2} \, dx$

Apply substitution

$x=\dfrac{1}{2}\tan u\\ \\dx=\dfrac{1}{2}\cdot \dfrac{1}{\cos ^2 u}du$

Then

$SA=2\pi \int\limits^2_0 x^2\sqrt{1+4x^2} \, dx=2\pi \int\limits^{\arctan(4)}_0 \dfrac{1}{4}\tan^2u\sqrt{1+\tan^2u} \, \dfrac{1}{2}\dfrac{1}{\cos^2u}du=\\ \\=\dfrac{\pi}{4}\int\limits^{\arctan(4)}_0 \tan^2u\sec^3udu=\dfrac{\pi}{4}\int\limits^{\arctan(4)}_0(\sec^3u+\sec^5u)du$

Now

$\int\limits^{\arctan(4)}_0 \sec^3udu=2\sqrt{17}+\dfrac{1}{2}\ln (4+\sqrt{17})\\ \\ \int\limits^{\arctan(4)}_0 \sec^5udu=\dfrac{1}{8}(-(2\sqrt{17}+\dfrac{1}{2}\ln(4+\sqrt{17})))+17\sqrt{17}+\dfrac{3}{4}(2\sqrt{17}+\dfrac{1}{2}\ln (4+\sqrt{17}))$

Hence,

$SA=\pi \dfrac{-\ln(4+\sqrt{17})+132\sqrt{17}}{32}$

3 0

3 years ago

Explain pls and thanks

murzikaleks [220]

Starting more simply, if we wanted to know how many students like pink in general, that's 68/100. We could do that for each single category and the fractions would add together to equal 1. Now say we wanted to know something about that 68/100 people. That 68 is our new 100%, or another way of looking at it is if we take however many people like pink and don't like black and those that do like black, they will equal 68/68.

The number of people that like pink but don't like black is 41/68 and those that like pink and black are 27/68. 27+41=68 For the question of your problem it is asking about those that do not like pink which you can tell from the table or use from my saying 68/100 like pink is 32. Now you can split that into those that do or don't like black, and the two results will equal 32/32.

7 0

3 years ago

1-5x + 3y 45<br>2x+3y = 24

Norma-Jean [14]

Answer:

The answer is 1-5x+135y

Step-by-step explanation: multiply the numbers 3 and 45 which give you 135

3 0

3 years ago

PLZZZZZZZZZZ HELP ME I REALLY DONT WNA FAIL

anygoal [31]

Answer:

the answer is 1/2 and then 3/4

3 0

3 years ago

ANswer today plz other wise its to late if you answer after 11:59 your to late plz answer before 11:59

Rom4ik [11]

Answer:

210 yd³

Step-by-step explanation:

V=LWH

V=(8 1/3)(4 1/5)(6)

V=(25/3)(21/5)(6)

V=(525/15)(6)

V=3150/15

V=210

Therefore, the volume of the prism is 210 yd³

5 0

3 years ago

Read 2 more answers