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3 years ago

What are the two ways you can find the distance between points (X1,Y1) and (x2,y2) in the coordinate

Mathematics

1 answer:

igomit [66]3 years ago

4 0

The first (and most typical) way to find distance of two points is by using the distance formula.

$distance=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }$

One alternative is the Manhattan metric, also called the taxicab metric. This option is much more complicated, and rarely used in high school math. d(x,y)=∑i|xi-yi|

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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

2 years ago

A circle has a radius of 19 cm. Find the radian measure of the central angle that intercepts an arc of length 4 cm.

Alona [7]

Answer:

1134

Step-by-step explanation:

$\pi \: radius \: 2$

=1134.114948

6 0

2 years ago

Write the equation of a line in point slope form that is PARALLEL 5x + 2y = 1 that passes through the point (- 2, - 3) .

aliya0001 [1]

Answer:

y = -5/2x - 13

Step-by-step explanation:

First, we have to find the slope of the original equation

Subtract 5x from both sides

5x + 2y = 1

- 5x - 5x

2y = -5x + 1

Divide both sides by 2

2y/2 = (-5x + 1)/2

y = -5/2x + 1/2

The slope of this equation is -5/2, so -5/2 has to be in our new parallel equation

y = -5/2x + b

Plug in the given x and y

-3 = -5/2(-2) + b

-3 = 10 + b

Subtract 10 from both sides

-3 = 10 + b

- 10 - 10

b = -13

This makes our equation: y = -5/2x - 13

7 0

2 years ago

Name

Sedaia [141]

Answer:

Step-by-step explanation:

19% of 72 = about 14%

42% of 16 = about 7%

47% of 118 = about 55%

67% of 296 = about 198%

7 0

2 years ago

If I think of a number halve it and subtract 2 results is 10.write equations and solve it please

gayaneshka [121]

Answer:

Step-by-step explanation:

let 'x' = number

x/2 - 2 = 10

add 2 to each side to get:

x/2 = 12

cross-multiply to get:

x = 24

6 0

2 years ago

Read 2 more answers