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3 years ago

Find two functions defined implicitly by the given relation y^2-64x^2=64

Mathematics

1 answer:

Reil [10]3 years ago

8 0

Answer: The two functions are

f(x) = sqrt(64x^2+64)

g(x) = -sqrt(64x^2+64)

Graphing these together forms a hyperbola

To get these two functions, we need to solve for y

y^2 - 64x^2 = 64

y^2 = 64x^2 + 64

y = sqrt(64x^2 + 64) or y = -sqrt(64x^2 + 64)

The last line is similar to how x^2 = 9 has two solutions (x = plus or minus 3)

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Solve for b. (b-7)m=r

deff fn [24]

(b-7)m=r

Use the distributive property to multiply b-7 by m.

bm-7m=r

Add 7m to both sides.

bm=r+7m

The equation is in standard form.

mb=7m+r

Divide both sides by m.

mb/m = 7m+r/m

Dividing by m undoes the multiplication by m.

b= 7m+r/m

Divide r+7m by m.

b= r/m+7

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2 years ago

( 3 + 2i ) + ( 6 - 8i )

natta225 [31]

9-6i is the answer, combine like terms

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3 years ago

Slope of -8,4 and 3,-4

nata0808 [166]

For this case we have that by definition, the slope of a line is given by:

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

Where:

$(x_ {1}, y_ {1})$ and $(x_ {2}, y_ {2})$ are two points through which the line passes

According to the statement we have:

$(x_ {1}, y_ {1}): (- 8,4)\\(x_ {2}, y_ {2}) :( 3, -4)$

Substituting we have:

$m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {-4-4} {3 - (- 8)} = \frac {-8} {3 + 8} = \frac {-8} {11} = - \frac {8} {11}$

Thus, the slope of the line is:

$m = - \frac {8} {11}$

Answer:

$m = - \frac {8} {11}$

3 0

3 years ago

PLEASE HELP

Ronch [10]

Answer:

1 and 5

Step-by-step explanation:

The squares have a side length of 10 and 1 square side is the radius of the half-circles. Since there are two half-circles, find the circumference for one full circle:

$C=2\pi r$

Insert the radius:

$r=10\\C=2\pi *10$

Simplify pi:

$C=2*3.14*10$

Simplify multiplication:

$C=6.28*10\\C=62.8$

The circumference of the circles is 62.8. Now find the perimeter of the exposed squares with side length 10. There are 4 exposed sides, which equals one square. Find the perimeter:

$P=10+10+10+10\\P=10+10+20\\P=10+30\\P=40$

Add the perimeter of the circle and the square together:

$P=62.8+40=102.8$

Now see which of the options gives you the perimeter:

1. $40+20\pi =102.8$ ****

2. $unavailable$

3. $120+20\pi =182.8$

4. $300+100\pi =614.2$

5. $10+10+10\pi +10+10+10\pi =102.8$ ****

Finito.

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2 years ago

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lianna [129]

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3 years ago