Determine the x and y intercepts <br><br> y = -x^2 + 6x

283838383838382828 + 83838383888282ab

natta225 [31]

2.8392222e+17

Step-by-step explanation:

283838383838382828 + 83838383888282=2.8392222e+17

5 0

2 years ago

Let L be a tangent line to the hyperbola x y = 2 at x = 9 . Find the area of the triangle bounded by L and the coordinate axes.

mafiozo [28]

Answer:

$A = 4$

Step-by-step explanation:

The equation of the slope of the tangent line L is obtained by deriving the equation of the hyperbola:

$y = \frac{2}{x}$

$y'=-2\cdot x^{-2}$

The numerical value of the slope is:

$y' = -2 \cdot (9)^{-2}\\y' = -\frac{2}{81}$

The component of the y-axis is:

$y = \frac{2}{9}$

Now, the tangent line has the following mathematical model:

$y = m \cdot x + b$

The value of the intercept is found by isolating it within the equation and replacing all known variables:

$b = y - m \cdot x$

$b = \frac{2}{9}-(-\frac{2}{81} )\cdot (9)\\b = \frac{4}{9}$

Thus, the tangent line is:

$y = -\frac{2}{81}\cdot x + \frac{4}{9}$

The vertical distance between a point of the tangent line and the origin is given by the intercept.

$d_{y} = \frac{4}{9}$

In order to find horizontal distance between a point of the tangent line and the origin, let equalize y to zero and clear x:

$-\frac{2}{81}\cdot x + \frac{4}{9}=0$

$-\frac{2}{9}\cdot x + 4 = 0$

$x = 18$

$d_{x} = 18$

The area of the triangle is computed by this formula:

$A = \frac{1}{2}\cdot d_{x}\cdot d_{y}$

$A = \frac{1}{2}\cdot (18)\cdot (\frac{4}{9} )$

$A = 4$

4 0

3 years ago

I need help with this , I understand the thingy but I forgot what to do to solve it

True [87]

Answer:

if the team keeps winning at this rate they will have one 20 out of 25 games. The newspaper projected 23 out of 25 games. there's a three-game difference between The trend of the team and the prediction of the newspaper. The difference is 3 out of 25. divide 3 by 25 and you get 0.12 = 12%

4 0

3 years ago

Can someone help I’m not good with word problems

pickupchik [31]

Answer:

I agree that this question can be confusing:

Apparently point A and point B must be on the same straight line (measured from the light house or the question would be nonsensical)

tan 13 = H / DA where H is height of lighthouse

tan 8 = H / DB tangent measured from point B

tan 13 / tan 8 = DB / DA

DB = .2309 / .1405 * 1279 = 2101 ft

DB - DA = 2101 - 1279 = 822.0 ft

3 0

2 years ago

Convert 10 hours into minutes

Neko [114]

Answer:

600 minutes

Step-by-step explanation:

60 minutes in an hour

60 × 10 is 600

8 0

2 years ago

Determine the x and y intercepts y = -x^2 + 6x - 8