2 years ago

Given the function f(x) = −5x2 − x + 20, find f(3).

Mathematics

1 answer:

SIZIF [17.4K]2 years ago

5 0

The answer is -28 I got you if you need more answers

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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

4 years ago

The quotient of a number and 2 is the same as the difference of the number doubled and 3. What is the number?

Yanka [14]

Hi,

x/2 = 2x - 3

x/2 - 2x = - 3

x = 3 /(3/2)

x = 3 * 2/3 = 2

The number is 2.

7 0

3 years ago

For each hour he babysits, Anderson earns $1 more than half of Carey’s hourly rate. Anderson earns $6 per hour. Which equation c

erastovalidia [21]

Carey earns c hourly
Anderson earns $6 hourly which is also 1+ c/2
So, 6=1+c/2
12=2+c
c=$10
<span>Carey earns $10 hourly</span>

6 0

3 years ago

Read 2 more answers

Evaluate loook at the pic

Vikki [24]

Answer:

Step-by-step explanation:

So the 3 to the power 2 is 9, so 9x2 is 18 so then minus the 1 and it’s 17.

6 0

3 years ago

Read 2 more answers

1. What kind of correlation is shown? (see #1 above)

klemol [59]

I this it would be constant correlation

3 0

3 years ago