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3 years ago

Given f(x) = -5(x - 2) + 21, what is the value of f(8)?

Mathematics

1 answer:

victus00 [196]3 years ago

6 0

Answer:

Step-by-step explanation:

f(8) = -5(8 - 2) + 21

= -30 + 21

= -9

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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

A machine fills 75 bottles of water each minute. Write an equation to represent the number of bottles b of water the machine can

Len [333]

Answer:

b = 75m

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

What is the horizontal asymptote

RSB [31]

Horizontal asymptotes are horizontal lines the graph approaches.

hope this helps :))

3 0

3 years ago

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16. A company spends $100 per day on fixed expenses such as electricity, rent, and the like. It also spends $35 per day on each

Paladinen [302]

C = Total Daily Cost
Total Daily Cost = (Salary per employee per day)×(Total no. of employees on that day) + Fixed Expenses.

C = 35x + 100

5 0

3 years ago

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A 35-foot tall pole is leading towards a building. To stop the pole from leaning further, a 48-foot long cable is secured from t

anygoal [31]

9514 1404 393

Answer:

38.5°

Step-by-step explanation:

A triangle solver can give an answer easily. The angle is 38.5°.

The law of cosines can be written to solve for an unknown angle C opposite side 'c' and flanked by sides 'a' and 'b'.

C = arccos((a² +b² -c²)/(2ab))

Here, we have a=35, b=48, c=30, so the angle is ...

C = arccos((35² +48² -30²)/(2·35·48)) = arccos(2629/3360) ≈ 38.515°

The angle the cable makes with the pole is about 38.5°.

6 0

3 years ago