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2 years ago

Find (a) the slope of the curve at the given point p, and (b) an equation of the tangent line at p. y=−2−9x2; p(2,−38)

Mathematics

1 answer:

Neporo4naja [7]2 years ago

6 0

Answer:

a) -36

b) y = -36x +34

Step-by-step explanation:

a) The slope is found using the derivative of the function.

f'(x) = dy/dx = 0 -9(2x) = -18x

Then at x=2, the slope is ...

f'(2) = -18·2 = -36

___

b) The point-slope form of the equation can be written as ...

y = -36(x -2) -38

Simplifying to slope-intercept form, we get ...

y = -36x +34

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timama [110]

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2 years ago

Two angels are supplementary. The measure of the large angle is four more than three times the measure of the small angle. Find

sashaice [31]

Answer:

The measure of the two supplementary angles is

Small angle = x = 44°

Large angle = y = 136

Step-by-step explanation:

Supplementary angles are two angles whose measures add up to 180° .

Let

Small angle = x

Large angle = y

x + y = 180°.... Equation 1

The measure of the large angle is four more than three times the measure of the small angle

Hence: y = 4 + 3x

We substitute 4 + 3x for y in Equation 1

x + 4 + 3x = 180°

4x + 4 = 180°

4x = 180° - 4

4x = 176

x = 176/4

x = 44°

Solve for y

y = 4 + 3x

y = 4 + 3(44)

y = 4 + 132

y = 136°

Therefore, the measure of the two supplementary angles is

Small angle = x = 44°

Large angle = y = 136

5 0

2 years ago

A rectangular swimming pool is twice as long as it is wide. A small concrete sidewalk surrounds the pool and is a constant 2 fee

Naddika [18.5K]

Answer:

The dimensions of the pool are:

Width: 8.944 feet

Length: 17.888 feet

Step-by-step explanation:

From Geometry, the area of a rectangle ( $A$ ), measured in square feet, is determined by the following equations:

$A = w\cdot l$ (1)

Where:

$w$ - Width, measured in feet.

$l$ - Length, measured in feet.

If we know that $w = x$ , $l = 2\cdot x$ and $A = 160\,ft^{2}$ , then we get the following second order polynomial:

$2\cdot x^{2}-160 = 0$ (1)

And we solve the expression for $x$ :

$2\cdot x^{2} = 160$

$x^{2} = 80$

$x = \sqrt{80}\,ft$

$x \approx 8.944\,ft$

Then, the dimensions of the pool are, respectively:

$w \approx 8.944\,ft$ and $l \approx 17.888\,ft$

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2 years ago

Type the expression that results from the following series of steps: start with x, divide 6, then subtract 1

Alexus [3.1K]

Answer:

x/6 - 1

Step-by-step explanation:

x divide 6 subtract 1

4 0

2 years ago

The Rachel’s daily expenses for 10 days are in the table.

Annette [7]

The correct answer is $44.20.
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442 / 10 = 44.2

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3 years ago

Find ​(a) the slope of the curve at the given point​ p, and ​(b) an equation of the tangent line at p. y=−2−9x2​; ​p(2​,−38​)

Find (a) the slope of the curve at the given point p, and (b) an equation of the tangent line at p. y=−2−9x2; p(2,−38)