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3 years ago

Line AB contains points A ( -3,5) and B (-3,3). Line AB has a slope that is

Mathematics

1 answer:

Margaret [11]3 years ago

6 0

Answer:

Negative

Step-by-step explanation:

If you put those points on a graph the line slopes down

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Use calculus to find the absolute maximum and minimum values of the function. (round all answers to three decimal places.) f(x)

Allisa [31]

Part A:

Given the function $f(x)=x+2\cos(x)$ , the absolute maximum or minimum occurs when $f'(x)=0$ .

$f'(x)=0 \\ \\ \Rightarrow1-2\sin{x}=0 \\ \\ \Rightarrow2\sin{x}=1 \\ \\ \Rightarrow\sin{x}= \frac{1}{2} \\ \\ \Rightarrow x=\sin^{-1}{\frac{1}{2}}= \frac{\pi}{6}$

Using the second derivative test,

$f''(x)=-2cosx \\ \\ \Rightarrow f''\left( \frac{\pi}{6} \right)=-2\cos{\left( \frac{\pi}{6} \right)}=-1.732$

Since the second derivative gives a negative number, the given function has a maximum point at $x=\frac{\pi}{6}$ .

And the maximum point is given by:

$f\left( \frac{\pi}{6} \right)=\frac{\pi}{6}+2\cos\left( \frac{\pi}{6} \right) \\ \\ =0.5236+2(0.8660)=0.5236+1.732 \\ \\ =\bold{2.256}$

i.e. $\left(\frac{\pi}{6},\ 2.256\right)$

Part B:

Given the function $f(x)=e^{-x}-e^{-2x}$ , the absolute maximum or minimum occurs when $f'(x)=0$ .

$f'(x)=0 \\ \\ \Rightarrow-e^{-x}+2e^{-2x}=0 \\ \\ \Rightarrow2e^{-2x}=e^{-x} \\ \\ \Rightarrow2e^{-x}=1 \\ \\ \Rightarrow e^{-x}=\frac{1}{2} \\ \\ \Rightarrow-x=\ln \frac{1}{2}=-0.6931 \\ \\ \Rightarrow x=0.6931$

Using the second derivative test,

$f''(x)=e^{-x}-4e^{-2x} \\ \\ \Rightarrow f''(0.6931)=e^{-0.6931}-4e^{-2(0.6931)} \\ \\ =0.5-4e^{-1.386}=0.5-4(0.25)=0.5-1 \\ \\ =-0.5$

Since the second derivative gives a negative number, the given function has a maximum point at $x=0.6931$ .

And the maximum point is given by:

$f(0.6931)=e^{-0.6931}-e^{-2(0.6931)} \\ \\ =0.5-e^{-1.386}=0.5-0.25=\bold{0.25}$

i.e. (0.693, 0.25)

3 0

3 years ago

The function models the number of accidents per 50 million miles driven as a function

sesenic [268]

Answer:

x=39, y=180

Step-by-step explanation:

f(x)=0.4x²-31.2x+788.4

For x=39 the graph reaches its lowest point.

The minimum value of y is:

x=39→y=f(39)=0.4(39)²-31.2(39)+788.4

y=f(39)=0.4(1,521)-1,216.8+788.4

y=f(39)=608.4-1,216.8+788.4

y=f(39)=180

5 0

4 years ago

Which is an equation of the line through (-1, -4) and parallel to 3x+y=5

kherson [118]

Answer:

Step-by-step explanation:

3x + y = 5 {subtract 3x from both sides}

y = -3x + 5 ← slope-intercept form

y=m₁x+b₁ ║ y=m₂x+b₂ ⇔ m₁ = m₂

{Two lines are parallel if their slopes are equal}

y = -3x + 5 ⇒ m₁ = -3 ⇒ m₂ = -3

(-1, -4) ⇒ x₁ = -1, y₁ = -4

The point-slope form:

y - (-4) = -3(x - (-1))

y + 4 = -3(x + 1)

y + 4 = -3x - 3 {subtact 4 from both sides}

<h3><u>y = -3x - 7 </u><u> ← slope-intercept form</u></h3>

7 0

3 years ago

What is the angle relationship between ∠KAJ and ∠GAF?

Ulleksa [173]

Answer:

vertical angles

Step-by -step explanation:

7 0

3 years ago

In the diagram, what is the value of x?

Ghella [55]

Answer:

x = 162

Step-by-step explanation:

the sum of the interior angles of a quadrilateral = 360°

sum the interior angles of the quadrilateral and equate to 360

90 + 60 + x + 48 = 360 , that is

198 + x = 360 ( subtract 198 from both sides )

x = 162

5 0

3 years ago