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Sladkaya [172]
3 years ago
7

Help with num 9 please. thanks​

Mathematics
1 answer:
Alik [6]3 years ago
8 0

Answer:

See Below.

Step-by-step explanation:

We want to show that the function:

f(x) = e^x - e^{-x}

Increases for all values of <em>x</em>.

A function is increasing whenever its derivative is positive.

So, find the derivative of our function:

\displaystyle f'(x) = \frac{d}{dx}\left[e^x - e^{-x}\right]

Differentiate:

\displaystyle f'(x) = e^x - (-e^{-x})

Simplify:

f'(x) = e^x+e^{-x}

Since eˣ is always greater than zero and e⁻ˣ is also always greater than zero, f'(x) is always positive. Hence, the original function increases for all values of <em>x.</em>

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Answer:

The distance between two points on the globe 30° north and 50° south at the equator is the same as latitude, roughly 69 miles. At 45 degrees north or south, the distance between is about 49 miles (79 km). The distance between longitudes reaches zero at the poles as the lines of meridian converge at that point.

Step-by-step explanation:

Sorry If it is wrong.

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2 years ago
One leg of a right triangle has length 7. The lengths of the other two sides are whole numbers. The length of the other leg is _
suter [353]
Sets of three integers that could be right triangles are called pythagorean triples. the only pythagorean triple including 7 is 7, 24, and 25. so the length of the other leg is 24 and the length of the hypotenuse is 25. hope this helped!
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3 years ago
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Step-by-step explanation: Calculator

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Find the vertex and length of the latus rectum for the parabola. y=-1/2(x-2)^2+8
victus00 [196]
Y = -(1/2)(x-2)² +8
Re write it in standard form:
(y-8) = -1/2(x-2)²  ↔ (y-k) = a(x-h)²

This parabola open downward (a = -1/2 <0), with a maximum shown in vertex
The vertex is (h , k) → Vertex(2 , 8)
focus(h, k +c )
 a = 1/4c → -1/2 = 1/4c → c = -1/2, hence focus(2, 8-1/2) →focus(2,15/2)

Latus rectum: y-value = 15/2

Replace in the equation y with 15/2→→15/2 = -1/2(x-2)² + 8
Or -1/2(x-2)² +8 -15/2 = 0
Solving this quadratic equation gives x' = 3 and x" = 2, then 
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4 0
3 years ago
Find the area of the composite figure below.<br> 6 9 <br> 15
CaHeK987 [17]

Answer:

180

Step-by-step explanation:

Triangle: 1/2BH

Square: BH

1. Split up the shapes

2. Use the area formula for square and triangle

Square area: 135

Triangle area: 45

3. Add

6 0
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