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guajiro [1.7K]
2 years ago
12

I need help PLEASE !!!! Write a cosine function that has an amplitude of 2, a midline of 4 and a period of 4.

Mathematics
1 answer:
stiv31 [10]2 years ago
5 0

Answer:

\mathbf{y = 2cos ( \dfrac{\pi}{2}(x - 0) + 4}

Step-by-step explanation:

The standardized cosine function is ;

\mathbf{y = Acos (Bx + C) +D}

Amplitude |A| = 2

Period \dfrac{2 \pi}{B }= 4

2π = 4B

B = \dfrac{2 \pi}{4}

B = \dfrac{\pi}{2}

Midline y = 4;  D = 4

Phase shift; since no phase shift is given; then C = 0

The cosine function: \mathbf{y = 2cos ( \dfrac{\pi}{2}(x - 0) + 4}

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Answer:314

Step-by-step explanation:

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3 years ago
The volume of the cell phone is 75 cubic centimeters. Write and solve an equation to find the height of the cell phone. Round yo
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Answer:

Equation: Height = \frac{75}{Area}

Step-by-step explanation:

<em>The question is incomplete as the dimension of the phone was not given.</em>

<em>However, the following explanation will guide you</em>

Given

Volume = 75\ in^3

Required

Determine the Height

Volume is calculated as thus;

Volume = Area * Height

Substitute 75 for Volume

75= Area * Height

Divide through by Area

Height = \frac{75}{Area}

<em>The above represent the equation to solve for Height</em>

<em>To solve for height, we need the dimension of the phone or the area.</em>

Take for instance; the length and width of the phone is 5 by 5 inches;

The height would be:

Height = \frac{75}{5 * 5}

Height = \frac{75}{25}

Height = 3\ inches

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3 years ago
Write an inequality with a solution of x &lt; -7 that you solve in 2 or more steps.
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Example: 2x + 6 < -8

There's 2 steps to solve this one.
2x + 6 < -8
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For the following demand equation compute the elasticity of demand and determine whether the demand is elastic, unitary, or inel
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Answer:

Demand is inelastic at p = 9 and therefore revenue will increase with

an increase in price.

Step-by-step explanation:

Given a demand function that gives <em>q</em> in terms of <em>p</em>, the elasticity of demand is

E=|\frac{p}{q}\cdot \frac{dq}{dp}  |

  • If E < 1, we say demand is inelastic. In this case, raising prices increases revenue.
  • If E > 1, we say demand is elastic. In this case, raising prices decreases revenue.
  • If E = 1, we say demand is unitary.

We have the following demand equation D(p)=-\frac{3}{4}p+29; p = 9

Applying the above definition of elasticity of demand we get:

E(p)=\frac{p}{q}\cdot \frac{dq}{dp}

where

  • p = 9
  • q = -\frac{3}{4}p+29
  • \frac{dq}{dp}=\frac{d}{dp}(-\frac{3}{4}p+29)

\frac{d}{dp}\left(-\frac{3}{4}p+29\right)=-\frac{d}{dp}\left(\frac{3}{4}p\right)+\frac{d}{dp}\left(29\right)\\\\\frac{d}{dp}\left(-\frac{3}{4}p+29\right)=-\frac{3}{4}

Substituting the values

E(9)=\frac{9}{-\frac{3}{4}(9)+29}\cdot -\frac{3}{4}\\\\E(9)=\frac{36}{89}\cdot -\frac{3}{4}\\\\E(9)=-\frac{27}{89}\approx -0.30337

|E(9)|=|\frac{27}{89}| < 1

Demand is inelastic at p = 9 and therefore revenue will increase with an increase in price.

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What is 20% off of 30 dollars
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5 dollars is the answer
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