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2 years ago

how to find the period, amplitude, and vertical shift of a sinusoidal graph. please explain in the simplest way possible, tyyyy

Mathematics

1 answer:

Kay [80]2 years ago

4 0

Answer:

Step-by-step explanation:

a) period is the length of one cycle ( one full squiggle ) If you are lucky and the graph is on exact numbers.. at a high point and to the next high point.. then just take that horizontal distance, that's one period also if it's not you could find the period, T, by using T = 2pi / k where k is a number that represents how fast , or how many times the wave cycles in one second or some other amount of time.

b) Amplitude is a number that goes right before the sinusoid, which is multiplied by it because, sin , cos, are at max 1 or at min -1

c) vertical shift is what is added , for upwards shift... before or after the sinusoid ie sin , cos, ect ect.

does this help?

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stepladder [879]

Answer:

$\displaystyle 64$

General Formulas and Concepts:

Calculus

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Limit Rule [Variable Direct Substitution]: $\displaystyle \lim_{x \to c} x = c$

Limit Rule [Variable Direct Substitution Exponential]: $\displaystyle \lim_{x \to c} x^n = c^n$

Limit Property [Multiplied Constant]: $\displaystyle \lim_{x \to c} bf(x) = b \lim_{x \to c} f(x)$

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle \lim_{x \to 0} f(x) = 4$

Step 2: Solve

Rewrite [Limit Property - Multiplied Constant]: $\displaystyle \lim_{x \to 0} \frac{1}{4}[f(x)]^4 = \frac{1}{4} \lim_{x \to 0} [f(x)]^4$
Evaluate limit [Limit Rule - Variable Direct Substitution Exponential]: $\displaystyle \lim_{x \to 0} \frac{1}{4}[f(x)]^4 = \frac{1}{4}(4^4)$
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Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Limits

Book: College Calculus 10e

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2 years ago

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Answer:

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Step-by-step explanation:

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2 years ago

A rectangular parcel of land has an area of 6,000 ft2. A diagonal between opposite corners is measured to be 10 ft longer than o

Drupady [299]

Answer:

50ft by 120ft

Step-by-step explanation:

Area of a rectangle = L × W

6000ft² = L × W

L = 6000/W

When a diagonal line divides a rectangle into 2 right angled triangles, the diagonal line = Hypotenuse of either of the triangle and it is the longest side.

The formula for a right angle triangle =

a² + b² = c²( c = hypotenuse)

We are told in the question that:

A diagonal between opposite corners is measured to be 10 ft longer than one side of the parcel

Let us assume the side that the hypotenuse is longer than = Width

Hence, the Diagonal = (W + 10)²

Therefore

L² + W² = (W + 10)²

Since L = 6000/W

W² + (6000/W)² = (W + 10)²

W² + (6000/W)² = (W + 10) (W + 10)

W² + (6000/W)² = W² + 10W + 10W + 100

W² + (6000/W)² = W² + 20W + 100

W² - W² + (6000/W)² = 20W+ 100

6000²/W² = 20W + 100

6000² = W²( 20W + 100)

6000² = 20W³ + 100W²

20W³ + 100W² - 6000² = 0

20W³ + 100W² - 36000000 = 0

20(W³ + 5W² - 1800000) = 0

Factorising the quadratic equation,

20(W − 120)(W² + 125W + 15000) = 0

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W = 120

Therefore,

W(Width) = 120feet

Since the Width = 120 feet

We can find the length

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The dimensions of the land, correct to the nearest foot is 50ft by 120ft

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2 years ago

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tresset_1 [31]

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2 years ago

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