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3 years ago

Which of the following is cot(theta) sec(theta) in simplified form? csc theta tan theta –1 1

Mathematics

1 answer:

Yakvenalex [24]3 years ago

5 0

Answer:

csc(theta)

Step-by-step explanation:

we have

cot(theta)*sec(theta)

we know that

cot(theta)=cos(theta)/sin(theta)

sec(theta)=1/cos(theta)

csc(theta)=1/sin(theta)

substitute in the given expression

cot(theta)*sec(theta)=(cos(theta)/sin(theta))*(1/cos(theta))

Simplify

(cos(theta)/sin(theta))*(1/cos(theta))=1/sin(theta)

and

1/sin(theta)=csc(theta)

therefore

cot(theta)*sec(theta)=csc(theta)

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Let f be defined by the function f(x) = 1/(x^2+9)

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(a)

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(b) The series

$\displaystyle \sum_{n=3}^\infty \frac1{n^2+9}$

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$\displaystyle\sum_{n=3}^\infty\frac1{n^2}$

$\displaystyle \sum_{n=1}^\infty \frac{(-1)^n (n^2+9)}{e^n}$

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$\displaystyle \sum_{n=1}^\infty \left|\frac{(-1)^n (n^2+9)}{e^n}\right|=\sum_{n=1}^\infty \frac{n^2+9}{e^n} < \sum_{n=1}^\infty \frac{n^2}{e^n} < \sum_{n=1}^\infty \frac1{e^n}=\frac1{e-1}$

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3 years ago

A 40-foot ladder is leaning against a building and forms a 29.32° angle with the ground. how far away from the building is the b

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The distance between the building and the ladder is 34.876 foot.

<h3>What is a Right Triangle?</h3>

A triangle in which one of the angle measure is equal to 90 degree is called a right triangle.

The ladder forms a right triangle with the building and the ground,

The length of the triangle is 40 foot

The angle made by the ladder is 29.32 degree

By using Trigonometric Ratios

cos 29.32 = Base / Hypotenuse

cos 29.32 = Base / 40

0.8718 × 40 = Base

Base = 34.876 foot

Base is the distance between the building and the ladder.

Base of the ladder = 34.876 foot

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2 years ago

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The surface area of a right triangular prism

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Scale factor = 1.2 feet / 6 cm = 0.2 ft/cm

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convert the units

9 cm = 9 cm × 0.2 ft/cm = 1.8 ft

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Surface area of actual ramp = 2(0.5 × 3.2 ft × 1.2 ft) + 2(2 ft × 1.8 ft) + (1.8 ft × 3.2 ft)

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