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3 years ago

What is Cot(x) / cos(x) ?

Mathematics

1 answer:

lutik1710 [3]3 years ago

8 0

Answer:

cosecx

Step-by-step explanation:

$\frac{cotx}{cosx} \\ = \frac{1}{tanx} \div cosx \\ = (1 \div \frac{sinx}{cosx} ) \div cosx \\ = \frac{cosx}{sinx} \times \frac{1}{cosx} \\ = \frac{1}{sinx} \\ = cosecx$

Note that:

$tanx = \frac{sinx}{cosx}$

$cotx = \frac{1}{tanx} = \frac{cosx}{sinx}$

$cosecx = \frac{1}{sinx}$

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Find the area between the graph of the function and the x-axis over the given interval, if possible.

vodomira [7]

Answer:

$A= -\frac{5}{-1} - \lim_{x\to\infty} \frac{5}{x-2} = 5-0 = 5$

So then the integral converges and the area below the curve and the x axis would be 5.

Step-by-step explanation:

In order to calculate the area between the function and the x axis we need to solve the following integral:

$A = \int_{-\infty}^1 \frac{5}{(x-2)^2}$

For this case we can use the following substitution $u = x-2$ and we have $dx = du$

$A = \int_{a}^b \frac{5}{u^2} du = 5\int_{a}^b u^{-2}du$

And if we solve the integral we got:

$A= -\frac{5}{u} \Big|_a^b$

And we can rewrite the expression again in terms of x and we got:

$A = -\frac{5}{x-2} \Big|_{-\infty}^1$

And we can solve this using the fundamental theorem of calculus like this:

$A= -\frac{5}{-1} - \lim_{x\to\infty} \frac{5}{x-2} = 5-0 = 5$

So then the integral converges and the area below the curve and the x axis would be 5.

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3 years ago

A right prism has a triangular base. The length of the base is 6 meters and the height of the base is 4 meters. The height of th

NNADVOKAT [17]

The volume of this right prism that has a triangular base is equal to 108 cubic meters.

<h3>The volume of a right prism.</h3>

Mathematically, the volume of a right prism is given by this formula:

V = L x W x H

<u>Where:</u>

L is the length.

W is the width.

H is the height.

V is the volume.

<u>Given the following data:</u>

Length of base = 6 meters.

Width of base = 4 meters. cm.

Height of prism = 4.5 meters.

Substituting the given parameters into the formula, we have;

V = 6 x 4 x 5

V = 108 cubic meters.

Read more on volume of prism here: brainly.com/question/3867601

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2 years ago

The pre approved amount of money that a bank is willing to lend a credit card holder is the credit

Rasek [7]

Sorry can’t answer

Step by step explanation

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3 years ago

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A bowl has the shape of a hemisphere whose diameter is 14 centimeters. If this bowl is filled with water, how many cubic centime

ASHA 777 [7]

Answer:

The cubic centimeters of water it will take to fill the bowl is 718.67 cm³

Step-by-step explanation:

Given;

diameter of the hemisphere, d = 14 cm

radius of the hemisphere, r = d/2 = 14/2 = 7 cm

The volume of the hemisphere is calculated as;

$V = \frac{2}{3} \pi r^3\\\\V = \frac{2}{3} \times \frac{22}{7} \times (7 \ cm)^3\\\\V = 718.67 \ cm^3$

The cubic centimeters of water it will take to fill the bowl is 718.67 cm³

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Help with rational equations

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Change all the terms so that they have a common denominator

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