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2 years ago

What is Formula of Volume of a pentagonal prism?

Mathematics

1 answer:

Vera_Pavlovna [14]2 years ago

7 0

Volume of the pentagonal prism =
Area of the pentagon• height of the prism

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Evaluate the expression under the given conditions. tan(2); cos() = 5 13 , in quadrant i

Nataliya [291]

The solution to given expression tan(2θ) is 22.615°

For given question,

We have been given an expression tan(2θ)

Given that cos(θ) = 5/13, and θ is in quadrant 1.

We know that the trigonometric identity

sin²θ + cos²θ = 1

⇒ cos²θ = (5/13)²

⇒ sin²θ = 1 - 25/169

⇒ sin²θ = 169 - (25/169)

⇒ sin²θ = 144/169

⇒ sin(θ) = 12/13

We know that the identity cos(2x) = cos²x - sin²x

⇒ cos(2θ) = cos²θ - sin²θ

⇒ cos(2θ) = 25/169 - 144/169

⇒ cos(2θ) = -119/169

And sin(2x) = 2sin(x)cos(x)

⇒ sin(2θ) = 2sin(θ)cos(θ)

⇒ sin(2θ) = 2 × 12/13 × 5/13

⇒ sin(2θ) = 120/169

We know that, tan(x) = sin(x)/cos(x)

⇒ tan(2θ) = sin(2θ)/cos(2θ)

⇒ tan(2θ) = (120/169) / (-119/169)

⇒ tan(2θ) = 120 / (-119)

⇒ tan(2θ) = -1.008

Since θ is in quadrant 1, tan(2θ) = 1.008

⇒ 2θ = arctan(1.008)

⇒ 2θ = 45.23

⇒ θ = 22.615°

Therefore, the solution to given expression tan(2θ) is 22.615°

Learn more about the expression here:

brainly.com/question/14961928

#SPJ4

7 0

2 years ago

1. Ruth Lockwood earns $2,917 a month as a supervisor for Acme

soldi70 [24.7K]

Answer:

a. 25%

b. $1560

c. $130

Step-by-step explanation:

If 75% is paid by company, the rest is paid by Ruth.

Out of 100%, 75% is paid by company, so Ruth pays 100 - 75 = 25%

Per year, the total amount paid is 6240, but Ruth pas 25% of this. So,

25% = 0.25

To get the answer, we multiply 0.25 with 6240.

0.25 * 6240 = 1560

So, $1560 is paid by Ruth annually.

Since 1560 is paid annually (in 12 months), each month Ruth has to pay:

1560/12 = $130

Hence, $130 is deducted each month from her paycheck

6 0

3 years ago

What is the Absoulte value of 3

aleksandr82 [10.1K]

Answer:

it's 3

Step-by-step explanation:

Number 3 is 3 units away from 0, and thus the absolute value of 3 is 3.

3 0

2 years ago

Jodie read 42 randomly chosen books from each library in her city. Each library is the same size.

ahrayia [7]

Answer:

Yes!

Step-by-step explanation:

The definition of Representative is

A representative sample is a group or set chosen from a larger statistical population or group of factors or instances that adequately replicates the larger group according to whatever characteristic or quality is under study

so your book is whats understudy and with that you'll know that yes, yes it is

3 0

2 years ago

The base change property can help in what type of scenarios? HELP ME!!!!!

Mekhanik [1.2K]

<h3>Base Change Property</h3><h3 />

The Base Change Property is very helpful in scenarios related to simplifying equations where the logarithmic terms have a varying base.

So to solve an equation, which possesses logarithmic functions, all logarithmic terms must have a similar base.

<h3>What is Base Change Property?</h3><h3 />

This refers to the base formula which is used to write a logarithm of a number with a base that is fixed as the ratio of two logarithms both having the same base but different from the base of the initial or original logarithm.

Change of Base Formula is given as:

$log_{b} a = \frac{Log_{c} a }{Log_{c} b}$

See the link below for more about Base Change Property:

brainly.com/question/15318682

6 0

2 years ago