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3 years ago

Find an irrational number and rational number between 5.2 and 5.5

2 answers:

alexandr1967 [171]3 years ago

8 0

rational number between 5.2 and 5.5 is 53/10 (cause 53/10 = 5.3)

irrational number between 5.2 and 5.5 is √29 (cause √29 = 5.385164....)

Harman [31]3 years ago

5 0

Step-by-step explanation:

Rational = 5.3

Irrational = 5.40400400040000....

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For positive acute angles A and B, it is known that cos A= 20/29 and tan B= 11/60. Find the value of cos(A + B) in simplest form

jek_recluse [69]

Answer:

$\displaystyle \cos(A + B) =\frac{969}{1769}$

Step-by-step explanation:

We are given that:

$\displaystyle \cos A=\frac{20}{29}\text{ and } \tan B=\frac{11}{60}$

Where A and B are positive acute angles.

And we want to find cos(A + B).

Recall that cosine is the ratio of the adjacent side to the hypotenuse. Using this information, find the opposite side with respect to Angle A:

$o=\sqrt{29^2-20^2}=21$

Tangent is the ratio of the opposite side to the adjacent side. Find the hypotenuse with respect to Angle B:

$h=\sqrt{11^2+60^2}=61$

In summary:

With respect to Angle A, the adjacent side is 20, opposite is 21, and the hypotenuse is 29.

With respect to Angle B, the adjacent side is 60, the opposite is 11, and the hypotenuse is 61.

We can rewrite our expression as:

$\displaystyle \cos(A+B)=\cos A\cos B-\sin A\sin B$

Using the above information, substitute in the appropriate values. Note that since A and B are positive acute angles, all trigonometric values will be positive. Hence:

$\displaystyle \cos(A + B)=\left(\frac{20}{29}\right)\left(\frac{60}{61}\right)-\left(\frac{21}{29}\right)\left(\frac{11}{61}\right)$

Simplify:

$\displaystyle \cos(A + B) =\frac{1200-231}{1769}=\frac{969}{1769}$

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3 years ago

Consider the data below. Find the change in the (a) mean, (b) median, and (c) mode when the

LuckyWell [14K]

Answer:

Step-by-step explanation:

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2 years ago

Identify the relationship between 1 and 2

Rufina [12.5K]

Answer:

Step-by-step explanation:

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2 years ago

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Dmitriy789 [7]

5 x (4 x 3) = (5 x 4) x 3

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2 years ago

Evan bought a rectangular doormat that is 1_2 meter long and 3__10 meter wide. What is the area, in square meters, of the doorma

Zarrin [17]

Answer:

3/20 m²

Step-by-step explanation:

Here is the complete and clear question :

Evan bought A rectangular doormat that was 1/2 a meter long and 3/10 a meter wide. What is the area, in square meters, of the doormat?

Characteristics of a rectangle

A rectangle is a quadrilateral
It has two parallel sides
the diagonals of a rectangle bisect each other and they are equal in length

Area of a rectangle = length x breadth

Area of the rectangular doormat = $\frac{1}{2}$ × $\frac{3}{10}$ = $\frac{3}{20}$ m²

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3 years ago