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3 years ago

Tan(x)=2

1 answer:

8 0

Tan(x)=2
Or for x=45 tan(x)=1
then for tan(x)=2 ; x must be superior to 45
Then the answer is d. 63.4 degrees

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Given: PRST is a square

xxTIMURxx [149]

Answer:

$(1-\sqrt{2})a^2$

Step-by-step explanation:

Consider irght triangle PRS. By the Pythagorean theorem,

$PS^2=PR^2+RS^2\\ \\PS^2=a^2+a^2\\ \\PS^2=2a^2\\ \\PS=\sqrt{2}a$

Thus,

$MS=PS-PM=\sqrt{2}a-a=(\sqrt{2}-1)a$

Consider isosceles triangle MSC. In this triangle

$MS=MC=(\sqrt{2}-1)a.$

The area of this triangle is

$A_{MSC}=\dfrac{1}{2}MS\cdot MC=\dfrac{1}{2}\cdot (\sqrt{2}-1)a\cdot (\sqrt{2}-1)a=\dfrac{(\sqrt{2}-1)^2a^2}{2}=\dfrac{(3-2\sqrt{2})a^2}{2}$

Consider right triangle PTS. The area of this triangle is

$A_{PTS}=\dfrac{1}{2}PT\cdot TS=\dfrac{1}{2}a\cdot a=\dfrac{a^2}{2}$

The area of the quadrilateral PMCT is the difference in area of triangles PTS and MSC:

$A_{PMCT}=\dfrac{(3-2\sqrt{2})a^2}{2}-\dfrac{a^2}{2}=\dfrac{(2-2\sqrt{2})a^2}{2}=(1-\sqrt{2})a^2$

5 0

3 years ago

Samuel paid $25.82 for gas this week, which was $3.47 less than he paid last week. How much had he paid last week?

Yuri [45]

Samuel was paid $29.29 last week.

Hope this helps

5 0

3 years ago

If a circle has a circumference of C, what is the area of the circle in terms of C?

Anettt [7]

First you have to write down the formula on how to get the circumference of the circle (C = 2pi * Radius) and the Area of the circle which is (A=Pi*Radius^2). In getting the radius you need to transform the formula of the circumference by making the radius to be the unknown variable so it would become(R=C/2pi), after that you need to replace the radius in the formula of the area by the transformed formula of the circumference and you will come up of the formula of (A=Pi(C/2pi)^2).

3 0

3 years ago

(60 + 10) 130 Solve for a

forsale [732]

Answer:

Step-by-step explanation:

here you go mate'

step 1

(60 + 10)130 equation

step 2

(60 + 10)130 simplify with the brackets

step 3

130(70) multiply the numbers

answer

9100

5 0

3 years ago

Plz help me with 3,4,and 6.Also what are the numbers on the sides called?

Elis [28]

3. 1*2* 1/3= 2/3 yd

4. 1/4 * 1/8 *2= 1/16in

6. 12 *4= 48ft

the numbers on the sides are the length, width and height. you multiply them all together to find the volume

4 0

3 years ago