Relate the value of the numbers 1 in 115,093,628

Mathematics

1 answer:

MAXImum [283]3 years ago

8 0

100,000,000 is 100 million

10,000,000 is 10 milllion

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Angle X and Angle Y are complementary angles. Given Angle Y is equal to 1/5th Angle X. Find the value of Angle X in degrees

Elis [28]

Answer:

75 degrees

Step-by-step explanation:

Complementary angles equal 90 degrees together. That is the case with angle X and Y. Set an equation to describe the situation.

Y=1/5X

X=5Y

Now, set another equation:

X+Y=90

Substitute the first equation into the second one.

5Y+Y=90

6Y=90

Y=15

Substitute this once again:

X+15=90

X=75

6 0

3 years ago

Convert the polar coordinates (-3, -60°) to Cartesian coordinates.

notsponge [240]

Answer:

(1.5,-2.6)

Step-by-step explanation:

Given the polar coordinates (-3,60°).

Let our Cartesian coordinates be (x,y)

#We know that when converting the rectangular coordinates (x,y) to polar (r,θ), then:

$r=\sqrt{x^2+y^2}\\\\\therefore r^2=x^2+y^2\\\\\theta=tan^{-1}(y/x)\\\therefore tan \theta=y/x$

#Using the illustration above, we can express our polar coordinates as:

$-3=\sqrt{x^2+y^2}\\\\-60\textdegree=tan^{-1}(y/x}$

#Solve simultaneously to solve for x and y:

$(-3)^2=x^2+y^2\ \ \ \ \ \ \ \ \ \ i\\\\tan(-0\texdegree)=y/x\ \ \ \ \ \ \ \ ...ii\\\\y=x\ tan(-60\textdegree)\ \ \ \ \ \ \ ...iii\\\\\#substitute\ y \ in\ i\\\\(-3)^2=x^2+(x \ tan (-60\textdegree))^2\\\\9=x^2+3x^2\\\\x=\sqrt{9/4}=1.5\\\\y=1.5\ tan(-60\textdegree)=-2.5981\approx-2.6$