30 POINTS PLZ HELP

Mathematics

2 answers:

belka [17]2 years ago

7 0

Answer:

1 : 2.56

Step-by-step explanation:

Since the sign and the banner are similar, their ratio of length to width should be the same. Hence, 32/45 = 20/x, with x being the width of the school banner.

32/45 = 20/x

32x = 20*45

x = 900/32

x = 28.125 inches

Now, we can calculate the area of the school banner and the sign:

Area of school banner:

28.125 * 20 = 562.5 square inches

Area of sign:

32 * 45 = 1440 square inches

Hence, the ratio of the area of banner to the area of sign is:

562.5 : 1440

1 : 2.56

Hope this helped!

Andrei [34K]2 years ago

3 0

Answer:

1 : 2.56

Step-by-step explanation:

plz mark brainly

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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:

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