PLEASE HELP ASAP MARKING BRAINLEIST + 50 POINTS

Mathematics

1 answer:

Lorico [155]1 year ago

3 0

Answer:

scale factor = $\frac{1}{5}$

Step-by-step explanation:

the scale factor is the ratio of corresponding sides, image to original, so

scale factor = $\frac{V'W'}{VW}$ = $\frac{1}{5}$

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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:

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

Hence, the Cartesian coordinates are (1.5,-2.6)

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2 years ago

On Monday morning the temperature was 38°F, but by the afternoon the temperature had risen 22°F. On Tuesday morning the temperat

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The temperature on Tuesday afternoon is below 38 degrees Fahrenheit. As it states in the question the temperature on Tuesday morning was 27 degrees Fahrenheit and rose 10 more degrees at noon. Which makes is 37 degrees Fahrenheit at noon on Tuesday. You get this by taking 27 degrees and adding 10 degrees.

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