Can someone help me please

Mathematics

1 answer:

VashaNatasha [74]2 years ago

7 0

Answer:

TQ = 10 $\sqrt{2}$

Step-by-step explanation:

The diagonal divides the square into 2 right triangles with the diagonal being the hypotenuse.

Using Pythagoras' identity in triangle TPQ

TQ² = PQ² + PT²

TQ² = 10² + 10² = 100 + 100 = 200 ( take square root of both sides )

TQ = $\sqrt{200}$ = $\sqrt{100(2)}$ = $\sqrt{100}$ × $\sqrt{2}$ = 10 $\sqrt{2}$

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A region with a 10-mile radius has a population density of about 1500 people per square mile. Find the number of people who live

riadik2000 [5.3K]

The total population in the region is 942000

<u>Step-by-step explanation:</u>

Radius of the region= 10 miles

Population density= 1500 per square mile

Area of the region = 2π(r x r)

= 2π(10 x 10)

=2(3.14) (100)

= 628 square miles

Population = 1500 x 628

= 942000

The total population in the region is 942000

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:

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