1. <br> ASA<br> SAS<br> HL<br> SSS<br> AAS<br><br> 2. PSR = __

Which is the equation for the line that has a slope of 12 and passes through the point (3, 20)?

sasho [114]

Answer:

y=12x-16

Step-by-step explanation:

y-y1=m(x-x1)

y-20=12(x-3)

y=12x-36+20

y=12x-16

4 0

3 years ago

A wire b units long is cut into two pieces. One piece is bent into an equilateral triangle and the other is bent into a circle.

mezya [45]

1. Divide wire b in parts x and b-x.

2. Bend the b-x piece to form a triangle with side (b-x)/3

There are many ways to find the area of the equilateral triangle. One is by the formula A= $\frac{1}{2}sin60^{o}side*side= \frac{1}{2} \frac{ \sqrt{3} }{2} (\frac{b-x}{3}) ^{2}= \frac{ \sqrt{3} }{36}(b-x)^{2}$
A= $\frac{ \sqrt{3} }{36}(b-x)^{2}=\frac{ \sqrt{3} }{36}( b^{2}-2bx+ x^{2} )=\frac{ \sqrt{3} }{36}b^{2}-\frac{ \sqrt{3} }{18}bx+ \frac{ \sqrt{3} }{36}x^{2}$

Another way is apply the formula A=1/2*base*altitude,
where the altitude can be found by applying the pythagorean theorem on the triangle with hypothenuse (b-x)/3 and side (b-x)/6

3. Let x be the circumference of the circle.

$2 \pi r=x$

so $r= \frac{x}{2 \pi }$

Area of circle = $\pi r^{2}= \pi ( \frac{x}{2 \pi } )^{2} = \frac{ \pi }{ 4 \pi ^{2} }* x^{2} = \frac{1}{4 \pi } x^{2}$

4. Let f(x)= $\frac{ \sqrt{3} }{36}b^{2}-\frac{ \sqrt{3} }{18}bx+ \frac{ \sqrt{3} }{36}x^{2}+\frac{1}{4 \pi } x^{2}$

be the function of the sum of the areas of the triangle and circle.

5. f(x) is a minimum means f'(x)=0

f'(x)= $\frac{ -\sqrt{3} }{18}b+ \frac{ \sqrt{3} }{18}x+\frac{1}{2 \pi } x$ =0

$\frac{ -\sqrt{3} }{18}b+ \frac{ \sqrt{3} }{18}x+\frac{1}{2 \pi } x=0$

$(\frac{ \sqrt{3} }{18}+\frac{1}{2 \pi }) x=\frac{ \sqrt{3} }{18}b$

$x= \frac{\frac{ \sqrt{3} }{18}b}{(\frac{ \sqrt{3} }{18}+\frac{1}{2 \pi }) }$

6. So one part is $\frac{\frac{ \sqrt{3} }{18}b}{(\frac{ \sqrt{3} }{18}+\frac{1}{2 \pi }) }$ and the other part is b- $\frac{\frac{ \sqrt{3} }{18}b}{(\frac{ \sqrt{3} }{18}+\frac{1}{2 \pi }) }$

4 0

3 years ago

Read 2 more answers

A) Antoine's family is taking a summer vacation through the northern united states on day one of the trips the family will be tr

kirill115 [55]

Answer:

Step-by-step explanation:

We are expected to convert from miles to kilometer

first day 85 miles =136.794km

Second day 125 mile=201.168km

third day 176 miles =283.245km

Total distance covered is

136.794km+201.168km+283.245km=621.207km

Therefore the total distance in kilometer is 621.207km

8 0

3 years ago

Someone pls help! Thanks!

dsp73

Answer:

is 1

Step-by-step explanation:

sorry if im wrong this is my first time doing this

4 0

2 years ago

Read 2 more answers

A map has a scale of 1 cm : 5 km. Determine how far apart two cities are if they are 4 cm apart on the map?

Kay [80]

Answer:

he is right its A

Step-by-step explanation:

5 0

3 years ago

1. ASA SAS HL SSS AAS 2. PSR = ___