What is the sine of angle a?<br> a. 12/13<br> b. 5/13<br> c. 5/12<br> d. 13/12

Maya visits the movie rental store. On on wall, therear 6 DVDs on each of 5 shelves. On other wall, there are 4 DVDs on each of

Brrunno [24]

All together there are 46 dvds

5 0

2 years ago

The vertices of triangle JKL, shown below, are J(2, 1), K(4, 4), and L(6, 2). If triangle JKL is translated 2 units to the left

julia-pushkina [17]

Answer:

L=(4,-2)

Step-by-step explanation:Left = -2 units and down = -4 units, left is x direction and down is y direction. (x,y).

8 0

2 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

Help me give alot of pointz

VashaNatasha [74]

Answer:

1. 2560000

2. 256000

3. 256000

4. 2560000

7 0

1 year ago

Read 2 more answers

Vincent rolls two dice. What is the probability his results are a multiple of four or the

Afina-wow [57]

Answer:

Sample space: 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 6.1, 6.2, 6.3, 6.4, 6.5, 6.6.

So the mutiples are 1.3, 2.2, 2.6, 3.1, 3.5, 4.4, 5.3, 6.2, and 6.6

Greather than 6 is 1.6, 2.5, 3.4, 3.6, 4.3, 4.5 4.6, 5.2, 5.4, 5.5, 5.6, 6.1, 6.3, 6.4, and 6.5.

So the prop is 24/36 or 2/3=66%

4 0

2 years ago

What is the sine of angle a? a. 12/13 b. 5/13 c. 5/12 d. 13/12