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This problem is a simple example of the application of the law of sines. The law of sines relates the sine of an angle of an oblique triangle to its opposite side length via proportions.

\(\frac{\sin A}{a}=\frac{\sin C}{c}\)

What is the area of the base of the pyramid?

In right triangle ABC, AB=10, AC=6 and BC=8 units. What is the distance from C to the midpoint of segment AB ?

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file:///Users/avapark/Desktop/Screen%20Shot%202018-06-01%20at%206.32.24%20PM.png

here is diagram

6! means   1*2*3*4*5*6

that are all multiply signs  :)

It is really good that you asked   

what do the factorials mean?  (do you add, multiply, divide, or subtract them?)

According to Charles' Law :

Volume  / Temperature  = Constant

Thus

300  / 30   =  10

Therefore

Volume / 60  = 10      multiply both sides by 60

Volume =  600 L

Have lots of fun :))

Here's  (a)

Draw BV  and TC

In triangles TAC and BAV,  TA  = BA, AC  = AV

Angle TAB  = angle VAC  and angle BAC  = angle BAC

So....angle TAB  + angle BAC  = angle VAC  + angle BAC

So...angle TAC  = angle VAB

So by SAS, triangle TAC  is congruent to triangle BAV

So  TC  = BV

Now.....call the intersection of  BV and TC, N

And call the intersection of  AC and BV, O

Note that  angle TCA  = angle BVA

And angle AOV  = angle NOC

So.....by AA similarity, triangle AOV  is similar to triangle NOC

But angle OAV  is right.....so...angle ONC  is also right.....

Thus.....TC  is perpendicular to BV

Take care, Penquino !!!

use the law of sines, angle n being 180-62-41=77

sin 41       sin 77

_____  =  ______  =  160.4

108               mp

Thanks alot

\(\frac{m}{3}+\frac14>\frac{3m}{8}\)

                                               Multiply both sides of the inequality by  24  .

\(24(\frac{m}{3}+\frac14)>24(\frac{3m}{8})\)

                                               Distribute the  24  to the terms in parenthesees.

\(\frac{24m}{3}+\frac{24}4>\frac{(24)(3)m}{8}\)

                                               Simplify each fraction.

\(8m+6>9m\)

                                               Subtract  8m  from both sides of the inequality.

\(6>9m-8m\\~\\ 6>m\\~\\ m<6\)

will do thx

Enjoy the Summer!

-2<= x<5

x>=6

x<-5

Here is a graph:

Effective rate =[ 1 + i/n]^n, where i =APR and n = Number of compounding periods

Effective rate =[1 + 0.08 / 4]^4

                      =[ 1.02]^4

                      = 1.08243216 -1 x 100 =8.243216% - Effective annual rate

(x-6)(x+2)

-------------   >= 0 

(x-5)(x+5)

x= 6 and x = -2

x  can not equal -5 or 5

Factor

This is an interesting question.

Here’s a composite graph of the parabolas x=time for y=0 for the back and front of the tuck’s bed, and the corresponding velocities for these range times. 

\(y=5+9t-\dfrac{1}{2}\cdot (9.8)t^2\\ y=7.5+9t-\dfrac{1}{2}\cdot (9.8)t^2\\ y=\text {velocity for time (t) to range target}\\ y=\frac{\left(t\cdot9.81\right)}{2\cdot\sin\left(45\right)}\\\)

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In EP's solution for the front of the truck bed, he adjusted the velocity by constraining the time component. In this case, with the increase in velocity the ball will pass over the front of the truck bed at time = 2.284, but it does not intersect y=0, here.  In range equations, both time and velocity are functions of distance and changing one affects the other.  

The ball with a velocity of 17.4m/s will cross y=0 in (17.4*2*sin(45)/9.81)= 2.51s at (17.4^2/9.8)= 30.86 meters. The target point of the truck will be at 7.5+(9*2.51)= 30.08 meters. So, the ball will land on the hood or the windshield.  

GA

In the complex number domain, every nth-order integer equation has exactly n solutions.

it is an isosceles triangle is one leg is 5 then so is the other.

It is right angles so not use Pythagorases theorum.