Answer: PR=14.5.
Step-by-step explanation:
1. If the area of PQR is 50, then (QR*PQ)/2=50, so QR*PQ=100 (the area of a triangle is the base*height/2).
2, The tangent of an angle is (the opposite side)/(the adjacent side). So, the tangent of angle P=QR/PQ. Angle P is 36 degrees, and the tangent of 36 degrees is 0.726542528. We can substitute this into the equation we found to get 0.726542528=QR/PQ.
3. Using the equations we found in Steps 1 and 2, we can create a system of equations:
We can solve this system of equations to get PQ=11.7319 and QR=8.52375.
4. Using Pythagorean theorem, we can say that PR^2=QR^2+PQ^2. If we substitute the values of PQ and QR into the equation, we can come to the conclusion that PR=14.5014410206, which simplifies to PR=14.5.
We would have two circles of 5cm diameter each, and a rectangle of the length pi*diameter and 2cm, so lets add them:
total = 2circles + rectangle
total = 2(2*pi*(5/2)^2) + pi*diameter*heigth
= 4*pi*(2.5)^2 + pi*5*2
= 109.9
that is the surface area of a bar soap 109.9 cm^2
Answer:
B
Step-by-step explanation:
you have a system of equations with altogether 3 variables.
that means any solution looks like a 3- dimensional point with 3 coordinates : (x, y, z)
the problem is, you have only 2 equations.
2 equations with 3 variables is similar to 1 equation and 2 variables : there are infinitely many solutions.
the only thing we need to check, if the 2 equations are kind of blocking or contradicting each other (to have no solution).
but I can do a "multiply the first equation by -2 and then add both equations" :
-2x - 6y - 2z = -160
7y + 2z = 28
-----------------------------
-2x + y = -132
it works well, nothing special came up. the resulting equation is possible. so, no contradiction. just infinitely many solutions.
You have to add imaginary part together and the real part. The sum will be 11+j6.
Answer:
Step-by-step explanation:
The Ishango bone is a bone tool, dated to the Upper Paleolithic era. It is a dark brown length of bone, the fibula of a baboon, with a sharp piece of quartz affixed to one end, perhaps for engraving. It was first thought to be a tally stick