Answer:
x=2.65
Step-by-step explanation:
First, we need to figure out how much the length of the sides is changing between the equations. In this case it is changing by a factor of 2.5. Now we need to work backwards. First use this equation:
This is because whatever the length of the side with x is, will be 14/2.5. So divide both sides by 2.5:
Next, add 5 to both sides:
Then divide both sides by 4:
Answer: Choice C
x/w and z/(y+v)
======================================================
Explanation:
All answer choices have that first fraction with a denominator of w. This implies that AB = w is the hypotenuse. This only applies to triangle ABD.
Focus on triangle ABD. It has an opposite leg of AD = x, when the reference angle is ABD (or angle B for short).
So we can say sin(ABD) = opposite/hypotenuse = AD/AB = x/w
x/w is one of the answers
-----------
Also note how y+v is the same for each denominator in the second fraction. y+v is the hypotenuse of triangle ABC. When the reference angle is ABD (aka angle ABC), the opposite side of this same triangle is AX = z
Therefore,
sin(ABD) = sin(ABC) = opp/hyp = AC/BC = z/(y+v)
z/(y+v) is the other answer
Side note: triangle ACD is not used at all.
The formula can also be proved using a trigonometric substitution . Each of above proofs will generalize to show that the volume of an ellipsoid with semi-axes A, B and C is just
(4/3)*Pi*A*B*C
Answer:
9...................................
