Answer:
32√5
Step-by-step explanation:
We have the right triangles PQA and PQB as well as the given right triangle QAB.
cot(PAQ) = 2/5 = QA/PQ
cot(PBQ) = 3/5 = QB/PQ
cot(PAQ) / cot(PBQ) = (2/5) / (3/5) = 2/3
cot(PAQ) / cot(PBQ) = (QA/PQ) / (QB/PQ) = QA / QB
QA / QB = 2/3
QA = (2/3) QB
QB = (3/2) QA
By the Pythagorean Theorem we have:
(QA)² + 32² = (QB)²
(QA)² + 32² = (3/2 QA)²
(QA)² + 1024 = (9/4) (QA)²
(5/4) (QA)² = 1024
(QA)² = (4/5)1024 = 4096/5
QA = 64/√5
Solve for PQ.
cot(PAQ) = QA/PQ
PQ = QA / cot(PAQ)
PQ = (64/√5) / (2/5) = 32√5
The height of the tower is 32√5.
Answer:
1. A. 4 terms
There are 4 different values in the expression, so therefore there are 4 terms.
2. D. 3x^2 + 6x + 10
To get the answer...
start with the original expression: 3x^2 + x + 10 + 5x
add the like terms together, in this case you'd add x + 5x
you'll get: 3x^2 + 6x + 10
I hope I could help :)
