Use the drawings provided to prove the following theorem.“The area of an acute triangle equals one-half the product of the lengths of two sides of a triangle and the sine of the included angle.”Given: Acute 
Prove: 
What will be an ideal response?
The area of 
is given by 
. Considering the auxiliary altitude 
from vertex B
is given by . Considering the auxiliary altitude from vertex Bto side 
, we see that 
is a right angle. Then 
in right triangle 
.
From 
, it follows that 
. By substitution, the area formula 
becomes 
so we have 
.
Mathematics
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Solve the problem.Find a curve through the point (-6, 1) whose length integral, 1 ? y ? 2, is L = 
A. x = 
B. x = -6
C. x = 
D. x = -6y5/2
Mathematics
Express the number in scientific notation.0.000315
A. 3.15 × 10-3 B. 3.15 × 104 C. 3.15 × 10-4 D. 3.15 × 10-5
Mathematics
Solve the problem.
=
A. 199 B. 9,900 C. 100 D. 2 E. none of these
Mathematics
Determine the domain and the range of the function.f(x) = x2 + 4x + 3
A. domain: all real numbers range: {y|y ? -1} B. domain: range: {x|x ? 2} range: {y|y ? 1} C. domain: all real numbers range: {y|y ? 1} D. domain: range: {x|x ? 2} range: {y|y ? -1}
Mathematics