Answer:
The height of the pole is 105ft,
Step-by-step explanation:
Let us call 
the height of the pole, then we know that the distance from the bottom of the pole to the anchor point is 49, or it is 
.
The wire length 
is 14 ft longer than height , hence
.
Thus we get a right triangle with hypotenuse 
, perpendicular , and base 
; therefore, the Pythagorean theorem gives
which upon expanding we get:
further simplification gives
,
which is a quadratic equation with solutions
Since the first solution 
will give the triangle base length of 
which is negative; therefore, we disregard it and pick the solution 
.
Hence, the height of the pole is 105ft.
Answer:
Step-by-step explanation:
Given: 
Initial value: y(1)=6
Let 
Variable separable
Integrate both sides
Initial condition, y(1)=6
Put C into equation
Solution:
or
Hence, The solution is or
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Answer:
a. 10x + 4; the answer is a polynomial
Step-by-step explanation:
The perimeter of a rectangle is the sum of the lengths of the 4 sides.
The closure property is that if you add polynomials, the sum is a polynomial.
A rectangle has two congruent lengths and two congruent widths.
Since the length of the rectangle is 3x + 5, there is another length of 3x + 5. The width is 2x - 3, so there is a second width of also 2x - 3.
Let's add the 4 sides together:
3x + 5 + 3x + 5 + 2x - 3 + 2x - 3 =
= 3x + 3x + 2x + 2x + 5 + 5 - 3 - 3
= 10x + 4
The perimeter is 10x + 4. Each side length is a polynomial, and the sum of the all the side length is also a polynomial. This shows there is closure for the addition of polynomials.
Answer: a. 10x + 4; the answer is a polynomial
