Answer:
The field will not fit
Step-by-step explanation:
To find the angle, we will use cosine rule;
c² = (a² + b² - 2abcosC)
C in this case is θ
Thus;
15² = (8² + 20² - 2(8 × 20)cos θ)
225 = (64 + 400 - 320cos θ)
464 - 225 = 320cos θ
cos θ = 239/320
θ = cos^(-1) 0.7469
θ = 41.68°
Thus angle is not less than 40° as recommended. Thus, the field will not fit.
Answer:
$465
Step-by-step explanation:
100 - 50/3 = 250/3
250/3 ÷ 100 = 5/6
$387.50 ÷ 5/6 = $465
9514 1404 393
Answer:
1 < x < 29
Step-by-step explanation:
The triangle inequality requires the sum of the two shortest sides exceed the longest side.
<u>When x and 14 are the shortest</u>:
x + 14 > 15
x > 1
<u>When 14 and 15 are the shortest</u>:
14 +15 > x
29 > x
Then the requirement for the length of x is ...
1 < x < 29
_____
<em>Additional comment</em>
The length of the third side of a triangle can be between the difference and sum of the two given sides.
Answer:
B
Step-by-step explanation:
see attachment
We can find this using the formula: L= ∫√1+ (y')² dx
First we want to solve for y by taking the 1/2 power of both sides:
y=(4(x+1)³)^1/2
y=2(x+1)^3/2
Now, we can take the derivative using the chain rule:
y'=3(x+1)^1/2
We can then square this, so it can be plugged directly into the formula:
(y')²=(3√x+1)²
<span>(y')²=9(x+1)
</span>(y')²=9x+9
We can then plug this into the formula:
L= ∫√1+9x+9 dx *I can't type in the bounds directly on the integral, but the upper bound is 1 and the lower bound is 0
L= ∫(9x+10)^1/2 dx *use u-substitution to solve
L= ∫u^1/2 (du/9)
L= 1/9 ∫u^1/2 du
L= 1/9[(2/3)u^3/2]
L= 2/27 [(9x+10)^3/2] *upper bound is 1 and lower bound is 0
L= 2/27 [19^3/2-10^3/2]
L= 2/27 [√6859 - √1000]
L=3.792318765
The length of the curve is 2/27 [√6859 - √1000] or <span>3.792318765 </span>units.
