GEOMETRY: What is the answer to this question?
1 answer:
If you're going to use technology to get help, you may as well use technology that can give you the answer immediately. A triangle solver (or your graphing calculator) can tell you
∠A ≈ 29.5°
∠B ≈ 115.4°
∠C ≈ 35.1°
You can rearrange the formula of the Law of Cosines to give you the angles unambiguously. (It often works best to start with the largest angle.) That law tells you
b² = a² + c²- 2ac·cos(B)
B = arccos((a² + c² - b²)/(2ac))
B = arccos((6² + 7² - 11²)/(2·6·7))
B = arccos(-36/84) ≈ 115.377°
Similarly,
A = arccos((b²+c²-a²)/(2bc)) = arccos(134/154) ≈ 29.526°
C = arccos((a²+b²-c²)/(2ab)) = arccos(108/132) ≈ 35.097°
Of course, once you have 2 angles you can find the third by subtracting their sum from 180°.
Once you have one angle, you can also use the Law of Sines to find another.
a/sin(A) = b/sin(B)
A = arcsin(a/b·sin(B)) = arcsin(6/11·sin(115.377°))
≈ arcsin(.492822) ≈ 29.526°
_____
Always maintain intermediate results to the full precision your calculator offers. Only round the final answer.
∠A ≈ 29.5°
∠B ≈ 115.4°
∠C ≈ 35.1°
You can rearrange the formula of the Law of Cosines to give you the angles unambiguously. (It often works best to start with the largest angle.) That law tells you
b² = a² + c²- 2ac·cos(B)
B = arccos((a² + c² - b²)/(2ac))
B = arccos((6² + 7² - 11²)/(2·6·7))
B = arccos(-36/84) ≈ 115.377°
Similarly,
A = arccos((b²+c²-a²)/(2bc)) = arccos(134/154) ≈ 29.526°
C = arccos((a²+b²-c²)/(2ab)) = arccos(108/132) ≈ 35.097°
Of course, once you have 2 angles you can find the third by subtracting their sum from 180°.
Once you have one angle, you can also use the Law of Sines to find another.
a/sin(A) = b/sin(B)
A = arcsin(a/b·sin(B)) = arcsin(6/11·sin(115.377°))
≈ arcsin(.492822) ≈ 29.526°
_____
Always maintain intermediate results to the full precision your calculator offers. Only round the final answer.
You might be interested in
Answer:
a)
b)
c)
Step-by-step explanation:
a)
We know that Revenue is our total income and cost is our total cost. Thus, profit is what's left after cost is subtracted from Income (revenue). Thus, we can say:
P(x) = R(x) - C(x)
Finding Profit Function (P(x)):
This is the profit function.
b)
The marginal profit is the profit earned when ONE ADDITIONAL UNIT of the product is sold. This is basically the rate of change of profit per unit. We find this by finding the DERIVATIVE of the Profit Function.
Remember the power rule for differentiation shown below:
Now, we differentiate the profit function to get the marginal profit function (P'):
This is the marginal profit function , P'.
c)
We need to find P'(4000) and P'(9500). So we basically put "4000" and "9500" in the marginal profit function's "x". The value is shown below:
and