As soon as I read this, the words "law of cosines" popped
into my head. I don't have a good intuitive feeling for the
law of cosines, but I went and looked it up (you probably
could have done that), and I found that it's exactly what
you need for this problem.
The "law of cosines" relates the lengths of the sides of any
triangle to the cosine of one of its angles ... just what we need,
since we know all the sides, and we want to find one of the angles.
To find angle-B, the law of cosines says
b² = a² + c² - 2 a c cosine(B)
B = angle-B
b = the side opposite angle-B = 1.4
a, c = the other 2 sides = 1 and 1.9
(1.4)² = (1)² + (1.9)² - (2 x 1 x 1.9) cos(B)
1.96 = (1) + (3.61) - (3.8) cos(B)
Add 3.8 cos(B) from each side:
1.96 + 3.8 cos(B) = 4.61
Subtract 1.96 from each side:
3.8 cos(B) = 2.65
Divide each side by 3.8 :
cos(B) = 0.69737 (rounded)
Whipping out the
trusty calculator:
B = the angle whose cosine is 0.69737
= 45.784° .
Now, for the first time, I'll take a deep breath, then hold it
while I look back at the question and see whether this is
anywhere near one of the choices ...
By gosh ! Choice 'B' is 45.8° ! yay !
I'll bet that's it !
Answer:
Step-by-step explanation:
Remark
All you need do is find the radius and put it into the formula V = (4/3) pi r^3.
Givens
d = 12 yards
r = d/2
Solution
r = 12 yds/2 = 6 yds
V = 4/3 pi r^3
V = 4/3 * 3.14 * 6*6*6
V = 904.32
Answer 904.4 yd^3
Using the equations for tangent and secant lines:
Let the unknown length of the line inside the circle = y
6^2 = 3 x (y+3)
Simplify:
36 = 3y+9
Subtract 9 from both sides:
27 =3y
Divide both sides by 3:
Y = 9
Now add to get x:
X = 9 + 3 = 12
X = 12
We can actually deduce here that the ordered pairs that make both inequalities true are:
<h3>What is inequality?</h3>
An inequality is known to be an expression that shows that certain variables or values are not equal to each other. It is usually seen in an inequality expression as:
- > (greater than)
- < (less than)
- ≥ (greater than or equal to)
- ≤ (less than or equal to).
We see the attached image that shows the graph of inequality and which completes the question.
The options that complete the question are:
A. –2, 2
B. (0, 0)
C. (1,1)
D. (1, 3)
E. (2, 2)
When we insert the values of each axes into the inequality expressions given, we will discover that the ordered pairs that the inequalities true is (1,1) and (2, 2).
Learn more about inequality on brainly.com/question/25275758
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