The mode is 33 because it is listed 3x's.
Answer:
mommymommymoomamayeahyeah
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:
(5/2, 29/2), and this represents a maximum
Step-by-step explanation:
g(x) = -2x^2 + 10x + 2 is a quadratic function with coefficients {-2, 10, 2}.
The formula for the axis of symmetry (which passes through the vertex) is
x = -b/ [2a]. Here, a = -2; b = 10. Therefore, the axis of symmetry is
x = -10/ [2(-2)] = -10/(-4) = 5/2
Evaluate the function g(x) = -2x^2 + 10x + 2 at x = 5/2 to determine the y-coordinate of the vertex:
g(5/2) = -2(5/2)^2 + 10(5/2) + 2, or
g(5/2) = -2(25/4) + 25 + 2, or
g(5/2) = -25/2 + 27, or
g(5/2) = 14.5
The vertex is thus (5/2, 29/2), and this represents a maximum, because the coefficient of the x^2 term is negative (the curve opens downward).
