Exact form is 8/7 , as a decimal its 1.142 and mixed number form its 1 1/7
The roots of the polynomial <span><span>x^3 </span>− 2<span>x^2 </span>− 4x + 2</span> are:
<span><span>x1 </span>= 0.42801</span>
<span><span>x2 </span>= −1.51414</span>
<span><span>x3 </span>= 3.08613</span>
x1 and x2 are in the desired interval [-2, 2]
f'(x) = 3x^2 - 4x - 4
so we have:
3x^2 - 4x - 4 = 0
<span>x = ( 4 +- </span><span>√(16 + 48) </span>)/6
x_1 = -4/6 = -0.66
x_ 2 = 2
According to Rolle's theorem, we have one point in between:
x1 = 0.42801 and x2 = −1.51414
where f'(x) = 0, and that is <span>x_1 = -0.66</span>
so we see that Rolle's theorem holds in our function.
Since we are given the lengths of 2 sides with the angle in
between, therefore by cosine law we can only construct 1 triangle from this. By
stating the angle in between, this constricts the possible number of triangles
that can be formed into 1.
By calculation, the length of the 3rd side is
calculated using cosine law:
c^2 = a^2 + b^2 – 2abcosθ
c^2 = 10^2 + 8^2 – 2(10)(8)cos40
c = 6.44 cm
ANSWER:
1 triangle
Answer:
4 : 9
Step-by-step explanation:
The requested ratio is ...
tile length : board length = (2/3 ft) : (1/2 yd) = (8 in) : (18 in)
= 8 : 18 = 4 : 9
_____
To make a unitless ratio, both parts must have the same units. Here, we chose to express the lengths in inches. We could have used feet or yards as well. (2/3 ft)×(1 yard)/(3 ft) = 2/9 yd or (1/2 yd)(3 ft/yd) = 3/2 ft. You get the same ratio with any of these:
(2/9 yd) : (1/2 yd) = (4 yd) : (9 yd) = 4 : 9 . . . . . multiply by 18
(2/3 ft) : (3/2 ft) = (4 ft) : (9 ft) = 4 : 9 . . . . . multiply by 6
Answer:
4/9
Step-by-step explanation:
11/18-1/6
The first step is to get a common denominator, which is 18. We can multiply 1/6 by 3/3 to get the denominator to 18
11/18 - 1/6 *3/3
11/18 - 3/18
8/18
Now we can simplify the fraction by dividing the top and bottom by 2
4/9
