1 answer:
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A graph of the equation shows the appropriate choice to be
C. 2
_____
If you would rather, you can look at the value of the discriminant. For the equation y = ax²+bx+c, the discriminant (d) is
d = b²-4ac
For your equation, this evaluates to
d = (-8)²-4(2)(5) = 64 -40 = 24
When the discriminant is positive, the function has two real roots (2 x-intercepts). When it is zero, there is only one x-intercept, and when it is negative, there are none (the roots are complex).
C. 2
_____
If you would rather, you can look at the value of the discriminant. For the equation y = ax²+bx+c, the discriminant (d) is
d = b²-4ac
For your equation, this evaluates to
d = (-8)²-4(2)(5) = 64 -40 = 24
When the discriminant is positive, the function has two real roots (2 x-intercepts). When it is zero, there is only one x-intercept, and when it is negative, there are none (the roots are complex).
Answer:
a) The coordinates are (0.431, -2.646) and (3.568,-7.354)
b) The tangent lines are
l₁ = (x-0.431)*2/3 - 2.646
l₂ = (x-3.568)2/3 - 7.354
Step-by-step explanation:
First, lets complete squares, by taking for each cordinate the square of a linear expression
0= x²−4x+y²+10y+13 = (x-2)²+ 4 + (y+5)²-25+13 = (x-2)²+(y+5)² - 8
Hence (x-2)² + (y+5)² = 8
Lets put y in function of x. We should obtain 2 functions f and g that represent the circle.
(y+5)² = 8 - (x-2)² = -x² + 4x + 4
Thus
Lets find the derivate of each function and the points in which they reach the value 2/3. In those points the tangent line will have a slope of 2/3.
We may just find the values of x which the derivate of f is either 2/3 or -2/3.
The quadratic has roots
one root is 3.568, which corresponds with g, and the other root is 0.431, corresponding to f.
Also g(3.568) = - 7.354 and f(0.431) = -2.646
This means that the coordinates are (0.431 , -2.646), (3.568 , -7.354) and the tangent lines are
l₁ = (x-0.431)*2/3 - 2.646
l₂ = (x-3.568)2/3 - 7.354
Answer:
Step-by-step explanation:
we know that
If two triangles are similar
then
the ratio of their corresponding sides are equal and the corresponding angles are also equal
In this problem
we have
Find the value of TS
substitute
see the attached figure to better understand the problem
