We are given the following:
- parabola passes to both (1,0) and (0,1)
<span> - slope at x = 1 is 4 from the equation of the tangent line </span>
<span>First, we figure out the value of c or the y intercept, we use the second point (0, 1) and substitute to the equation of the parabola. W</span><span>hen x = 0, y = 1. So, c should be equal to 1. The</span><span> parabola is y = ax^2 + bx + 1 </span>
<span>Now, we can substitute the point (1,0) into the equation,
</span>0 = a(1)^2 + b(1) + 1
<span>0 = a + b + 1
a + b = -1 </span>
<span>The slope at x = 1 is equal to 4 which is equal to the first derivative of the equation.</span>
<span>We take the derivative of the equation ,
y = ax^2 + bx + 1</span>
<span>y' = 2ax + b
</span>
<span>x = 1, y' = 2
</span>4 = 2a(1) + b
<span>4 = 2a + b </span>
So, we have two equations and two unknowns,<span> </span>
<span>2a + b = 4 </span>
<span>a + b = -1
</span><span>
Solving simultaneously,
a = 5 </span>
<span>b = -6</span>
<span>Therefore, the eqution of the parabola is y = 5x^2 - 6x + 1 .</span>
Answer:
An ISOSCELES TRIANGLE
Step-by-step explanation:
Given a triangle ABC with vertices at A(-5, 4), B(4, 1), and C(1, -8), to know the type of triangle this is, we need to find the three sides of the triangles by taking the distance between the points.
Distance between two points is expressed as:
D = √(x2-x1)²+(y2-y1)²
For side |AB|:
A(-5, 4) and B(4, 1)
|AB| = √(4-(-5))²+(1-4)²
|AB| = √9²+3²
|AB| = √90
For side |BC|
B(4, 1), and C(1, -8)
|BC| =√(1-4)²+(-8-1)²
|BC| = √3²+9²
|BC| = √90
For side |AC|:
A(-5, 4) and C(1, -8).
|AC| = √(1-(-5))²+(-8-4)²
|AC| = √6²+12²
|AC| = √36+144
|AC| = √180
Based on the distances, it is seen that side AB and BC are equal which shows that two sides of the triangle are equal. A triangle that has two of its sides to be equal is known as an ISOSCELES TRIANGLE. Therefore the term that correctly describes the triangle is an isosceles triangle.
2464 ÷ 2 = 1232 ;
1232 is half of 2464.
Answer:
3.5 miles
Step-by-step explanation:
