Can someone check my work please?
1 answer:
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Given:
An exponential function passes through the points (0, 12000) and (2, 3000).
To find:
The values of a and b.
Solution:
We have,
...(i)
It passes through the point (0,12000). Putting x=0 and f(x)=12000 in (i), we get
Given function passes through the point (2,3000). Putting x=2, a=12000 and f(x)=3000 in (i), we get
Taking square root on both sides.
For an exponential function b cannot be negative. So, .
Therefore, the value of a is 12000 and the value of b is .
Answer:
The three given points are the vertices of a right triangle.
Step-by-step explanation:
To determine that the three points are the vertices of a right triangle let us find the distance between each two points
The formula of the distance is
∵ = 6 and
= -6
∵ = 9 and
= -6
∴ =
∴ = 3
∵ = 6 and
= -6
∵ = 9 and
= 1
∴ =
∴ =
∵ = 9 and
= 1
∵ = 9 and
= -6
∴ =
∴ = 7
<em>Let us use the fact that if the square of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle at the vertex which opposite to the longest side</em>
∵ The longest side is
∵ The other two sides are 3 and 7
∵ ( )² = 58
∵ (3)² + (7)² = 9 + 49 = 58
∴ ( )² = (3)² + (7)²
- By using the fact above
∴ The triangle is a right triangle
The three given points are the vertices of a right triangle.