If m and n are two positive real numbers whose product is 10, what is the minimum value of m + 2n
2 + 2(4)
I must assume that you meant t=1 (not t=?1). If t=1, here's what we'd do:
1. Find the x and y values corresponding to t=1. They are:
x=(1)^7+1=2 and y=(1)^8+1=2. (Please note: write t^8 instead of t8, and write t^7 instead of t7.)
2. The slope of the tangent line to the graph is
dy/dt 8t^7+1
dy/dx = ---------- = ---------------- with 1 substituted for t
dx/dt 7t^6
Thus, dy/dx (at t=1) = 9/7
3. Now we have both a point (2,2) on the graph and the slope of the tangent line to the curve at that point: 9/7
4. The tangent line to the curve at (2,2) is found by using the point-slope formula:
y-y1 = m(x-x1)
which comes out to y-2 = 9/7(x-2), or 7y-14 = 9(x-2). You could, if you wished, simplify this result further (e. g., by solving for y in terms of x).
Direct Variation. Since k<span> is constant (the same for every point), we can find </span>k<span> when given any point by dividing the y-coordinate by the x-coordinate. For example, if y varies directly as x , and y = 6 when x = 2 , the constant of variation is </span>k<span> = = 3 . Thus, the equation describing this direct variation is y = 3x .</span>
Answer:
1: No Solutions
2:Infinite solutions
3: One Solution
Step-by-step explanation:
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