Answer:
- b ≤ 10, which means <em>number of books less than or equal to 10.</em>
Explanation:
In mathematical language a<em> constraint</em> is a limitation on the values that a variable can take.
In this case, the constraint is given by the fact that there are 10 books in the reading list from which Henry can choose to read this week.
So, the number of books that he can read is 1, 2, 3, ..., 10 (at most). This is, 10 books is an upper bound.
To represent an upper bound, you use the inequality symbol ≤, which means less than or equal to.
Henry can read as many as 10 books, so that is less than or equal to 10.
If you call b the number of books, the constrain may be written as:
constraint is a condition of an optimization problem that the solution must satisfy. There are several types of constraints—primarily equality constraints, inequality constraints, and integer constraints. The set of candidate solutions that satisfy all constraints is called the feasible set.[1
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).
Answer:
3D shape = cone
height = 3 units
diameter = 6 units
Step-by-step explanation:
3D shape = cone
height = 5 - 2 = 3 units
radius = 0 - (-3) = 3 units
diameter = 2 × radius = 2 × 3 = 6 units
Answer: the peaches were a lighter shade of orange
