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nydimaria [60]
3 years ago
12

Consider the surface z = x 2+4y 2+1. Suppose you are walking on this surface directly above a curve C in the xy-plane, where the

parameterized curve C is given by C : x(t) = cost, y(t) = sin t. Find the values of t for which you are walking uphill (increasing z).
Mathematics
1 answer:
Bess [88]3 years ago
5 0

With x(t)=\cos t and y(t)=\sin t, we have

z(t)=x(t)^2+4y(t)^2+1

z(t)=\cos^2t+4\sin^2t+1

z(t)=3\sin^2t+2

Then z(t) has critical points where

\dfrac{\mathrm dz}{\mathrm dt}=6\sin t\cos t=3\sin2t=0

\implies\sin2t=0\implies2t=n\pi\implies t=\dfrac{n\pi}2

where n is any integer.

z(t) is increasing wherever \sin2t>0, which happens for

\dfrac{2n\pi}2

\boxed{n\pi

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A manufacturer makes two types of handmade fancy paper bags. Type A and Type B. Two designers a cutter and a finisher need to wo
Vlad1618 [11]

Answer:

  • 18 Type A bags
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Step-by-step explanation:

The graph shows the constraints and the boundaries of the feasible region. The maximum profit will be had with the manufacture of 18 Type A bags and 24 Type B bags.

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The inequality describing the constraint on cutter hours is ...

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The inequality describing the constraint on finisher hours is ...

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The boundary lines of the solution regions of these inequalities intersect at ...

  (a, b) = (18, 24)

The profit function is such that it doesn't pay to make all of one type or the other bags. The most profit is had for the mix ...

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On the graph, the line representing the profit function will be as far as possible from the origin at the point of maximum profit.

4 0
3 years ago
15/4÷3/4 I need the ans
Vladimir [108]
Use the stay, change, flip method. 
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7 0
3 years ago
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In the coordinate plane, you are given JKL with J(2, 3), K(10,4), and L(6, 10). Using the distance formula, classify JKL
Marrrta [24]

Answer:

Perimeter of JKL = 22.55 unit (Approx.)

Step-by-step explanation:

Given:

Coordinate of J = (2,3)

Coordinate of K = (10,4)

Coordinate of L = (6,10)

Find:

Perimeter of JKL

Computation:

Distance = √(x1 - x2)² + (y1 - y2)²

Distance between JK = √(2 - 10)² + (3 - 4)²

Distance between JK = √64 + 1

Distance between JK = √65

Distance between JK = 8.06 unit

Distance between KL = √(10 - 6)² + (4 - 10)²

Distance between KL = √16 + 36

Distance between KL = √52

Distance between KL = 7.21 unit

Distance between LJ = √(6 - 2)² + (10 - 3)²

Distance between LJ = √4 + 49

Distance between LJ = √53

Distance between LJ = 7.28 unit

Perimeter of JKL = Distance between JK + Distance between KL + Distance between LJ

Perimeter of JKL = 8.06 + 7.21 + 7.28

Perimeter of JKL = 22.55 unit (Approx.)

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Step-by-step explanation:

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