A map has a scale of 2 inches = 50 miles. If the

Mathematics

1 answer:

Inessa05 [86]2 years ago

3 0

Answer:

175 miles apart.

Step-by-step explanation:

This is because 2 goes into seven 3 times and half of 50 is 25 so for 1 inch it would be 25 miles. 50+50+50+25=175 miles.

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Please help me

scZoUnD [109]

4x+y>-6
y>-4x-6
Then:
(-1,-1)
if x=-1; and y=-1

-1>-4(-1)-6
-1>4-6
-1>-2;
(-1,-1) is a solution for this in-equation.

(0,-9)
0>-4(-9)-6
0>36-6
0>30 this is not true, therefore (0,-9) is not a solution.

(4,-20)
-20>-4(4)-6
-20>-16-6
-20>-22 This is true, therefore (4,-20) is a solution.

(2,0)
0>-4(2)-6
0>-8-6
0>-14 This is true, therefore (2,0) is a solution.

(-3,6)
6>-4(-3)-6
6>12-6
6>6 This is not true, therefore (-3,6) is not a solution for this in-equality.

Answer: The next pairs are solutions to this inequality: (-1,-1) , (4,20), (2,0).

8 0

2 years ago

A hiker is hiking in a valley. The height of the valley is h(x,y)=4x2+y2 where x and y are the east-west and north-south distanc

Ainat [17]

Answer:

A. $\frac{\partial{h}}{\partial{t}}=0$

Step-by-step explanation:

A. The problems asked for 2 ways to solve it, expanding the equation with the substitution x(t)=2 cos(t) and y(t)=4 sin(t) to differentiate it . The other way is by chain rule.

Expanding and differentiating:

We start by substituting x(t)=2 cos(t) and y(t)=4 sin(t) in h(x,y)=4x2+y2:

$h(x,y)=4x^{2}+y^{2}= 4(2cos(t))^{2}+(4sin(t))^{2}\\h(x,y)=4(4cos^{2}(t))+(16sen^{2}(t))\\h(x,y)=16cos^{2}(t)+16sen^{2}(t)=16(sen^{2}(t)+cos^{2}(t))\\h(x,y)=16$

So, in the path that the hiker chose:

$\frac{\partial{h}}{\partial{t}}=0$

Chain rule:

We start differentiating h(x,y) using chain rule as follows:

$\frac{\partial{h}}{\partial{t}}= \frac{\partial{h}}{\partial{x}}\frac{\partial{x}}{\partial{t}}+\frac{\partial{h}}{\partial{y}}\frac{\partial{y}}{\partial{t}}$

Now, it´s easy to find all these derivatives:

$\frac{\partial{h}}{\partial{x}}=8x\\\frac{\partial{x}}{\partial{t}}=-2sin(t)\\\frac{\partial{h}}{\partial{y}}=2y\\\frac{\partial{y}}{\partial{t}}=4cos(t)$