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Mathematics

1 answer:

den301095 [7]3 years ago

8 0

Answer:

Step-by-step explanation:

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Civil engineer wants to estimate the maximum number of cars that can safely travel on a particular road at a given speed. He ass

pychu [463]

$N(s)= \frac{89s}{14+14( \frac{s}{17})^2 }
\\
\\N'(s)= (\frac{89s}{14+14( \frac{s}{17})^2 } )'= \frac{89\times 14(1+( \frac{s}{17})^2)-89s\times \frac{28}{17} }{14^2(1+( \frac{s}{17})^2)} 
\\
\\N'(s)=0
\\
\\89\times 14(1+( \frac{s}{17})^2)-89s\times \frac{28}{17}=0
\\
\\1+( \frac{s}{17})^2- \frac{2s}{17} =0
\\
\\289+s^2-34s=0
\\
\\s^2-34s+289=0
\\
\\(s-17)^2=0
\\
\\s=17
$

5 0

3 years ago

Identify whether each equation has no solution, one solution, or infinitely many solutions.

butalik [34]

Answer:

infinitely many
one solution
no solution
one solution

Step-by-step explanation:

1. 4x−x=2x+x

Simplifies to 3x = 3x, which is true for all values of x. Hence there are infinitely many solutions.

___

2. 2x+1=5

True only for x=2; one solution.

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3. 4x+2=5x−x+4

Simplifies to ...

4x +2 = 4x +4

2 = 4 . . . . . . . not true for any value of x; no solution.

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4. 2(x+4)=4(x+2)

Simplifies to ...

2x +8 = 4x +8

0= 2x . . . . . . . . . subtract 2x+8

True only for x=0; one solution.

5 0

3 years ago

A local bagel shop produces two products: bagels (B) and croissants (C). Each bagel requires 6 ounces of flour, 1 gram of yeast,

KengaRu [80]

Answer:

see below

Step-by-step explanation:

If we let X represent the number of bagels produced, and Y the number of croissants, then we want ...

(a) Max Profit = 20X +30Y

(b) Subject to ...

6X +3Y ≤ 6600 . . . . . . available flour

X + Y ≤ 1400 . . . . . . . . available yeast

2X +4Y ≤ 4800 . . . . . . available sugar

_____

Production of 400 bagels and 1000 croissants will produce a maximum profit of $380.

In the attached graph, we have shaded the areas that are NOT part of the solution set. (X and Y less than 0 are also not part of the solution set, but are left unshaded.) This approach can sometimes make the solution space easier to understand, since it is white.

The vertex of the solution space that moves the profit function farthest from the origin is the one we are seeking. The point that does that is (X, Y) = (400, 1000).