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3 years ago

Enter the value of the exponential expression 5 0 .

Mathematics

1 answer:

cluponka [151]3 years ago

4 0

Answer:

Step-by-step explanation:

5^0

Any number other than 0 raised to the power of zero is 1

5^0 =1

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12:27

Step-by-step explanation:

27 - 15 = 12

There are 12 girls and 15 boys.

12:27 is the ratio of girls to the total amount of students.

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Step-by-step explanation:

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A number is being written in scientific notation. The student moves the decimal point to the left 3 places and _____.

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A number is being written in scientific notation. The student moves the decimal point to the left 3 places and A<span>. multiplies by 10^-3.</span>

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The Ace Novelty company produces two souvenirs: Type A and Type B. The number of Type A souvenirs, x, and the number of Type B s

Molodets [167]

Answer:

500 type A; 3500 type B

Step-by-step explanation:

The method of Lagrange multipliers can solve this quickly. For objective function f(x, y) and constraint function g(x, y)=0 we can set the partial derivatives of the Lagrangian to zero to find the values of the variables at the extreme of interest.

These functions are ...

$f(x,y)=4x+2y\\g(x,y)=2x^2+y-4$

The Lagrangian is ...

$\mathcal{L}(x,y,\lambda)=f(x,y)+\lambda g(x,y)\\\\\text{and the partial derivatives are ...}\\\\\dfrac{\partial \mathcal{L}}{\partial x}=\dfrac{\partial f}{\partial x}+\lambda\dfrac{\partial g}{\partial x}=4+\lambda (4x)=0\ \implies\ x=\dfrac{-1}{\lambda}\\\\\dfrac{\partial \mathcal{L}}{\partial y}=\dfrac{\partial f}{\partial y}+\lambda\dfrac{\partial g}{\partial y}=2+\lambda (1)=0\ \implies\ \lambda=-2$

$\dfrac{\partial\mathcal{L}}{\partial\lambda}=\dfrac{\partial f}{\partial\lambda}+\lambda\dfrac{\partial g}{\partial\lambda}=0+2x^2+y-4=0\ \implies\ y=4-2x^2\\\\\text{We know $\lambda$, so we can find x and y:}\\\\x=\dfrac{-1}{-2}=0.5\\\\y=4-2\cdot 0.5^2=3.5$

Since x and y are in thousands, maximum profit is to be had when the company produces ...

500 Type A souvenirs, and 3500 Type B souvenirs

3 0

3 years ago