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3 years ago

The divison of the whole bumber N by 13 gives a quotient of 15 and a remainder of 12. Find N

1 answer:

7 0

N/13 = 15 with a remainder of 12:

Multiply both sides of this eq'n by 13, to eliminate fractions:

15N = 13(15) + 12 = 195 + 12 = 207

Let's check our answer.

Divide 13 into 207. Using a calculator, we find the quotient is 15.923.

The remainder is 0.923 times 13, or 12.

The number N is 207

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2 years ago

Find the minimum and maximum of f(x, y, z) = y + 4z subject to two constraints, 2x + z = 4 and x2 + y2 = 1. g

yuradex [85]

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$1+2\lambda_2y=0\implies\lambda_2y=-\dfrac12\implies8y=-x$

$x^2+y^2=1\implies (-8y)^2+y^2=65y^2=1\implies y=\pm\dfrac1{\sqrt{65}}$
$y=\pm\dfrac1{\sqrt{65}}\implies x=\mp\dfrac8{\sqrt{65}}$
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We have two critical points to consider: $\left(-\dfrac8{\sqrt{65}},\dfrac1{\sqrt{65}},4+\dfrac{16}{\sqrt{65}}\right)$ and $\left(\dfrac8{\sqrt{65}},-\dfrac1{\sqrt{65}},4-\dfrac{16}{\sqrt{65}}\right)$ .

At these points, we respectively have a maximum of $16+\sqrt{65}$ and a minimum of $16-\sqrt{65}$ .

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2 years ago

Which phrase describes the variable expression z+ 8?

grigory [225]

Answer:

Step-by-step explanation:

In math increased means that you are adding.

Have a good day and a good rest of your week!

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2 years ago