Wow OK so the first number I came to was 72 so that's
bagels 6x12=72
apples 8x9=72
cookies 12x6=72
juice boxes 9x8=72

72/4=18 so she could make their lunch for 18 days

7 0

3 years ago

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If x − 3 = 1, then what is the value of x² − 3x − 1 ?

Kruka [31]

Let's find x. This will allow us to find the value of the second expression.
x - 3 = 1
x = 4

Now, we can simply plug this x-value into the second expression to obtain 4^2 - 3(4) - 1 = 3.

Thus, our answer is 3.

7 0

3 years ago

Integration: How would I get to this answer?

Scrat [10]

Given that $y$ attains a maximum at $x=1$ , it follows that $y'=0$ at that same point. So integrating once gives

$\displaystyle\int\frac{\mathrm d^2y}{\mathrm dx^2}\,\mathrm dx=\int-8x\,\mathrm dx$
$\dfrac{\mathrm dy}{\mathrm dx}=-4x^2+C_1$
$\implies -4(1)^2+C_1=0\implies C_1=4$

and so the first derivative is $y'=-4x^2+4$ .

Integrating again, you get

$\displaystyle\int\frac{\mathrm dy}{\mathrm dx}\,\mathrm dx=\int(-4x^2+4)\,\mathrm dx$
$y=-\dfrac43x^3+4x+C_2$

You know that this curve passes through the point (2, -1), which means when $x=2$ , you have $y=-1$ :

$-1=-\dfrac43(2)^3+4(2)+C_2$
$\implies C_2=\dfrac53$

and so

$y=-\dfrac43x^3+4x+\dfrac53$

7 0

4 years ago