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3 years ago

9

Caroline wants to give 8 friends equal size packets of flower seeds to her friends. She has 1/2 pound of flower seeds. How much

will each packet of seeds weigh?

1 answer:

Katena32 [7]3 years ago

4 0

You just have to divide the 1/2 a pound by 8, or equivalently multiply by (1/8):

(1/2)*(1/8) = 1/16 of a pound

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Answer:

a. (4, 1)

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

<u>Algebra I</u>

Solving systems of equations using substitution/elimination

Step-by-step explanation:

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<u>Step 2: Solve for </u><em><u>x</u></em>

<em>Elimination</em>

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<u>Step 3: Solve for </u><em><u>y</u></em>

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An open box is to be made by using a piece of sheet metal with the dimensions of 4m by 2m. Determine the dimensions the box shou

Natali5045456 [20]

Answer:

Dimensions: 0.4 by 3.2 by 1.2

Step-by-step explanation:

I'm assuming here that we are cutting out squares out of each of the metal's corners:

Let x = the length of each cut-out square,

Each base (of the desired net square folded) is 4-2x, and 2-2x respectively,

Volume = x(4-2x)(2-2x)

= 4x^3 - 12x + 8x

Now we take the derivative:

$\frac{d}{dx}\left[4x^3-12x^2+8x\right]\\\\= \frac{d}{dx}\left(4x^3\right)-\frac{d}{dx}\left(12x^2\right)+\frac{d}{dx}\left(8x\right)\\\\= 12x^2-24x+8$

We equate to 0 (0 for max volume), and solve using the quadratic formula:

$12x^2-24x+8=0,\\\\x_{1,\:2}=\frac{-\left(-24\right)\pm \sqrt{\left(-24\right)^2-4\cdot \:12\cdot \:8}}{2\cdot \:12}\\\\= \frac{-\left(-24\right)\pm \:8\sqrt{3}}{2\cdot \:12}\\\\\mathrm{Separate\:the\:solutions}:\\\\x_1=\frac{-\left(-24\right)+8\sqrt{3}}{2\cdot \:12},\:x_2=\frac{-\left(-24\right)-8\sqrt{3}}{2\cdot \:12}\\\\x =\frac{3+\sqrt{3}}{3},\:x=\frac{3-\sqrt{3}}{3}\\\\x=1.57735\dots ,\:x=0.42264\dots$

So we approximate the side lengths to be 1.6 and 0.4 respectively. But when we plug in 1.6 for x, we get the volume as negative. Therefore x has to be 0.4.

Side lengths: 0.4, 4-2(0.4) => 3.2, 2-2(0.4) => 1.2

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3 years ago