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3 years ago

Help asap pleaseeee !!!!!!

Mathematics

1 answer:

natima [27]3 years ago

8 0

Answer:

C. ⅓ × (8 + 7) + 12

Step-by-step explanation:

Let's translate each statement given to numerals and symbols first:

Twelve => 12

One-third => ⅓

Sum of 8 and 7 => (8 + 7)

Representing this statement altogether will be:

⅓ of (8 + 7) = ⅓ × (8 + 7)

If 13 is added, we would get:

⅓ × (8 + 7) + 12

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A cylinder shaped can needs to be constructed to hold 500 cubic centimeters of soup. The material for the sides of the can costs

iogann1982 [59]

Answer:

r=3.628cm

h=12.093cm

Step-by-step explanation:

For this problem we are going to use principles, concepts and calculations from multivariable calculus; mainly we are going to use the Lagrange multipliers method. This method is thought to help us to find a extreme value of a multivariable function 'F' given a restriction 'G'. F represents the function that we want to optimize and G is just a relation between the variables of which F depends. The Lagrange method for just one restriction is:

$\nabla F=\lambda \nabla G$

First, let's build the function that we want to optimize, that is the cost. The cost is a function that must sum the cost of the sides material and the cost of the top and bottom material. The cost of the sides material is the unitary cost (0.03) multiplied by the sides area, which is $A_s=2\pi rh$ for a cylinder; while the cost of the top and bottom material is the unitary cost (0.05) multiplied by the area of this faces, which is $A_{TyB}=2\pi r^2$ for a cylinder.

So, the cost function 'C' is:

$C=2\pi rh*0.03+2\pi r^2*0.05\\C=0.06\pi rh+0.1\pi r^2$

The restriction is the volume, which has to be of 500 cubic centimeters:

$V=500=\pi r^2h\\500=\pi hr^2$

So, let's apply the Lagrange multiplier method:

$\nabla C=\lambda \nabla V\\\frac{\partial C}{\partial r}=0.06\pi h+0.2\pi r\\\frac{\partial C}{\partial h}=0.06\pi r\\\frac{\partial V}{\partial r}=2\pi rh\\\frac{\partial V}{\partial h}=\pi r^2\\(0.06\pi h+0.2\pi r,0.06\pi r)=\lambda (2\pi rh,\pi r^2)$

At this point we have a three variable (h,r, λ)-three equation system, which solution will be the optimum point for the cost (the minimum). Let's write the system:

$0.06\pi h+0.2\pi r=2\lambda \pi rh\\0.06\pi r=\lambda \pi r^2\\500=\pi hr^2$

(In this kind of problems always the additional equation is the restricion, in this case, V=500).

Let's divide the first and second equations by π:

$0.06h+0.2r=2\lambda rh\\0.06r=\lambda r^2\\500=\pi hr^2$

Isolate λ from the second equation:

$\lambda =\frac{0.06}{r}$

Isolate h from the third equation:

$h=\frac{500}{\pi r^2}$

And then, replace λ and h in the first equation:

$0.06*\frac{500}{\pi r^2} +0.2r=2*(\frac{0.06}{r})r\frac{500}{\pi r^2} \\\frac{30}{\pi r^2}+0.2r= \frac{60}{\pi r^2}$

Multiply all the resultant equation by $\pi r^{2}$ :

$30+0.2\pi r^3=60\\0.2\pi r^3=30\\r^3=\frac{30}{0.2\pi } =\frac{150}{\pi}\\r=\sqrt[3]{\frac{150}{\pi}}\approx 3.628cm$

Then, find h by the equation $h=\frac{500}{\pi r^2}$ founded above:

$h=\frac{500}{\pi r^2}\\h=\frac{500}{\pi (3.628)^2}=12.093cm$

4 0

3 years ago

it takes 18 3/8 inches of wood to make a frame for a small picture if Ms Jones has 108 inches of wood how many frames can she ma

scZoUnD [109]

It would make 5 complete frames, and about 8/10 of another frame.
108 / 18.375 = 5.8&*)&^&%*$*
I used a calculator.
You could keep adding 18 and 3/8 over and over again until you get right under 108 if you're good at math like me, but most people would have to add 18 and 3/8 separately.

Thanks, and if you liked my answer, please consider giving me the brainliest answer, because I need 5 of them to get to the next level.

6 0

4 years ago

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There are 16 boys and 18 girls what is the probability of the boys name

ExtremeBDS [4]

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3 years ago

Find the Roots of the quadratic equation.<br> 2x2 + 7 – 30 = 0

DIA [1.3K]

Answer:

x=−5/2,6