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strojnjashka [21]
2 years ago
10

Please help!! will list brainlist!!!!!

Mathematics
1 answer:
vivado [14]2 years ago
4 0

Answer:

b. 3t ≥ 36

Step-by-step explanation:

She gets $3 per three-pointer. The variable <em>t</em> stands for three-pointer. So in mathematical terms, it would be 3<em>t</em>.

She wants a minimum of 36 dollars, therefore the sign would be ≥. This means 3<em>t </em>has to be greater than or equal to 36.

So, 3<em>t</em> ≥ 36

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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
What is the solution to the equation?
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Belina bought 4 1/2 yards of red fabric. She also bought 6 yards of white fabric. How many inches of white fabric than red fabri
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First, I will made 4 1/2 into the decimal which is 4.5. Then, I add 6 with 4.5 to find the total fabric that Belinda will buy which is 10.5 in total. As a result, Belinda buys total 10.5 white and red fabrics.
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The egation is 58/0.79=73
the cocoa ways 73% of the grams and 73% of 58 is 42 so the cocoa weighs 42 grams in total

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A circle containing the point (6, 1) has its center at (3, 5). Complete the description of the changes in the circumference and
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Step-by-step explanation:

eue7e7euydhdhrydyydhdhdhdhhr

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