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3 years ago

Briefly describe this graph of a Femis wheel.

Mathematics

1 answer:

son4ous [18]3 years ago

8 0

Answer: This is a periodic relation.

Step-by-step explanation:

This is a periodic relation, that can be modeled with a sinusoidal relation, that relates the height as a function of time.

Then we can write this as h(t) = A*sin(C*t + F) + B

Where A is the amplitude, C is a constant that depends on the period, F is a phase shift, and B is the midpoint of the function.

2*A is the distance between the maximum height and the minimum height.

B is the middle height of the Femis Wheel.

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A box with a square base and open top must have a volume of 296352 c m 3 . We wish to find the dimensions of the box that minimi

mestny [16]

Answer:

Base Length of 84cm
Height of 42 cm.

Step-by-step explanation:

Given a box with a square base and an open top which must have a volume of 296352 cubic centimetre. We want to minimize the amount of material used.

Step 1:

Let the side length of the base =x

Let the height of the box =h

Since the box has a square base

Volume, $V=x^2h=296352$

$h=\dfrac{296352}{x^2}$

Surface Area of the box = Base Area + Area of 4 sides

$A(x,h)=x^2+4xh\\$Substitute h=\dfrac{296352}{x^2}\\A(x)=x^2+4x\left(\dfrac{296352}{x^2}\right)\\A(x)=\dfrac{x^3+1185408}{x}$

Step 2: Find the derivative of A(x)

$If\:A(x)=\dfrac{x^3+1185408}{x}\\A'(x)=\dfrac{2x^3-1185408}{x^2}$

Step 3: Set A'(x)=0 and solve for x

$A'(x)=\dfrac{2x^3-1185408}{x^2}=0\\2x^3-1185408=0\\2x^3=1185408\\$Divide both sides by 2\\x^3=592704\\$Take the cube root of both sides\\x=\sqrt[3]{592704}\\x=84$

Step 4: Verify that x=84 is a minimum value

We use the second derivative test

$A''(x)=\dfrac{2x^3+2370816}{x^3}\\$When x=84$\\A''(x)=6$

Since the second derivative is positive at x=84, then it is a minimum point.

Recall:

$h=\dfrac{296352}{x^2}=\dfrac{296352}{84^2}=42$

Therefore, the dimensions that minimizes the box surface area are:

Base Length of 84cm
Height of 42 cm.

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3 years ago

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aniked [119]

Answer:

Step-by-step explanation:

Yes

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3 years ago

The first three steps in determining the solution set of the system of equations algebraically are shown in the table. y = −x2 +

lianna [129]

You have a system of equations $\left \{ {{y = -x^2+2x-9} \atop {y =-6x+6}} \right.$ .

1. Substitude right side of second equation into the left side of the first equation: $-6x+6=-x^2+2x-9$ .

2. Solve this equation:
$x^2-2x+9-6x+6=0, \\ x^2-8x+15=0, \\ D=(-8)^2-4\cdot 1\cdot 15=64-60=4, \\ \sqrt{D}=2, \\ x_{1,2}=\dfrac{8\pm 2}{2 } =3,5$ .

3. Find y:
for $x_1=3, y_1=-6\cdot 3+6=-18+6=-12$ ,
for $x_2=5, y_2=-6\cdot 5+6=-30+6=-24$ .

4. The solutions of the system are: (3,-12) and (5,-24).
Answer: Correct choice is A.

7 0

3 years ago

Read 2 more answers

Thrice the product of two and "Y".

love history [14]

Answer:

Step-by-step explanation:

We need to solve the statement ' Thrice the product of two and "Y" '.

Thrice means 3 times and product means multiply. It means we have to multiply 3,2 and Y.

Let the result is R. It can be calculated as follows :

$R=3\times 2\times Y$