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2 years ago

Area of each link pls

Mathematics

1 answer:

Juliette [100K]2 years ago

6 0

Answer:

the first one(orange)is 63.2 and the second one is 36

Step-by-step explanation:

how to find the area of something the formula is base x height =area

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1. Suppose we have a six-sided die that we roll once. Let ai represent the event that the result is i. Let Bj represent the even

Alex787 [66]

Using the probability concept, it is found that there is a

a) 0.2 = 20% probability that 3 is obtained.

b) 0.3333 = 33.33% probability that 6 is obtained.

c) 0.6667 = 66.67% probability of a number greater than 3.

d) 0.6667 = 66.67% probability of an even number.

A probability is the number of desired outcomes divided by the number of total outcomes.

Item a:

There are 5 numbers greater than 1, one of which is 3, hence:

$p = \frac{1}{5} = 0.2$

0.2 = 20% probability that 3 is obtained.

Item b:

There are 3 numbers greater than 3, one of which is 6, hence:

$p = \frac{1}{3} = 0.3333$

0.3333 = 33.33% probability that 6 is obtained.

Item c:

There are 3 even numbers, two of which are greater than 3, hence:

$p = \frac{2}{3} = 0.6667$

0.6667 = 66.67% probability of a number greater than 3.

Item d:

There are 3 numbers greater than 3, two of which are even, hence:

$p = \frac{2}{3} = 0.6667$

0.6667 = 66.67% probability of an even number.

A similar problem is given at brainly.com/question/25667645

4 0

3 years ago

Kevin and Randy Muise have a jar containing 70 coins, all of which are either quarters or nickels. The total value of the coins

Nikitich [7]

Answer:

50 nickels, 20 quarters.

Step-by-step explanation:

System of equations (q = # of quarters, n = # of nickels):

q + n = 70, 0.25q + 0.05n = 7.50

the first equation can be changed to q = 70 - n, so we are able to substitute q with 70 - n.

So, it will look like 0.25*70 - 0.25n + 0.05n = 7.50. This can be simplified to 0.2n = 10, which means that n = 50.

Knowing that we can solve q + 50 = 70, which means that q = 20.

6 0

4 years ago

Use the method of Lagrange multipliers to find the dimensions of the rectangle of greatest area that can be inscribed in the ell

Tanzania [10]

Answer:

Length (parallel to the x-axis): $2 \sqrt{2}$ ;

Height (parallel to the y-axis): $4\sqrt{2}$ .

Step-by-step explanation:

Let the top-right vertice of this rectangle $(x,y)$ . $x, y >0$ . The opposite vertice will be at $(-x, -y)$ . The length the rectangle will be $2x$ while its height will be $2y$ .

Function that needs to be maximized: $f(x, y) = (2x)(2y) = 4xy$ .

The rectangle is inscribed in the ellipse. As a result, all its vertices shall be on the ellipse. In other words, they should satisfy the equation for the ellipse. Hence that equation will be the equation for the constraint on x and y.

For Lagrange's Multipliers to work, the constraint shall be in the form: $g(x, y) =k$ . In this case

$\displaystyle g(x, y) = \frac{x^{2}}{4} + \frac{y^{2}}{16}$ .

Start by finding the first derivatives of $f(x, y)$ and $g(x, y)$ with respect to x and y, respectively:

$f_x = y$ ,
$f_y = x$ .

$\displaystyle g_x = \frac{x}{2}$ ,
$\displaystyle g_y = \frac{y}{8}$ .

This method asks for a non-zero constant, $\lambda$ , to satisfy the equations:

$f_x = \lambda g_x$ , and

$f_y = \lambda g_y$ .

(Note that this method still applies even if there are more than two variables.)

That's two equations for three variables. Don't panic. The constraint itself acts as the third equation of this system:

$g(x, y) = k$ .

$\displaystyle \left\{ \begin{aligned} &y = \frac{\lambda x}{2} && (a)\\ &x = \frac{\lambda y}{8} && (b)\\ & \frac{x^{2}}{4} + \frac{y^{2}}{16} = 1 && (c)\end{aligned}\right.$ .

Replace the $y$ in equation $(b)$ with the right-hand side of equation $(b)$ .

$\displaystyle x = \lambda \frac{\lambda \cdot \dfrac{x}{2}}{8} = \frac{\lambda^{2} x}{16}$ .

Before dividing both sides by $x$ , make sure whether $x = 0$ .

If $x = 0$ , the area of the rectangle will equal to zero. That's likely not a solution.

If $x \neq 0$ , divide both sides by $x$ , $\lambda = \pm 4$ . Hence by equation $(b)$ , $y = 2x$ . Replace the $y$ in equation $(c)$ with this expression to obtain (given that $x, y >0$ ) $x = \sqrt{2}$ . Hence $y = 2x = 2\sqrt{2}$ . The length of the rectangle will be $2x = 2\sqrt{2}$ while the height will be $2y = 4\sqrt{2}$ . If there's more than one possible solutions, evaluate the function that needs to be maximized at each point. Choose the point that gives the maximum value.