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3 years ago

15

A restaurant offers a $12 dinner special that has 5 choice for an appetizer, 13 choices for an entree and 4 choice for a dessert

how many different meals are available when you select an appetizer an entree and dessert?

1 answer:

SashulF [63]3 years ago

6 0

Answer:

jcc6ajwu717266w3222

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Line segment Q R , Line segment R S and Line segment S Q are midsegments of ΔWXY.

Llana [10]

Answer:

14.50 cm

Step-by-step explanation:

Based on the midsegment theorem:

The midsegment connecting two sides of triangle is parallel to the third side of the triangle and the length of the midsegment line is half the length of the third side parallel to the midsegment.

From the diagram ;

QR // ZY

XY = 2 * 2.93 = 5.86

RS // XZ

XZ = 2 * 2.04 = 4.08

QS // XY

XY = 2 * 2.28 = 4.56

The perimeter :

(XY + XZ + XY)

5.86 + 4.08 + 4.56

= 14.50 m

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3 years ago

The local museum had 10,000 visitors in 1995.

lora16 [44]

Answer:

Step-by-step explanation:

Vbvvbnn. N m

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3 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.

7 0

3 years ago

Find all points having an x-coordinate of 5 whose distance from the point (2, 6) is 5

galina1969 [7]

Answer:

(5,2) and (5,10)

Step-by-step explanation:

we know that

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

we have

$points\ (2,6),(5,y)\\d=5$

substitute in the formula

$5=\sqrt{(y-6)^{2}+(5-2)^{2}}$

solve for y

$5=\sqrt{(y-6)^{2}+(3)^{2}}$

$5=\sqrt{(y-6)^{2}+9}$

square both sides

$25=(y-6)^{2}+9$

$(y-6)^{2}=25-9$

$(y-6)^{2}=16$

square root both sides

$y-6=\pm4$

$y=6\pm4$

$y=6+4=10$

$y=6-4=2$

therefore

The points are

(5,2) and (5,10)

6 0

3 years ago

Helpppppppp plssssdds

sashaice [31]

Answer:

A. 8.008, 8.08, 8.081, 8.09

B. 14.200, 14.204, 14.210, 14.240

Step-by-step explanation:

4 0

3 years ago