Roberto invested money into two mutual funds. During the first year, Fund

Please help me what is the answer I need help fast

Vera_Pavlovna [14]

the first step is to convert the diameter into a radius measure by using the formula d=2r

when we solve the formula the radius is calculated to be 1.5

use the surface area formula above and your height and radius measurement to find out the area of sheet metal you would need.

2pi(1.5)^2+2pi(1.5)(5)

using 3.14 for pi this equates to 61.23in^2

3 0

3 years ago

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2. A guy wire for a tree is 20 ft. long, making a 21o angle with the ground. How far is the base of the tree from a stake anchor

Alenkasestr [34]

Answer:

the base of the tree from a stake anchoring the wire is 18.7 ft long

Step-by-step explanation:

A guy wire for a tree is 20 ft. long, making a 21 degree angle with the ground.

It forms a right angle triangle. the hypotenuse of the triangle is 20 ft

The adjacent side of the given angle 21 degree is the base of the tree from a stake

Let x be the base length

$cos(theta)=\frac{adjacent}{hypotenuse}$

$cos(21)=\frac{x}{20}$

$20cos(21)=x$

$x=18.7$

the base of the tree from a stake anchoring the wire is 18.7 ft long

3 0

4 years ago

Of the 1,500 muffins a bakery sold in one day, 1/3 were chocolate. how many chocolate muffins did the bakery sell?

lara [203]

That'd be one third of 1500 muffins, or 500 muffins.

3 0

3 years ago

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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

Write the equation for the linear function. A={(x,y): (0,2)(-2,0)(-3,1)...}

Kay [80]

Answer:

y=x+2

Step-by-step explanation:

To find the equation of a line or linear function, you need at least two points that lie on the line. This is to find the slope or gradient of the line if it's not given. Let's use the two points (0,2) and (-2,0). The first coordinate in each point is X and the second is the y coordinate.

GRADIENT/SLOPE=[y1-y2]/[x1-x2]

=[2-0]/[0-2]=1

The equation of a linear function is given. by Y-y1=m(X-x1)

Y-2=1(X-0)

Y=X+2

VERIFICATION OF SOLUTION

You may want to verify whether you are right by substituting values of x to see if you can obtain corresponding y values.

Example: if x=0, y=0+2=2.This confirms first point

6 0

3 years ago