Write down an expression for the range of k consecutive integers.

Tamiku [17]

Midpoint formula:

x, y = (x2+x1/2), (y2+y1/2)

x, y= (3+8/2), (4-4/2)

x, y= (5.5), (0)

Therefor the midpoint is (5.5, 0)

Hope I helped :)

7 0

4 years ago

The flight of a cannonball toward a hill is described by the parabola y=2+0.12x- 0.0004x^2

Stells [14]

The computation shows that the placw on the hill where the cannonball land is 3.75m.

<h3>How to illustrate the information?</h3>

To find where on the hill the cannonball lands

So 0.15x = 2 + 0.12x - 0.002x²

Taking the LHS expression to the right and rearranging we have:

-0.002x² + 0.12x -.0.15x + 2 = 0.

So we have -0.002x²- 0.03x + 2 = 0

I'll multiply through by -1 so we have

0.002x² + 0.03x -2 = 0.

This is a quadratic equation with two solutions x1 = 25 and x2 = -40 since x cannot be negative x = 25.

The second solution y = 0.15 * 25 = 3.75

Learn more about computations on:

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Complete question:

The flight of a cannonball toward a hill is described by the parabola y = 2 + 0.12x - 0.002x 2 . the hill slopes upward along a path given by y = 0.15x. where on the hill does the cannonball land?

6 0

2 years ago

For the diagram below, form an equation and then solve it to calculate the value of x

Talja [164]

You apply the sum of interior angles formula ie. (n-2)180. n=number of sides
since a pentagon has 5 sides it will be (5-2)180=540.
now add everything. x-5+x-6+2x-7+x+2x-2=540.
Solve for x: 7x-20=540
7x=540+20
7x=560
x=560/7
x=80

8 0

3 years ago

Find the area of the shaded region where s 18. Round your answer to two decimal places.

lisabon 2012 [21]

Answer:

B

Step-by-step explanation:

17.3&

7 0

3 years ago

You have D dollars to buy fence to enclose a rectangular plot of land (see figure at right). The fence for the top and bottom co

alex41 [277]

The perimeter of the rectangular plot of land is given by the expression below

$P=2x+2y$

On the other hand, since the available money to buy fence is D dollars,

$\begin{gathered} D=4(2x)+3(2y) \\ \Rightarrow D=8x+6y \\ D\rightarrow\text{ constant} \end{gathered}$

Furthermore, the area of the enclosed land is given by

$A=xy$

Solving the second equation for x,

$\begin{gathered} D=8x+6y \\ \Rightarrow x=\frac{D-6y}{8} \end{gathered}$

Substituting into the equation for the area,

$\begin{gathered} A=(\frac{D-6y}{8})y \\ \Rightarrow A=\frac{D}{8}y-\frac{3}{4}y^2 \end{gathered}$

To find the maximum possible area, solve A'(y)=0, as shown below

$\begin{gathered} A^{\prime}(y)=0 \\ \Rightarrow\frac{D}{8}-\frac{3}{2}y=0 \\ \Rightarrow\frac{3}{2}y=\frac{D}{8} \\ \Rightarrow y=\frac{D}{12} \end{gathered}$

Therefore, the corresponding value of x is

$\begin{gathered} y=\frac{D}{12} \\ \Rightarrow x=\frac{D-6(\frac{D}{12})}{8}=\frac{D-\frac{D}{2}}{8}=\frac{D}{16} \end{gathered}$ <h2>Thus, the dimensions of the fence that maximize the area are x=D/16 and y=D/12.</h2><h2>As for the used money,</h2> $\begin{gathered} top,bottom:\frac{8D}{16}=\frac{D}{2} \\ Sides:\frac{6D}{12}=\frac{D}{2} \end{gathered}$ <h2>Half the money was used for the top and the bottom, while the other half was used for the sides.</h2>

7 0

1 year ago