Translate the following statement into a mathematical equation:

An angry student murdered Tommy the Turtle near the northern fence of the park. Using yellow tape,Ranger Dave is marking off a r

pishuonlain [190]

Answer:

60ft

Step-by-step explanation:

Let's x, y be the width and length of the surrounding rectangle. Since the area is 450 sq feet, this means xy = 450 or y = 450/x

The perimeter of this rectangle is (since there are 3 sides only)

f(x,y) = 2x + y

This is something we need to minimize. We can start by substituting y = 450/x

f(x) = 2x + 450/x

Let's take the first derivative of this function and set it to 0

$f'(x) = 2 - \frac{450}{x^2} = 0$

$2 = \frac{450}{x^2}$

$x^2 = 450 / 2 = 225$

$x = \sqrt{225} = 15ft$

y = 450 / 15 = 30ft

so the minimum perimeter that needs taping over is

f(x,y) = 2x + y = 2*15 + 30 = 60ft

5 0

3 years ago

What is the measure of AngleDCF? Three lines extend from point C. The space between line C D and C E is 75 degrees. The space be

gizmo_the_mogwai [7]

Answer:

∠DCF = 129°

Step-by-step explanation:

We assume that line CE is between lines CD and CF.

The angle sum theorem applies:

∠DCF = ∠DCE +∠ECF

∠DCF = 75° +54°

∠DCF = 129°

4 0

3 years ago

Read 2 more answers

The combined area of the 3 windowpanes and frame shown below is 924 in.2. The frame is of uniform width. What is the side length

wariber [46]

Answer:

Option A. $x=10\ in$

Step-by-step explanation:

we know that

The combined area of the 3 windowpanes and frame is equal to

$(3x+12)(x+12)=924\\ \\3x^{2}+36x+ 12x+144=924\\ \\ 3x^{2}+48x-780=0$

using a graphing tool to solve the quadratic equation

The solution is $x=10\ in$

see the attached figure

5 0

3 years ago

Given the curve y=3x^5+6x^4-4x^3+1 find it's turning point and point of inflection

g100num [7]

Maximum and minimum turning points at (-2|33); (0.4|0.928)

Inflection points at (-1.472|21.195); (0|1); (0.272|0.957)

3 0

2 years ago

Which figure is the image produced by applying the composition T 0,3 o R0,90 to figure R?

Lyrx [107]

We are given original image R.

It is being translated by (0,3) first and then rotated by a positive angle 90 degrees.

Translation by (0,3) represents (x,y) --> (x, y+3) rule.

Positive 90 degree rotation represents, counterclockwise rotation.

The rule for counterclockwise rotation is (x,y) --> (-y,x).

Therefore, final rule for would be

(x,y) --> ( -y,x+3 )

Let us take a coordinate of R on y-axis as (0,-4).

Now if we apply rule (x,y) --> ( -y,x+3 ) we get

(0,-4) --> (-(-4), 0+3) = (4,3).

Let us check the figure with coordinate (4,3).

We can clearly see that Figure H has transformed coordinate (4,3).

<h3>Therefore, correct option is first option A. figure H.</h3>

8 0

3 years ago