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Licemer1 [7]
3 years ago
6

A beach has to enclose a rectangular area, because some endangered species are nesting there. They have 200 feet of rope to rope

off the area with. What is the maximum area that they can rope off?
Mathematics
1 answer:
GuDViN [60]3 years ago
4 0
The maximum area enclosed is a square, then the area will be :

side^2 = (perimeter/4)^2 = (200 feet/4)^2 =  50^2 feet^2 = 2500 feet^2.

We can prove that this is a square:

Call x one side, then the other side is: (200 -2x) / 2 = 100 - x

And the area , S = x(100-x) = 100x - x^2

Maximum area => S' = 0 = 100 -2x => 2x = 100 => x =100/2 = 50

=> 100 - x = 100 - 50 = 50.

Then, when showed that the two sides are equal to 50 feet, and the shape enclosed is a square with area = 2500 ft^2.

 
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WILL MEDAL
Valentin [98]
P(x) = 3x + 200
x=4 ⇒ p(4) = 3(4)+200=12+200=212
x=15 ⇒ p(15) = 3(15)+20=45+200=245

n(x) = 200(1.04)^x
x=4 ⇒ n(4) = 200 (1.04)^4 = 233.97
x=15⇒n(15)=200(1.04)^15 = 360.19

Then n(x) has the highest value in 4 years; n(x) has the highest value in 15 years
 

4 0
3 years ago
The estimated difference of 3209 and 1893, when rounded off to the nearest ten is
almond37 [142]

Answer:

= (3209) - (1893) \\  = 1.32 \times  {10}^{3}  \\  = 1320

\small{ \star{ \underline{ \blue{becker}}}}

8 0
3 years ago
Read 2 more answers
14+y = 3y+2, Find y with a step-by-step explanation.
mrs_skeptik [129]

Answer:

y= 6

Step-by-step explanation:

1. Rearrange the terms before the equal sign: 14+y=3y+2-> y+14=3y+2

2. Subtract 14 from both sides: y+14=3y+2-> y=3y-12

                                                     -14       -14

3. Subtract 3y from both sides: y=3y-12-> y-3y= -12

                                                -3y  -3y  

4. Combine like terms: y-3y= -12-> -2y= -12

                                      1-3 keep the y

5. Divide both sides by -2: -2y= -12-> y= 6

                                              /2    /2

6. So, you're left with y= 6

6 0
3 years ago
A piece if wire 40cm is bent to form a right angled triangle whose hypotenuse is 17cm long find the other two sides of triangle
hjlf

Answer: 150mm

Step-by-step explanation:

Take the two adjecent sides of the triangle to be x and y and X is the angle opposite the side, x.

From the trigonometric identities for a right-angled triangle, it is known that

x=170sin X and;

y=170cos X

Thus the perimeter of the triangle is given by

170sin X + 170cos X + 170 = 400

170(sin X + cos X) = 400 - 170

170(sin X + cos X) = 230

sin X + cos X = 230/170 = 1.3529

Squaring both sides hence,

sin^2(X) + 2sin X.cos X + cos^2(X) = 1.8304

Recall that sin^2(X) + cos^2(X) = 1 and 2sin X.cos X = sin 2X.

Thus, the former expression gives;

1 + sin 2X = 1.8304

sin 2X = 0.8304

2X = arcsin (0.8304)

2X = 56.14° or (180 - 56.14)° = 56.14° or 123.86° for X existing within a triangle.

X = 56.14/2 or 123.86/2

X = 28.07° or 61.93°

Thus the two adjacent sides are ;

x = 170 sin (28.07) = 80mm

y = 170 cos (28.07) = 150mm

Using the value of 61.93° as X would give the same values but interchanged for x and y.

I hope you find this useful.

5 0
3 years ago
If y varies directly with x, find the missing value below.<br><br> (2, -34) and (x, 85)
DedPeter [7]

Answer:

X= -5

Step-by-step explanation:

y varies directly with x,

so y=kx

-34=k×2

k= -17

85= -17× X

X= -5

8 0
3 years ago
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