Problema Solution
You have 800 feet of fencing and you want to make two fenced in enclosures by splitting one enclosure in half. What are the largest dimensions of this enclosure that you could build?
Answer provided by our tutors
Make a drawing and denote:
x = half of the length of the enclosure
2x = the length of the enclosure
y = the width of the enclosure
P = 800 ft the perimeter
The perimeter of the two enclosures can be expressed P = 4x + 2y thus
4x + 3y = 800
Solving for y:
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y = 800/3 - 4x/3
The area of the two enclosure is A = 2xy.
Substituting y = 800/3 - 4x/3 in A = 2xy we get
A = 2x(800/3 - 4x/3)
A =1600x/3 - 8x^2/3
We need to find the x for which the parabolic function A = (- 8/3)x^2 + (1600/3)x has maximum:
x max = -b/2a, a = (-8/3), b = 1600/3
x max = (-1600/3)/(2*(-8/3))
x max = 100 ft
y = 800/3 - 4*100/3
y = 133.33 ft
2x = 2*100
2x = 200 ft
Answer:
1. y = 14.718
2. ??
3. y = 39.794°
Step-by-step explanation:
<em>HINT the side we already know and the side we are trying to find, we use the first letters of their names and the phrase "SOHCAHTOA" to decide which function:
</em>
SOH...
Sine: sin(θ) = Opposite / Hypotenuse
...CAH...
Cosine: cos(θ) = Adjacent / Hypotenuse
...TOA
Tangent: tan(θ) = Opposite / Adjacent
1. Sine: sin(θ) = Opposite / Hypotenuse
sin(42°) = y / 22
so on your calculator enter 42 then sin = 0.669
0.669 = y/22 multiply both sides by 22 to get y
y = 14.718
2. is there any other information??
3. The two sides we know are Opposite 40 and Adjacent 48.
SOHCAHTOA tells us we must use Tangent.
Calculate Opposite/Adjacent = 40/48 = 0.833
Find the angle from your calculator using tan-1
Tan y° = opposite/adjacent = 40/48 = 0.833
tan-1 of 0.833 = 39.794°
Answer:
g(-1) = -5
g(2a+1) = 16a+11
Step-by-step explanation:
Substitute the given value into the function and evaluate.
So for g(x) = 8x+3
You substitute g(-1)
So g(-1) = 8(-1)+3
That is how you get -5
Then g(2a+1)
So g(2a+1) = 8(2a+1)+3
Thats how you get 16a+11
Hope this helps. Mark as brainlist
Answer:
x = log(33)/(3·log(2))
Step-by-step explanation:
The relevant logarithm relation is ...
log(a^b) = b·log(a)
__
Taking the logarithm of both sides of your equation gives ...
2^(3x) = 33
log(2^(3x)) = log(33)
(3x)·log(2) = log(33)
The coefficient of x is 3·log(2). Dividing by that gives the value of x:
x = log(33)/(3·log(2))
x ≈ 1.51851/(3·0.301030) ≈ 1.6814647
