Ok so I like to go in steps with these questions- first draw a picture and identify your variables.
W=width
L= 3w-1
Now we know that length times width gets us area so we plug in our variables into the area equation.
200 = w(3w-1)
When you foil that equation you end up with a quadratic : 3w^2-w-200 = 0
Either factor that or use the quadratic formula to get
w= 8.33 and w= -8
Since you can't have a negative dimension you need to use 8.33 and plug it back into your length equation.
Final answer:
w= 8.33ft
l= 23.99ft
*Now I simplified the decimals a little bit so you end up with 199.8ft^2 for the area so just add a few decimals on here and there*
5/3 each friend gets 3/5 of the trail mix
Answer:
the angle between their paths is <em>100.8°</em>
Step-by-step explanation:
From the given information, you can construct a triangle, just like the one in the figure.
We will use the <em>Cosine Rule</em> which is:
c² = b² + a² - 2 b c cos(θ)
where
- c = 16 miles
- b = 8 miles
- a = 12 miles
Therefore,
2 b c cos(θ) = b² + a² - c²
cos(θ) = (b² + a² - c²) / 2 b c
θ = cos⁻¹( (b² + a² - c²) / (2 b c) )
θ = cos⁻¹( (8² + 12² - 16²) / 2(8)(16) )
<em>θ = 100.8°</em>
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Therefore, the angle between their paths is <em>100.8°</em>
Let the width = w.
The length is 6 times the width, so the length is 6w.
The perimeter is 70.
P = 2L + 2W
70 = 2(6w) + 2(w)
70 = 12w + 4w
70 = 14w
5 = w
The width is 5.
The length is 6 times the width, so the length is 6 * 5 = 30
Area of rectangle = LW
A = 5 * 30 = 150
