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AfilCa [17]
3 years ago
9

The two shorter sides of a triangle are the same length. The length of the longer side is 5 m longer than each of the shorter si

des. The perimeter of the triangle is 29 m.
What is the length of the longest side of the triangle?

8 m

12 m

13 m

17 m
Mathematics
1 answer:
Korolek [52]3 years ago
3 0
13 m.
29 - 5 = 24
24/3=8
8+5=13
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An island is 1 mi due north of its closest point along a straight shoreline. A visitor is staying at a cabin on the shore that i
Elanso [62]

Answer:

The visitor should run approximately 14.96 mile to minimize the time it takes to reach the island

Step-by-step explanation:

From the question, we have;

The distance of the island from the shoreline = 1 mile

The distance the person is staying from the point on the shoreline = 15 mile

The rate at which the visitor runs = 6 mph

The rate at which the visitor swims = 2.5 mph

Let 'x' represent the distance the person runs, we have;

The distance to swim = \sqrt{(15-x)^2+1^2}

The total time, 't', is given as follows;

t = \dfrac{x}{6} +\dfrac{\sqrt{(15-x)^2+1^2}}{2.5}

The minimum value of 't' is found by differentiating with an online tool, as follows;

\dfrac{dt}{dx}  = \dfrac{d\left(\dfrac{x}{6} +\dfrac{\sqrt{(15-x)^2+1^2}}{2.5}\right)}{dx} =  \dfrac{1}{6} -\dfrac{6 - 0.4\cdot x}{\sqrt{x^2-30\cdot x +226} }

At the maximum/minimum point, we have;

\dfrac{1}{6} -\dfrac{6 - 0.4\cdot x}{\sqrt{x^2-30\cdot x +226} } = 0

Simplifying, with a graphing calculator, we get;

-4.72·x² + 142·x - 1,070 = 0

From which we also get x ≈ 15.04 and x ≈ 0.64956

x ≈ 15.04 mile

Therefore, given that 15.04 mi is 0.04 mi after the point, the distance he should run = 15 mi - 0.04 mi ≈ 14.96 mi

t = \dfrac{14.96}{6} +\dfrac{\sqrt{(15-14.96)^2+1^2}}{2.5} \approx 2..89

Therefore, the distance to run, x ≈ 14.96 mile

6 0
3 years ago
The function f(x) varies directly with x and f(x)=12 when x=8
malfutka [58]
F(x) = kx
12 = 8k
k = 12/8 = 3/2

Required equation is f(x) = 3/2 x
4 0
3 years ago
13 / 1/4 jrjhdbfhfnfndnsnd
gtnhenbr [62]
The answer would be 52
7 0
3 years ago
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A 9 inch candle burns -2/3 inch per hour. How long will it take the candle to burn completely?
Luda [366]
Gbbdnn sbxrbrndmndnsmxnnnbbbd
5 0
3 years ago
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A rectangle has a length of x + 5 and width of x - 3. What is the area of the rectangle? Write the answer as a polynomial in sta
goldfiish [28.3K]

Answer:

Step-by-step explanation:

Area = length * width

length: x + 3

width: x - 5

A = (x + 3)(x - 5)

Simplify (x + 3)(x - 5) using the FOIL method:

 

1. First numbers: multiply the first number of each binomial together--x*x = x%5E2

2. Outer numbers: multiply the outer number of each binomial (out of the entire expression, the number farthest to the left (x) and the number farthest to the right (-5))--x*-5 = -5x

3. Inner numbers: multiply the inner number of each binomial--3*x = 3x

4. Last numbers: multiply the last number of each binomial--3*-5 = -15

==> Now, add all of the results together and combine like terms: x%5E2+-+5x+%2B+3x+-+15 = x%5E2+-+2x+-+15

Therefore, A = x%5E2+-+2x+-+15

8 0
3 years ago
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