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astra-53 [7]
3 years ago
12

!!!!!!!!!!!!!!!!!!!!!

Mathematics
2 answers:
S_A_V [24]3 years ago
8 0

Answer:

A

Step-by-step explanation:

Delicious77 [7]3 years ago
4 0

Answer:

Im gona guess C but im not 100%

Step-by-step explanation:

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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
2 years ago
A line has an x-intercept of 4 and a y-intercept of -2. What is the equation of the line?
Evgesh-ka [11]

Answer:

y=x/2-2

Step-by-step explanation:

it's actually 1/2 times x is how your supposed to write it (like a fraction)

7 0
3 years ago
a recipe for cookies calls for 3/5 of a cup of brown sugar and make 6 cookies if you adjust the recipe to make a cookies how muc
sineoko [7]
Find 3/5 in a decimal and it 6 to get 0.6 + 6 + 6.6 then convert it back to a fraction and you have c cups and 3/5 cup
4 0
3 years ago
Line FG is represented by the equation 8x+3y=10. Which value is the slope of a line perpendicular to line FG
Naddika [18.5K]

Answer:

The correct answer is 3/8

Step-by-step explanation:

It was in my practice and I had gotten it correct.

4 0
3 years ago
The hypotenuse of a 30o-60o-90o triangle measures 4 square 3 inches. What is the length of the shorter leg?
Fofino [41]

<u><em>Answer:</em></u>

The shorter leg is 2\sqrt{3} inches

<u><em>Explanation:</em></u>

The 30°-60°-90° is a special type of right-angled triangles

<u>It has the following special side length:</u>

The length of the side opposite to the 30° is \frac{1}{2} the length of the hypotenuse

The length of the side opposite to the 60° is \frac{\sqrt{3} }{2} of the hypotenuse

<u>Now, we know that</u> the lengths of the sides in a triangle are proportional to the angles

<u>This means that</u> the shortest side will be the one opposite to the smallest angles

In our case, the shortest side will be the one opposite to the 30° angle

We are given that the hypotenuse of the triangle is 4\sqrt{3} in

<u>From the above:</u>

Shorter leg = leg opposite to 30° = \frac{1}{2} * hypotenuse = \frac{1}{2} * 4\sqrt{3} = 2\sqrt{2} inches

Hope this helps :)

5 0
3 years ago
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