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2 years ago

Please help me with these 6 through 10 :)

Mathematics

1 answer:

drek231 [11]2 years ago

3 0

6.) constant = 75

7.) open sentence = 6 + 22 = 28

8.) equation = 17 + b = 47

9.) solution = when x + 37 = 62, x = 25

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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 tin man has a head that is a cylinder with a cone on top. the height of the cylinder is 12 inches and the height of the cone i

lisov135 [29]

I believe your answer is b.

3 0

2 years ago

Read 2 more answers

What are the potential solutions of In(x2 - 25) = 0?

Paha777 [63]

Answer:

$x=\pm\sqrt{26}$

Step-by-step explanation:

$ln(x^2-25)=0$

$e^{ln(x^2-25)}=e^0$

$x^2-25=1$

$x^2=26$

$x=\pm\sqrt{26}$

7 0

2 years ago

A pine tree measured 40½ feet tall. Over the next 7½ years, it grew to a height of 57 feet. During the 7½ years, what was the av

Anit [1.1K]

I got 2.2 feet each year

6 0

3 years ago

Can someone please help me out? It would really make me happier if you did.

asambeis [7]

Answer:

B) 8 and 24.

Step-by-step explanation:

Just by looking at the answer choices, since one number must be three times the other, we can determine that the correct answer is B.

Regardless, let's work this out mathematically. Let the first number be a and the second number be b.

Their difference is 16. Hence:

$a-b=16$

The first number is three times the second number. So:

$a=3b$

Substitute:

$3b-b=16$

Solve for b. Subtract:

$2b=16$

And divide both sides by two:

$b=8$

So, the second number is 8.

And since the first number is three times the second, the first number is 24.

Our answer is B as expected.

5 0

2 years ago