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3 years ago

Find an explicit formula for the arithmetic sequence 170, 85, 0, -85,....

2 answers:

7 0

The arithmetic sequence is x - 85 for each one.

170 - 85 = 85
85 - 85 = 0
0 - 85 = -85
and so on

so you subtract 85 each time

hope this helps

Mamont248 [21]3 years ago

3 0

Answer:

170-85(n-1)

Step-by-step explanation:

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Solid: A square pyramid. The square base has side lengths of 5. The 4 triangular sides have a base of 5 and height of 7. What is

lina2011 [118]

Answer:

95 square units

Step-by-step explanation:

Surface area of pyramid = 4(side area) + base

Solve for the base first.

Area of base = s*s = 5*5 = 25

Next solve for one of the sides.

Area of triangle = 1/2 b*h = 1/2 5*7 = 17.5

Plug these back into our original equation.

Surface area of pyramid = 4(side area) + base

Surface area of pyramid = 4(17.5) + 25

Surface area of pyramid = 70 + 25 = 95 square units

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3 years ago

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Reuben is making a replica of the US flag for his school project.

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P1=2.5+2.5+4.75+4.75=14.5 cm

0.5 cm - 1 in
2.5 cm - 5 in
4.75 cm - 9.5 in

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3 years ago

Distance between two ships At noon, ship A was 12 nautical miles due north of ship B. Ship A was sailing south at 12 knots (naut

frozen [14]

Answer:

a) $\sqrt{144-288t+208t^2}$ b.) -12knots, 8 knots c) No e) $4\sqrt{13}$

Step-by-step explanation:

We know that the initial distance between ships A and B was 12 nautical miles. Ship A moves at 12 knots(nautical miles per hour) south. Ship B moves at 8 knots east.

We know that at time t , the ship A has moved $12\dot t (n.m)$ and ship B has moved $8\dot t (n.m)$ . We also know that the ship A moves closer to the line of the movement of B and that ship B moves further on its line.

Using Pythagorean theorem, we can write the distance s as:

$\sqrt{(12-12\dot t)^2 + (8\dot t)^2}\\s=\sqrt{144-288t+144t^2+64t^2}\\s=\sqrt{144-288t+208t^2}$

We want to find $\frac{ds}{dt}$ for t=0 and t=1

$\sqrt{144-288t+208t^2}|\frac{d}{dt}\\\\\frac{ds}{dt}=\frac{1}{2\sqrt{144-288t+208t^2}}\dot (-288+416t)\\\\\frac{ds}{dt}=\frac{208t-144}{\sqrt{144-288t+208t^2}}\\\\\frac{ds}{dt}(0)=\frac{208\dot 0-144}{\sqrt{144-288\dot 0 + 209\dot 0^2}}=-12knots\\\\\frac{ds}{dt}(1)=\frac{208\dot 1-144}{\sqrt{144-288\dot 1 + 209\dot 1^2}}=8knots$

We know that the visibility was 5n.m. We want to see whether the distance s was under 5 miles at any point.

Ships have seen each other = $s\leq 5\\\\\sqrt{144-288t+208t^2}\leq 5\\\\144-288t+208t^2\leq 25\\\\199-288t+208t^2\leq 0$

Since function $f(x)=199-288x+208x^2$ is quadratic, concave up and has no real roots, we know that $199-288x+208x^2>0$ for every t. So, the ships haven't seen each other.

Attachedis the graph of s(red) and ds/dt(blue). We can see that our results from parts b and c were correct.

Function ds/dt has a horizontal asympote in the first quadrant if

$\lim_{t \to \infty} \frac{ds}{dt}$

So, lets check this limit:

$\lim_{t \to \infty} \frac{ds}{dt}=\lim_{t \to \infty} \frac{208t-144}{\sqrt{144-288t+208t^2}}\\\\=\lim_{t \to \infty} \frac{208-\frac{144}{t}}{\sqrt{\frac{144}{t^2}-\frac{288}{t}+208}}\\\\=\frac{208-0}{\sqrt{0-0+208}}\\\\=\frac{208}{\sqrt{208}}\\\\=4\sqrt{13}$

Notice that:

$4\sqrt{13}=\sqrt{12^2+5^2}$ =√(speed of ship A² + speed of ship B²)

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3 years ago

A store owner give 5% discount on all his bicycles. For a bicycle prices at $24,000 (without discount) he decides to give an add

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Answer:

23999.98

Step-by-step explanation:

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2 years ago

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( 1 0 3) + (4 1 7) The first entry of the resulting matrix is:

Mamont248 [21]

Hello!

When adding matrices you add the numbers that are in the same position

1 + 4 = 5

0 + 1 = 1

3 + 7 = 10

The answer is (5 1 10)

Hope this helps!

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3 years ago

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