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Andrew [12]
3 years ago
10

Find x.______________a0

Mathematics
1 answer:
velikii [3]3 years ago
4 0

Answer:

x=4

Step-by-step explanation:

Before we find x, we need to set up this triangle a little more. We need to find the triangle's altitude before we can solve for x. We will use the heartbeat method to find the altitude.

Let altitude = y; solve for y:

\frac{2}{y}=\frac{y}{6}

y^2=12

y=\sqrt{12}

y=2\sqrt{3}

Now that we know the altitude, we can use the Pythagorean Theorem to find the hypotenuse (x).

a^2+b^2=c^2

2^2+(2\sqrt{3})^2=c^2

4+12=c^2

c^2=16

c=4

Since c and x are the same; c is just the hypotenuse in the Pythagorean Theorem.

x=4

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suppose that the current canadian dollar to US dollar exchange rate is 0.80 CAD = $1 US and that the U.S. dollar price of an App
Deffense [45]

Answer: 256 CAD

Step-by-step explanation:

Hi, to answer this question we simply have to multiply the price in US dollars of the iphone (320) and multiply it by 0.80 ( Canadian dollar to US dollar exchange rate)

Mathematically speaking:

Since:

$1 US = 0.80 CAD  

$320 x0.80 = 256 CAD

Feel free to ask for more if needed or if you did not understand something.

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3 years ago
A black line is shorter than a white line.the white line is shorter than a gray line. Is the black line longer or shorter than t
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Black is shorter than grey

Hope this helps
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3 years ago
Read 2 more answers
4) Choose the correct inequality for this situation.
Ksenya-84 [330]

Answer:

B. 21x + 40 ≤ 124

Step-by-step Explanation:

Maximum amount budgeted = $124 (this means they can't spend more than this)

x = number of people

Cost per head = $21

Given that Mr Walter already spent $40, which is part of the money budgeted, the number of people that can go canoeing cam be expressed with the following inequality:

21x + 40 ≤ 124

(note: the amount total to be spent will either be equal to or greater than $124, because it's the maximum amount budgeted for spending).

6 0
3 years ago
Kelsey’s bank charged her $17.50 for using her debit card at ATMs that are not owned by her bank 7 times in the last month. What
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4 0
2 years ago
Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interv
sleet_krkn [62]

Answer:

(0, 16]

Step-by-step explanation:

∑ₙ₌₁°° (-1)ⁿ⁺¹ (x−8)ⁿ / (n 8ⁿ)

According to the ratio test, if we define L such that:

L = lim(n→∞) |aₙ₊₁ / aₙ|

then the series will converge if L < 1.

aₙ = (-1)ⁿ⁺¹ (x−8)ⁿ / (n 8ⁿ)

aₙ₊₁ = (-1)ⁿ⁺² (x−8)ⁿ⁺¹ / ((n+1) 8ⁿ⁺¹)

Plugging into the ratio test:

L = lim(n→∞) | (-1)ⁿ⁺² (x−8)ⁿ⁺¹ / ((n+1) 8ⁿ⁺¹) × n 8ⁿ / ((-1)ⁿ⁺¹ (x−8)ⁿ) |

L = lim(n→∞) | -n (x−8) / (8 (n+1)) |

L = (|x−8| / 8) lim(n→∞) | n / (n+1) |

L = |x−8| / 8

For the series to converge:

L < 1

|x−8| / 8 < 1

|x−8| < 8

-8 < x−8 < 8

0 < x < 16

Now we check the endpoints.  If x = 0:

∑ₙ₌₁°° (-1)ⁿ⁺¹ (0−8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° -(-1)ⁿ (-8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° -(8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° -1 / n

This is a harmonic series, and diverges.

If x = 16:

∑ₙ₌₁°° (-1)ⁿ⁺¹ (16−8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° (-1)ⁿ⁺¹ (8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° (-1)ⁿ⁺¹ / n

This is an alternating series, and converges.

Therefore, the interval of convergence is:

0 < x ≤ 16

Or, in interval notation, (0, 16].

4 0
3 years ago
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