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victus00 [196]
3 years ago
14

What is the 13th term of the arithmetic sequence? A. 3 B. 3 1/2 C. 4 D. 3 3/4

Mathematics
1 answer:
konstantin123 [22]3 years ago
4 0
Here, a = 3/4, d = 1 - 3/4 = 1/4, n = 13
a(n) =  a + ( n - 1)d
a(n) = 3/4 + (13-1)1/4
a(n) = 3/4 + 12/4
a(n) = 3/4 + 3
a(n) = 15/4
a(n) = 3 3/4

In short, Your Answer would be Option D

Hope this helps!
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Paul biked 55 miles in 10 hours . what is the unit rate of miles per hour
irinina [24]

Answer:

5.5 miles per hour

Step-by-step explanation:

Since he travels a total of 55 miles in 10 hours, you need to divide.

55/10 = 5.5

total hours/total miles = miles per hour

3 0
3 years ago
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In the figure below, AB is a diameter of circle P.
salantis [7]

Answer:

( 41° * π * radius) / 180

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2 years ago
Santos is a lifeguard and spots a drowning child 50 meters along the shore and 60 meters from the shore to the child. Santos run
Amanda [17]

Answer:

Santos should run approximately 36.145 meters along the shore

Step-by-step explanation:

The given parameters are;

The distance along the shore of the child = 50 meters

The distance from the shore of the child = 60 meters

The rate at which Santos can run = 4 m/s

The rate he can swim = 0.9 m/s

Let 'x' represent the distance he runs along the shore

We have;

The time he spends running on the shore, t₁ = x/4

The time he spends swimming, t₂ = (√(60² + (50 - x)²)/0.9

The total time, T = t₁ + t₂ = x/4 + (√(60² + (50 - x)²)/0.9

To find the maximum, we have;

dT/dx = 0 = d(x/4 + (√(60² + (50 - x)²)/0.9)/dx = 1/4 - (50 - x)/(0.9·(√(60² + (50 - x)²) = 0

1/4 - (50 - x)/(0.9·(√(60² + (50 - x)²) = 0

Simplifying using a graphing calculator gives;

\dfrac{x - 2000}{9} = \sqrt{x^2-100\cdot x+6,100}

1519·x² - 151900·x + 3505900 = 0

x = (151900 ± √((-151900)² - 4×1519×3505900))/(2 × 1519)

x ≈ 63.86 m or x ≈ 36.145 m

We note that the distance from a point x = 63.83 meters and 36.145 meters from where Santos spots the girl to the location of the girl are the same

Therefore, Santos should run approximately 36.145 meters along the shore before jumping into to the water in order to save the child

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2 years ago
Subject is Trigonometry. Solve for X.
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