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san4es73 [151]
3 years ago
7

A spring is hanging from a ceiling. The length L(t) (in cm) of the spring as a function of time t (in seconds) can be modeled by

a sinusoidal expression of the form a*sin(b*t) +d. At t=0, when the spring is exactly in the middle of its oscillation, its length is 7 cm. After 0.5 seconds the spring reaches its maximum length, which is 12 cm. Find L(t).
Mathematics
1 answer:
Zanzabum3 years ago
6 0

Answer:

  L(t) = 5·sin(πt) +7

Step-by-step explanation:

The middle of the oscillation of the given function occurs when t=0. At that point, ...

  L(0) = d = 7

The next maximum of the oscillation occurs when the argument of the sine function is π/2.

  b·t = π/2

  b = π/(2t) = π/(2·0.5) = π

At that maximum, the length is 12, so we have ...

  L(0.5) = a·sin(0.5π) +7 = 12

  a = 5

The function L(t) is ...

  L(t) = 5·sin(πt) +7

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1. Which of the following IS TRUE about an asymptote lines?
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If you help me I'll mark you branliest and give five star rating​
Olenka [21]

Answer:

See explanation for answer, hope it helps

Step-by-step explanation:

Toss; 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

Total number of heads so far; 1, 1, 1, 1, 2, 3, 4, 4, 4, 5

Relative Frequency of heads so far;

\frac{1}{1} = 1.0 = 100%

\frac{1}{2} = 0.5 = 50%

\frac{1}{3} = 0.33 = 33%

\frac{1}{4} = 0.25 = 25%

\frac{2}{5} = 0.4 = 40%

\frac{3}{6} = 0.5 = 50%

\frac{4}{7} = 0.57 = 57%

\frac{4}{8} = 0.5 = 50%

\frac{4}{9} = 0.44 = 44%

\frac{5}{10} = 0.5 = 50%

Total number of tails so far; 0 1, 2, 3, 3, 3, 3, 4, 5, 5

Relative Frequency;

\frac{0}{1} = 0 = 0%

\frac{1}{2} = 0.5 = 50%

\frac{2}{3} = 0.66 = 66%

\frac{3}{4} = 0.75 = 75%

\frac{3}{5} = 0.6 = 60%

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8 0
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quester [9]

Answers:

Step 1 is distributive property

Step 2 is distributive property (again)

Step 3 is commutative property

===============================================

Explanation:

The distributive property is the idea of multiplying the outer value by each inside value in the parenthesis. In general, the rule is a*(b+c) = a*b+a*c. We have the outer term 'a' multiplied by each inner term b and c. Then we add the products. The distributive property is used twice to multiply the two binomials. Your teacher and/or book may refer to it as the FOIL rule. FOIL stands for "first, outer, inner, last" which is a handy way to remember the order in how to multiply binomials.

The commutative property is the idea of adding or multiplying two values in any order we want. In this case, we're focusing on adding. This allows us to swap the terms to go from -5y^2+9x^2 to 9x^2+(-5y^2) = 9x^2-5y^2

4 0
3 years ago
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