The sinusoidal function graph has a period of 2·π and a minimum point
with coordinates (-0.5·n·π, -6) where n = -5, -1, 3, ...
Response:
- The minimum value of the function is -6
<h3>How to find the minimum value of a function?</h3>
The minimum value of a function is the lowest vertex value of the
function.
The given graph description, is the graph of the following function;
f(t) = 0.5·sin(t) - 5.5
The minimum value is given at the location where, sin(t) = -1, which gives;
f(t) = 0.5 × (-1) - 5.5 = -6
The minimum value of the function is therefore;
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The weight of the kitten will be no less than the weight of the puppy in 1.4 + 1.2x ≥ 2.8 + 0.5x week.
<h3>What is Inequality?</h3>
Statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
Given:
A puppy weighs 2.8 pounds at birth and gained about 0.5 pounds per week.
A kitten weighs 1.4 pounds at birth and gains about 1.2 pounds per week.
puppy: 2.8 + 0.5x
Kitten: 1.4 + 1.2x
As, kitten is no less than puppy.
Kitten ≥ puppy
1.4 + 1.2x ≥ 2.8 + 0.5x
hence, the weight of the kitten will be no less than the weight of the puppy in 1.4 + 1.2x ≥ 2.8 + 0.5x week.
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5/8+ 2/5
= 25/40+ 16/40
= 41/40
= 1 1/40
The final answer is 1 1/40~
The function is a sine function and, the height of the ball at equilibrium is a feet
<h3>How to determine the height at equilibrium?</h3>
The function of the height is given as:
h = a sin(b (t - h)) k
The above function is a sine function, and the amplitude of the function is the variable a
The amplitude is the height of the ball at equilibrium
Hence, the height of the ball at equilibrium is a feet
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