Kajal holds a ruler in some wavy water. The depth of the water t seconds after she starts measuring it, in cm, is given byD(t)=50−23sin(π(t+0.23)).After she starts measuring, when is the first time the depth of the waves is at its average value? Give an exact answer.When t=□ seconds
Q. Kajal holds a ruler in some wavy water. The depth of the water t seconds after she starts measuring it, in cm, is given byD(t)=50−23sin(π(t+0.23)).After she starts measuring, when is the first time the depth of the waves is at its average value? Give an exact answer.When t=□ seconds
Average Depth Value: The average value of the depth is given by the constant term in the equation, which is 50cm.
Finding Average Depth: To find when the depth is at its average value, we set D(t) equal to 50 cm.50=50−23sin(π(t+0.23))
Isolating Trigonometric Function: Subtract 50 from both sides to isolate the trigonometric function.0=−23sin(π(t+0.23))
Solving for Sine Function: Divide both sides by −23 to solve for the sine function.0=sin(π(t+0.23))
Finding Average Value of Sine: The sine function is zero at its average value, which occurs at multiples of π. So we need to find the smallest positive t such that π(t+0.23) is a multiple of π.π(t+0.23)=0
Solving for t: Divide both sides by π to solve for t.t+0.23=0
Final Result: Subtract 0.23 from both sides to find t.t=−0.23
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