Section 7 5 Formulas Applications and Variation Direct

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Section 7. 5 Formulas, Applications and Variation

Section 7. 5 Formulas, Applications and Variation

Direct Variation When a situation is modeled by a linear function of the form

Direct Variation When a situation is modeled by a linear function of the form f(x) = kx or y = kx, where k is a nonzero constant, we say that there is direct variation that y varies directly as x that y is proportional to x The number k is called the variation constant, or the constant of proportionality.

Direct Variation Find k if y varies directly as x given y=30 when x=5,

Direct Variation Find k if y varies directly as x given y=30 when x=5, then find the equation y varies directly as x use the direct variation formula y = kx 30 = k(5) → 6=k Equation → y = 6 x

Direct Variation The number of calories burned while dancing is directly proportional to the

Direct Variation The number of calories burned while dancing is directly proportional to the time spent. It takes 25 minutes to burn 110 calories, how long would it take to burn 176 calories when dancing.

Direct Variation The number of calories burned while dancing is directly proportional to the

Direct Variation The number of calories burned while dancing is directly proportional to the time spent. It takes 25 minutes to burn 110 calories, how long would it take to burn 176 calories when dancing. y = kx It takes 25 minutes to burn 110 calories → 4. 4 ca/min = k how long would it take to burn 176 calories 110 ca = k(25 min) 176 ca = (4. 4 ca/min)(x) → 40 min = x It will take 40 minutes to burn 176 calories

Inverse Variation When a situation is modeled by a rational function of the form

Inverse Variation When a situation is modeled by a rational function of the form f(x) = k/x or y = k/x, where k is a nonzero constant, we say that there is inverse variation that y varies inversely as x that y is inversely proportional to x The number k is called the variation constant, or the constant of proportionality.

Inverse Variation Find k if y varies inversely as x given y = 27

Inverse Variation Find k if y varies inversely as x given y = 27 when x = 1/3, then find the equation y varies inversely as x = inverse variation formula y = k/x 27 = k/(1/3) Equation → → 9=k y = 9/x

Inverse Variation The frequency of a string is inversely proportional to its length. A

Inverse Variation The frequency of a string is inversely proportional to its length. A violin string that is 33 cm long vibrates with a frequency of 260 Hz. What is the frequency when the string is shortened to 30 cm?

Inverse Variation The frequency of a string is inversely proportional to its length. A

Inverse Variation The frequency of a string is inversely proportional to its length. A violin string that is 33 cm long vibrates with a frequency of 260 Hz. What is the frequency when the string is shortened to 30 cm? y=k/x A violin string that is 33 cm long vibrates with a frequency of 260 Hz = k / 33 cm → 8580 HZ/cm = k What is the frequency when the string is shortened to 30 cm

Joint Variation Y varies jointly as x and z if, for some nonzero constant

Joint Variation Y varies jointly as x and z if, for some nonzero constant k, y = kxz

Joint Variation The drag Force F on a boat varies jointly as the wetted

Joint Variation The drag Force F on a boat varies jointly as the wetted surface area A and the square of the velocity of the boat. If the boat traveling 6. 5 mph experiences a drag force of 86 N when the wetted surface area is 41. 2 ft² find the wetted surface area of a boat traveling 8. 2 mph with a drag force of 94 N

Joint Variation The drag Force F on a boat varies jointly as the wetted

Joint Variation The drag Force F on a boat varies jointly as the wetted surface area A and the square of the velocity of the boat. If the boat traveling 6. 5 mph experiences a drag force of 86 N when the wetted surface area is 41. 2 ft² find the wetted surface area of a boat traveling 8. 2 mph with a drag force of 94 N y = kxz² 86 N = k(41. 2 ft²)(6. 5 mph)² →k =. 049405 N/ft²mph² N (Newtons) = kg⋅m/s 2

Homework Section 7. 5 44, 50, 57, 59, 69, 71, 73, 75, 77, 80

Homework Section 7. 5 44, 50, 57, 59, 69, 71, 73, 75, 77, 80