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docker41 [41]
3 years ago
7

Enter an equation for the function that includes the points.Give your answer in a(b)x. In the event that a=1 , give your answer

in form (b)x. (2,2/3) and 3,5/9 The equation is f(x)=
Mathematics
1 answer:
Andrews [41]3 years ago
7 0

Answer:

f(x) = \frac{24}{25} * \frac{5}{6}^x

Step-by-step explanation:

Given

(x_1,y_1) = (2,\frac{2}{3})

(x_2,y_2) = (3,\frac{5}{9})

Required

Write the equation of the function f(x) = ab^x

Express the function as:

y = ab^x

In: (x_1,y_1) = (2,\frac{2}{3})

y = ab^x

\frac{2}{3} = a * b^2 --- (1)

In (x_2,y_2) = (3,\frac{5}{9})

y = ab^x

\frac{5}{9} = a * b^3 --- (2)

Divide (2) by (1)

\frac{5}{9}/\frac{2}{3} = \frac{a*b^3}{a*b^2}

\frac{5}{9}/\frac{2}{3} = b

\frac{5}{9}*\frac{3}{2} = b

\frac{5}{3}*\frac{1}{2} = b

\frac{5}{6} = b

b = \frac{5}{6}

Substitute 5/6 for b in (1)

\frac{2}{3} = a * b^2

\frac{2}{3} = a * \frac{5}{6}^2

\frac{2}{3} = a * \frac{25}{36}

a = \frac{2}{3} * \frac{36}{25}

a = \frac{2}{1} * \frac{12}{25}

a = \frac{24}{25}

The function: f(x) = ab^x

f(x) = \frac{24}{25} * \frac{5}{6}^x

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Kendra swims 126 miles in 3 days, what is the constant rate that Kendra swims per day? a. 40 miles per day c. 42 miles per day b
Leni [432]

Answer:

c. 42 miles per day

Step-by-step explanation:

From the information given, you can use a rule of three to calculate the constant rate that Kendra swims per day given that she swims 126 miles in 3 days:

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5 0
3 years ago
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Zigmanuir [339]

Answer:

6 units

Step-by-step explanation:

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the volume of hemisphere is 1527.4cm^3.find the radius of the hemisphere to the nearest whole whole number.(take π to be 22/7)​
skelet666 [1.2K]

Answer:

radius of the hemisphere = 9 cm approx

Step-by-step explanation:

Volume of hemisphere = \frac{2}{3} \pi r^{3}

1527.4 = \frac{2}{3} * \frac{22}{7} * r^{3}

\frac{7*15274*3}{2*22*10} = r^{3}

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r^{3} = 729

r = \sqrt[3]{729}

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3 years ago
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