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3 years ago

Question 13. Please

Mathematics

1 answer:

Sonbull [250]3 years ago

8 0

Answer:

Step-by-step explanation:

Δ OPG is right with hypotenuse OG being the radius of the circle

Using Pythagoras' identity in the right triangle

OG² = OP² + PG²

[ PG = 11 , since OP is the perpendicular bisector of FG ]

OG² = 8² + 11² = 64 + 121 = 185

Δ OQS is right with hypotenuse OS being the radius

Using Pythagoras' identity

OS² = QS² + OQ² , that is

185 = 13² + x²

185 = 169 + x² ( subtract 169 from both sides )

16 = x² ( take the square root of both sides )

4 = x → d

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Answer:

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

Step-by-step explanation:

Given

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

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Required

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

Express the function as:

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$y = ab^x$

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

$y = ab^x$

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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)

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

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

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

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

$a = \frac{24}{25}$

The function: $f(x) = ab^x$

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

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