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3 years ago

If ANYONE could help ASAP Pls

Mathematics

1 answer:

Goryan [66]3 years ago

7 0

ANSWER

The correct answer is C

EXPLANATION

This is the composition the two functions

We have

$a(x) = 3x + 1$

and

$b(x) = \sqrt{x - 4}$

$(b \circ \: a)(x) = b(a(x))$

$(b \circ \: a)(x) = b(3x + 1)$

We substitute to obtain,

$(b \circ \: a)(x) = \sqrt{(3x + 1) - 4}$

$(b \circ \: a)(x) = \sqrt{3x - 3}$

The domain of this function can be found by solving,

$3x - 3 \geqslant 0$

This implies that

$3x \geqslant 3$

Or

$x \geqslant 1$

In interval notation, we have,

$[1, \infty )$

The correct answer is option C

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3 years ago

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Answer:

Month 4

Step-by-step explanation:

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This equation has the following form:

$y = C_1 (2^{x-1})$

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x is the number of months: {1, 2, 3, 4, 5 ... x}

x = 1 represents month 1.

So:

$Charles\ City\ (km) = 5(2^{x-1})$

For Tinsel Town we know that the number of kilometers built in the first month is 21 and increases at a fixed rate of 5 kilometers per month. This can be modeled by a linear equation.

$Tinsel\ Town\ (km) = 21 + 5(x-1)$

Where x is the number of months. x: {1, 2, 3, 4, 5 ...}

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Then we equal both equations and clear x.

$5 (2^{x-1}) = 21 + 5(x-1)\\\\5 (2^{x-1}) - (21 + 5(x-1)) = 0$

Clearing x from this equation is very difficult, so to find x, we iterate until we get the value of x that causes the equation to approach 0.

For x = 3

$5(2^{3-1}) - (21 +5(3-1)) = 0\\\\20- 31= -11$

For x = 4

$5(2^{4-1}) - (21 +5(4-1)) = 0\\\\40 - 36 = 4$

The value must be between x = 3 and x = 4

For x = 3.8

$5 (2^{3.8-1}) - (21 +5(3.8-1)) = 0\\\\34.82 - 35 = 0.18$

Then x ≈ 3.8 months.

Finally we have that By the end of the fourth month the total length of the cycle lanes in Charles City exceeds the length in Tinsel Town

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