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3 years ago

This is a tough one :/ If f(x) = -x + 7 and g(x) = radical of x– 3, what is (f º g)(4)

Mathematics

1 answer:

Jlenok [28]3 years ago

6 0

Answer:

Step-by-step explanation:

To solve, first plug in 4 as your x value for your g(x) equation.

$g(4)=\sqrt{4-3} \\g(4)=\sqrt{1} \\g(4)=1$

Next, plug in the value of g(4) into your f(x) equation for x.

$f(1)=-1+7\\f(1)=6$

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Triss [41]

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Step-by-step explanation:

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3 years ago

Read 2 more answers

Solve the differential. This was in the 2016 VCE Specialist Maths Paper 1 and i'm a bit stuck

Nimfa-mama [501]

$\sqrt{2 - x^{2}} \cdot \frac{dy}{dx} = \frac{1}{2 - y}$
$\frac{dy}{dx} = \frac{1}{(2 - y)\sqrt{2 - x^{2}}}$

Now, isolate the variables, so you can integrate.
$(2 - y)dy = \frac{dx}{\sqrt{2 - x^{2}}}$
$\int (2 - y)\,dy = \int\frac{dx}{\sqrt{2 - x^{2}}}$
$2y - \frac{y^{2}}{2} = sin^{-1}\frac{x}{\sqrt{2}} + \frac{1}{2}C$

$4y - y^{2} = 2sin^{-1}\frac{x}{\sqrt{2}} + C$
$y^{2} - 4y = -2sin^{-1}\frac{x}{\sqrt{2}} - C$
$(y - 2)^{2} - 4 = -2sin^{-1}\frac{x}{\sqrt{2}} - C$
$(y - 2)^{2} = 4 - 2sin^{-1}\frac{x}{\sqrt{2}} - C$

$y - 2 = \pm\sqrt{4 - 2sin^{-1}\frac{x}{\sqrt{2}} - C}$
$y = 2 \pm\sqrt{4 - 2sin^{-1}\frac{x}{\sqrt{2}} - C}$

At x = 1, y = 0.
$0 = 2 \pm\sqrt{4 - 2sin^{-1}\frac{1}{\sqrt{2}} - C}$
$-2 = \pm\sqrt{4 - 2sin^{-1}\frac{1}{\sqrt{2}} - C}$

$4 - 2sin^{-1}\frac{1}{\sqrt{2}} - C > 0$
$\therefore 2 = \sqrt{4 - 2sin^{-1}\frac{1}{\sqrt{2}} - C}$

$4 = 4 - 2sin^{-1}\frac{1}{\sqrt{2}} - C$
$0 = -2sin^{-1}\frac{1}{\sqrt{2}} - C$
$C = -2sin^{-1}\frac{1}{\sqrt{2}} = -2\frac{\pi}{4}$
$C = -\frac{\pi}{2}$

$\therefore y = 2 - \sqrt{4 + \frac{\pi}{2} - 2sin^{-1}\frac{x}{\sqrt{2}}}$

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3 years ago

9 inches

Semmy [17]

What is 9 inches? Is 9 inches the diameter? Or the radius? What?

The equation for circumference is pi x diameter.

So assuming the 9 inches is the diameter:

Pi x 9 = 28.2743339

Circumference = 28.274 (3 d.p.)

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3 years ago

What number sentence is true?

meriva

D would be true because if you think about it in percentage wise
2/8= 25%
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2/3 is automatically greater than 2/8
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3 years ago

As an apprentice to a chef you are preparing a recipe that says to bake the dish for 3/4 of a hour how many minutes should you b

Shalnov [3]

Answer:
You should bake the dish for 45 minutes.

Explanation:
So you have 60 minutes in an hour and if you divide that in 4 you get 15. And for the last step you add 15 three times or just multiply 15*3 and get 45.
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2 years ago