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3 years ago

Please help fast Question is below v v v v v v

Mathematics

2 answers:

zvonat [6]3 years ago

4 0

They would cost $8.75. If you take out 30% from the original price, that is how much they would be.

Lorico [155]3 years ago

4 0

Answer:

They would cost $8.75

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

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

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

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

6 0

3 years ago

Round to the nearest whole number. Simplify (5(12 - 2)2 + 7]/3=

mario62 [17]

(5(12-2)2+7)/3

(5(10)2+7)/3

(50(2)+7)/3

(100+7)/3

107/3

35.66666...

7 0

3 years ago

However, since we have 3 sets of 4, what can we do with the two exponents to avoid expansion?

Anvisha [2.4K]

Answer:

To avoid expansion, you can just use the power of a power rule and multiply the two exponents from the start.

Step-by-step explanation:

(<em>x</em>^4)^3

= <em>x</em>^4×3

= <em>x</em>^12

4 0

2 years ago

The box plots show the average gas mileage, in miles per gallon, of cars and minivans tested by a certain company.

mr_godi [17]

Answer:

b.The interquartile range for cars is about 7 mpg, and the interquartile range for minivans is about 3 mpg.

Step-by-step explanation:

i got it right

4 0

3 years ago

Read 2 more answers

1) Find the measure of ∠θ. Round to one decimal place.

I am Lyosha [343]

Answer/Step-by-step explanation:

Reference angle = θ

Opposite side = 11.9

Adjacent side = 10

Applying the trigonometric ratio, TOA, we have:

Tan θ = opp/adj

Tan θ = 11.9/10

θ = tan^{-1}(11.9/10)

θ = 49.9584509° ≈ 50.0° (to one d.p)

Apply pythagorean theorem to find AB:

Thus:

AB = √(11.9² + 10²)

AB = √241.61

AB ≈ 15.5 (to 1 d.p)

3 0

3 years ago