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Nata [24]
3 years ago
11

Lin has a maximum of $40 to spend at the movies. The movie ticket costs $10. After purchasing the ticket, she can spend d dollar

s to buy food items at the movies.
Which inequality can be used to find the possible values for d?
Mathematics
1 answer:
Dahasolnce [82]3 years ago
7 0

Answer:

d ≤ 30

Step-by-step explanation:

40 - 10 = 30

she will be able to spend at most 30 dollars

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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}
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Now, isolate the variables, so you can integrate.
(2 - y)dy = \frac{dx}{\sqrt{2 - x^{2}}}
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(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}
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4 - 2sin^{-1}\frac{1}{\sqrt{2}} - C > 0
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C = -\frac{\pi}{2}

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6 0
4 years ago
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Klio2033 [76]
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6 0
3 years ago
Jane travels7 mph less than2 times as fast as Mike. Starting at the same point and traveling in the same direction, they are198
Sphinxa [80]

Let:

Vj = Speed of jane

Vm = Speed of mike

d = distance

t = time

Jane travels 7 mph less than 2 times as fast as Mike, therefore:

Vj = 2Vm - 7

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distance = speed*time

Distance traveled by mike:

d=Vm*t = Vm*6

Distance traveled by jane:

d + 198 = Vj*6

where:

Vj = 2Vm - 7

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Now, let:

d=Vm*6 (1)

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Divide both sides by 6:

240/6 = 6Vm/6

40 = Vm

Vm = 40mph

Replace Vm into this equation Vj = 2Vm - 7 :

Vj = 2(40) - 7 = 80 - 7 = 73mph

4 0
2 years ago
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