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Marta_Voda [28]
3 years ago
14

Parabolas y=−2x^2 and y=2x^2 +k intersect at points A and B that are in the third and the fourth quadrants respectively. Find k

if length of the segment AB is 5.

Mathematics
1 answer:
OverLord2011 [107]3 years ago
8 0

Answer:

-25  

Step-by-step explanation:

(1)   y = -2x²

(2) y =   2x² + k     Subtract (1) from (2)

    0 =  4x² + k      Subtract 4x² from each side

    k = -4x²

The parabolas are <em>symmetrical about the y-axis.</em>

Segment AB = 5, so x = +2.5 and x = +2.5.

k = -4(±2.5)² = -4 × 6.25 = -25

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Answer:

Step-by-step explanation:

The rate of change of temperature of the coffee with respect to time is expressed by the differential equation

dT/dt=k(T−A) when k = -1 and A = 23. The equation will become:

dT/dt = -(T-23)

If the coffee cools at the rate of 1°C per minute, then dT/dt = -1 and T = 70

Substituting into the equation:

-1 = k(70-23)

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k = -1/47

k = -0.0213

Substituting k = -0.0213 into the original equation, the differential equation will be:

dT/dt=k(T−A)

dT/dt = -0.0213(T-23)

dT/dt = -0.0213T+0.489

To get the value of T, we will use variable separable method

dt = dT/-0.0213T+0.489

Integrate both sides

t = -0.0213ln(-0.0213T+0.489)

At t = 1 minute

1 = -0.0213ln(-0.0213T+0.489)

1/-0.0213 = ln(-0.0213T+0.489)

-46.95 = ln(-0.0213T+0.489)

Apply exp to both sides

e^-46.95 = e^ln(-0.0213T+0.489)

4.073×10^-21= -0.0213T+0.489

-0.0213T = 4.073×10^-21-0.489

-0.0213T = -0.489

T = 0.489/0.0213

T = 22.96°C

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At the start of the year a summer holiday to Spain cost £650. It increased by 11% in
olga nikolaevna [1]

Answer:

Final cost = £779

Step-by-step explanation:

It is given that:

Cost of summer holiday =  £650

Amount increased by 11%

Increased cost = 11% of 650

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