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ki77a [65]
3 years ago
7

Find the possible values of c such that the line with equation y = 2x + c twice intersects the parabola with equation y = x^2 +

3x
Mathematics
2 answers:
11111nata11111 [884]3 years ago
8 0

Answer:

c > -¼

Step-by-step explanation:

x² + 3x = 2x + c

x² + x - c = 0

Since they intersect at 2 points,

B²-4AC > 0

(1)²-4(1)(-c) > 0

1 + 4c > 0

c > -¼

Maru [420]3 years ago
4 0

Answer:

C>-1/4

Step-by-step explanation:

Two have intersection it must be:

2x+c= x^2+3x, i.e,

x^2+x-c=0

Solution of its equation is:

x_{1,2}=\frac{-1+-\sqrt{1^2+4c}}{4c}

If we we want two solution we must have that:

1+4c>0

So c>-1/4.

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2 years ago
Identify the coefficient and the exponent for each term of 8x ^ 4 - 2x
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4 0
3 years ago
A veterinary researcher takes a random sample of 60 horses presenting with colic. The average age of the random sample of horses
Licemer1 [7]

Answer:

Probability that a sample mean is 12 or larger for a sample from the horse population is 0.0262.

Step-by-step explanation:

We are given that a veterinary researcher takes a random sample of 60 horses presenting with colic. The average age of the random sample of horses with colic is 12 years. The average age of all horses seen at the veterinary clinic was determined to be 10 years. The researcher also determined that the standard deviation of all horses coming to the veterinary clinic is 8 years.

So, firstly according to Central limit theorem the z score probability distribution for sample means is given by;

                    Z = \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } ~ N(0,1)

where, \bar X = average age of the random sample of horses with colic = 12 yrs

            \mu = average age of all horses seen at the veterinary clinic = 10 yrs

   \sigma = standard deviation of all horses coming to the veterinary clinic = 8 yrs

         n = sample of horses = 60

So, probability that a sample mean is 12 or larger for a sample from the horse population is given by = P(\bar X \geq 12)

   P(\bar X \geq 12) = P( \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } \geq \frac{12-10}{\frac{8}{\sqrt{60} } } ) = P(Z \geq 1.94) = 1 - P(Z < 1.94)

                                                 = 1 - 0.97381 = 0.0262

Therefore, probability that a sample mean is 12 or larger for a sample from the horse population is 0.0262.

4 0
3 years ago
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