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stellarik [79]
3 years ago
8

Functions f(x) and g(x) are shown below:

Mathematics
1 answer:
hoa [83]3 years ago
6 0

f(x) is a multiple of the cosine function. g(x) is a multiple of the sine function. Both the cosine function and the sine function have a maximum value of 1, so the magnitude of the multiple will determine which function has the largest maximum value.

The multiple for f is 2; the multiple for g is 3, which is greater than 2. Hence g(x) has a larger maximum value than f(x).

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Mopeds (small motorcycles with an engine capacity below 50 cm3) are very popular in Europe because of their mobility, ease of op
Anika [276]

Answer:

The probability that the maximum speed is at most 49 km/h is 0.8340.

Step-by-step explanation:

Let the random variable<em> </em><em>X</em> be defined as the maximum speed of a moped.

The random variable <em>X</em> is Normally distributed with mean, <em>μ</em> = 46.8 km/h and standard deviation, <em>σ</em> = 1.75 km/h.

To compute the probability of a Normally distributed random variable we first need to convert the raw score of the random variable to a standardized or <em>z</em>-score.

The formula to convert <em>X</em> into <em>z</em>-score is:

z=\frac{X-\mu}{\sigma}

Compute the probability that the maximum speed is at most 49 km/h as follows:

Apply continuity correction:

P (X ≤ 49) = P (X < 49 - 0.50)

                = P (X < 48.50)

                =P(\frac{X-\mu}{\sigma}

*Use a <em>z</em>-table for the probability.

Thus, the probability that the maximum speed is at most 49 km/h is 0.8340.

8 0
3 years ago
Calculate the discriminant to determine the number solutions. y = x ^2 + 3x - 10
Nataly_w [17]

1. The first step is to find the discriminant itself. Now, the discriminant of a quadratic equation in the form y = ax^2 + bx + c is given by:

Δ = b^2 - 4ac

Our equation is y = x^2 + 3x - 10. Thus, if we compare this with the general quadratic equation I outlined in the first line, we would find that a = 1, b = 3 and c = -10. It is easy to see this if we put the two equations right on top of one another:

y = ax^2 + bx + c

y = (1)x^2 + 3x - 10

Now that we know that a = 1, b = 3 and c = -10, we can substitute this into the formula for the discriminant we defined before:

Δ = b^2 - 4ac

Δ = (3)^2 - 4(1)(-10) (Substitute a = 1, b = 3 and c = -10)

Δ = 9 + 40 (-4*(-10) = 40)

Δ = 49 (Evaluate 9 + 40 = 49)

Thus, the discriminant is 49.

2. The question itself asks for the number and nature of the solutions so I will break down each of these in relation to the discriminant below, starting with how to figure out the number of solutions:

• There are no solutions if the discriminant is less than 0 (ie. it is negative).

If you are aware of the quadratic formula (x = (-b ± √(b^2 - 4ac) ) / 2a), then this will make sense since we are unable to evaluate √(b^2 - 4ac) if the discriminant is negative (since we cannot take the square root of a negative number) - this would mean that the quadratic equation has no solutions.

• There is one solution if the discriminant equals 0.

If you are again aware of the quadratic formula then this also makes sense since if √(b^2 - 4ac) = 0, then x = -b ± 0 / 2a = -b / 2a, which would result in only one solution for x.

• There are two solutions if the discriminant is more than 0 (ie. it is positive).

Again, you may apply this to the quadratic formula where if b^2 - 4ac is positive, there will be two distinct solutions for x:

-b + √(b^2 - 4ac) / 2a

-b - √(b^2 - 4ac) / 2a

Our discriminant is equal to 49; since this is more than 0, we know that we will have two solutions.

Now, given that a, b and c in y = ax^2 + bx + c are rational numbers, let us look at how to figure out the number and nature of the solutions:

• There are two rational solutions if the discriminant is more than 0 and is a perfect square (a perfect square is given by an integer squared, eg. 4, 9, 16, 25 are perfect squares given by 2^2, 3^2, 4^2, 5^2).

• There are two irrational solutions if the discriminant is more than 0 but is not a perfect square.

49 = 7^2, and is therefor a perfect square. Thus, the quadratic equation has two rational solutions (third answer).

~ To recap:

1. Finding the number of solutions.

If:

• Δ < 0: no solutions

• Δ = 0: one solution

• Δ > 0 = two solutions

2. Finding the number and nature of solutions.

Given that a, b and c are rational numbers for y = ax^2 + bx + c, then if:

• Δ < 0: no solutions

• Δ = 0: one rational solution

• Δ > 0 and is a perfect square: two rational solutions

• Δ > 0 and is not a perfect square: two irrational solutions

6 0
3 years ago
What is the product of 14/5
MAXImum [283]

Answer:

2.8

Step-by-step explanation:

Just divide and get the answer

3 0
3 years ago
14 more than the prouduct of the three and nine
Varvara68 [4.7K]
41
3 times 9 is 27
27+14=41
5 0
3 years ago
Read 2 more answers
Take away 32 from the product of 6 and a number
Sphinxa [80]
6x-32 is the expression that you are looking for
4 0
3 years ago
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