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3 years ago

14

Show that p(x)=2x3−5x2−10x+5 has a real root.

1 answer:

FromTheMoon [43]3 years ago

6 0

Let's pick an arbitrary value of 5.

$P(5) = 2(5)^{3} - 5(5)^{2} - 10(5) + 5$
$= 2(125) - 125 - 50 + 5$
$= 250 - 125 - 50 + 5$
$= 80 > 0$

Let's pick another arbitrary value: 1

$P(1) = 2 - 5 - 10 + 5$
$= -8 < 0$

Between these two values, the polynomial is continuous. This means for the two polynomial points to be satisfied, there must be at least one root between these two points.

We can either use the Intermediate Value Theorem or Newton's method to make a better approximation from there.

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3 years ago

Read 2 more answers

Use average rates of change to determine if the function in the table is Linear or Non-linear.

nevsk [136]

We have been given a table of values of a function. We are asked to determine whether the given function is linear or nonlinear.

We know that a function is linear when its rate of change (slope) is constant.

Let us find slope for each of the given points using slope formula.

$m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{-3-0}{4-1}=\frac{-3}{3}=-1$

Similarly, we will find the slopes using other given coordinates.

$m=\frac{-6-(-3)}{7-4}=\frac{-6+3}{3}=\frac{-3}{3}=-1$

$m=\frac{-9-(-6)}{10-7}=\frac{-9+6}{3}=\frac{-3}{3}=-1$

Since the rate of change for each set of points is $-1$ , so the rate of change is constant.

Therefore, the given function is linear.

3 0

3 years ago

Sasha buys two ribbons of equal length. She cuts 9 pieces of the same length, L, from the first ribbon and finds that 5 inches a

nikitadnepr [17]

Answer:

50 inches.

Step-by-step explanation:

Let the length of the each ribbon was x.

Now, she cuts 9 pieces of same length L which means total length is 9L.

Now, doing the same she was left with 5 inches of ribbon. Hence, we have

[tex[9L+5=x.....(1)[/tex]

Similarly, we can write a equation for the second situation.

$2L+40=x......(2)$

From equation 1 and 2,

$9L+5=2L+40\\\\7L=35\\\\L=5$

Plugging this value in equation 1,

$9(5)+5=x\\\\x=45+5\\x=50$

Therefore, the length of each ribbon when she bought them was 50 inches.

3 0

3 years ago

Suppose a random sample of n measurements is selected from a binomial population with probability of success p = .39. Given n =

Oksi-84 [34.3K]

Answer:

The answer is below

Step-by-step explanation:

a) Given that the number of sample (n) = 300, therefore since n > 30, the distribution of the sample means is going to be normally distributed.

b) The mean of the distribution of sample means (also known as the Expected value of M) is equal to the population mean μ.

$\mu_x=\mu=np=300*0.39=117$

c) The standard deviation of the distribution of sample means is called the Standard Error of M, it is given by:

$\sigma_x=\sqrt{np(1-p)} =\sqrt{300*0.39(1-0.39)} =8.44$

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3 years ago

2^24 x 3^2 x 1 hhhhhhhhhhhhhhhhhh

AysviL [449]

Answer:

The answer is 5184. Hope it helps luv

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3 years ago