Find the area of the composite figure:

What are the solutions of the equation 9x4 – 2x2 – 7 = 0? Use u substitution to solve. tions of the equation 9

skelet666 [1.2K]

Answer:

Step-by-step explanation:

Let $u^2=x^4\\u = x^2$

Subbing in:

$9u^2-2u-7=0$

a = 9, b = -2, c = -7

The product of a and c is the aboslute value of -63, so a*c = 63. We need 2 factors of 63 that will add to give us -2. The factors of 63 are {1, 63}, (3, 21}, {7, 9}. It looks like the combination of -9 and +7 will work because -9 + 7 = -2. Plug in accordingly:

$9u^2-9u+7u-7=0$

Group together in groups of 2:

$(9u^2-9u)+(7u-7)=0$

Now factor out what's common within each set of parenthesis:

$9u(u-1)+7(u-1)=0$

We know this combination "works" because the terms inside the parenthesis are identical. We can now factor those out and what's left goes together in another set of parenthesis:

$(u-1)(9u+7)=0$

Remember that $u=x^2$

so we sub back in and continue to factor. This was originally a fourth degree polynomial; that means we have 4 solutions.

$(x^2-1)(9x^2+7)=0$

The first two solutions are found withing the first set of parenthesis and the second two are found in other set of parenthesis. Factoring $(x^2-1)$ gives us that x = 1 and -1. The other set is a bit more tricky. If

$9x^2+7=0$ then

$9x^2=-7$ and

$x^2=-\frac{7}{9}$

You cannot take the square root of a negative number without allowing for the imaginary component, i, so we do that:

$x=$ ± $\sqrt{-\frac{7}{9} }$

which will simplify down to

$x=$ ± $\frac{\sqrt{7} }{3}i$

Those are the 4 solutions to the quartic equation.

5 0

3 years ago

What is the missing numerator?

Vsevolod [243]

Answer:

The answer is 3

Step-by-step explanation:

........

7 0

2 years ago

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Given that the Grand Canyon is 6001 ft deep, approximately how long would it take for the apple to reach the

Andru [333]

20.7 seconds because it’ll go fast as hell

7 0

3 years ago

SOMEONE HELP MEH...

Phoenix [80]

Answer:

I think it's the first or third

7 0

3 years ago

Read 2 more answers

In recent years, only 79% of the fruit sold at Fred's Fruit stand has been any good. Fred recently started buying fruit from new

Juli2301 [7.4K]

Answer:

The p-value of the test is 0.0485 < 0.05, also less than 0.07, so there is sufficient evidence to conclude that there is a statistically significant increase in the percentage of good fruit, for both significance levels, thus the change in significance levels do not change the conclusion.

Step-by-step explanation:

79% of the fruit sold at Fred's Fruit stand has been any good. Test if there has been an increase.

At the null hypothesis, we test if there has been no increase, that is, the proportion is still of 79%, so:

$H_0: p = 0.79$

At the alternative hypothesis, we test if there has been an increase, that is, more than 79% being good, so:

$H_1: p > 0.79$

The test statistic is:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, $\sigma$ is the standard deviation and n is the size of the sample.

0.79 is tested at the null hypothesis:

This means that $\mu = 0.79, \sigma = \sqrt{0.79*0.21}$

In a random sample if 475 pieces, 85 were bad.

So 475 - 85 = 390 were good, and:

$n = 475, X = \frac{390}{475} = 0.8211$

Value of the test statistic:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{0.8211 - 0.79}{\frac{\sqrt{0.79*0.21}}{\sqrt{475}}}$

$z = 1.66$

P-value of the test and decision:

The p-value of the test is the probability of finding a sample proportion above 0.8211, which is 1 subtracted by the p-value of Z = 1.66.

Looking at the z-table, z = 1.66 has a p-value of 0.9515.

1 - 0.9515 = 0.0485

The p-value of the test is 0.0485 < 0.05, also less than 0.07, so there is sufficient evidence to conclude that there is a statistically significant increase in the percentage of good fruit, for both significance levels, thus the change in significance levels do not change the conclusion.

5 0

3 years ago