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3 years ago

8

How many true solutions does the equation sinx=cosx-1 have over the interval 0 is less than or equal to x which is less than or

equal to 2(pi)?

2 answers:

gogolik [260]3 years ago

8 0

Answer:

1. C

2. B

3. A, E

4. B

Step-by-step explanation:

FrozenT [24]3 years ago

7 0

$sinx=cosx-1 \\ \\ 
sinx-cosx=-1$

Using the identity: $sinx-cosx=- \sqrt{2}cos( \frac{ \pi }{4}+x)$ , we get:

$- \sqrt{2}cos( \frac{ \pi }{4}+x)=-1 \\ \\ 
cos( \frac{ \pi }{4}+x)= \frac{1}{ \sqrt{2} } \\ \\ 
$

There are two solutions to this equation:

1)
$\frac{ \pi }{4}+x= \frac{ \pi }{4} \\ \\ 
x=0$

Since the period of cosine is 2π, so 0 + 2π = 2π will also be a solution to the given equation

2)
$\frac{ \pi }{4}+x= \frac{7 \pi }{4} \\ \\ 
x= \frac{3 \pi }{2}$

Therefore, there are 3 solutions to the given trigonometric equation.

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Which shows the expressions in the order they would appear on a number line from least to greatest?

Ganezh [65]

2^3 = 8
11/9 = 1.22
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least to greatest : 11/9, sqrt 5 , sqrt 11 , sqrt 20, 2^3

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3 years ago

A thermometer at the park shows a reading of 86° Fahrenheit.

Marina86 [1]

No he will not.
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3 years ago

Read 2 more answers

Test scores of the student in a school are normally distributed mean 85 standard deviation 3 points. What's the probability that

Mrrafil [7]

Answer:

The probability that a random selected student score is greater than 76 is $\\ P(x>76) = 0.99865$ .

Step-by-step explanation:

The Normally distributed data are described by the normal distribution. This distribution is determined by two <em>parameters</em>, the <em>population mean</em> $\\ \mu$ and the <em>population standard deviation</em> $\\ \sigma$ .

To determine probabilities for the normal distribution, we can use <em>the standard normal distribution</em>, whose parameters' values are $\\ \mu = 0$ and $\\ \sigma = 1$ . However, we need to "transform" the raw score, in this case <em>x</em> = 76, to a z-score. To achieve this we use the next formula:

$\\ z = \frac{x - \mu}{\sigma}$ [1]

And for the latter, we have all the required information to obtain <em>z</em>. With this, we obtain a value that represent the distance from the population mean in standard deviations units.

<h3>The probability that a randomly selected student score is greater than 76</h3>

To obtain this probability, we can proceed as follows:

First: obtain the z-score for the raw score x = 76.

We know that:

$\\ \mu = 85$

$\\ \sigma = 3$

$\\ x = 76$

From equation [1], we have:

$\\ z = \frac{76 - 85}{3}$

Then

$\\ z = \frac{-9}{3}$

$\\ z = -3$

Second: Interpretation of the previous result.

In this case, the value is <em>three</em> (3) <em>standard deviations</em> <em>below</em> the population mean. In other words, the standard value for x = 76 is z = -3. So, we need to find P(x>76) or P(x>-3).

With this value of $\\ z = -3$ , we can obtain this probability consulting <em>the cumulative standard normal distribution, </em>available in any Statistics book or on the internet.

Third: Determination of the probability P(x>76) or P(x>-3).

Most of the time, the values for the <em>cumulative standard normal distribution</em> are for positive values of z. Fortunately, since the normal distributions are <em>symmetrical</em>, we can find the probability of a negative z having into account that (for this case):

$\\ P(z>-3) = 1 - P(z>3) = P(z$

Then

Consulting a <em>cumulative standard normal table</em>, we have that the cumulative probability for a value below than three (3) standard deviations is:

$\\ P(z$

Thus, "the probability that a random selected student score is greater than 76" for this case (that is, $\\ \mu = 85$ and $\\ \sigma = 3$ ) is $\\ P(x>76) = P(z>-3) = P(z$ .

As a conclusion, more than 99.865% of the values of this distribution are above (greater than) x = 76.

<em>We can see below a graph showing this probability.</em>

As a complement note, we can also say that:

$\\ P(z3)$

$\\ P(z3)$

Which is the case for the probability below z = -3 [P(z<-3)], a very low probability (and a very small area at the left of the distribution).

5 0

3 years ago

Please help me I need the answer

IceJOKER [234]

Answer:

hola.................

6 0

3 years ago

A consumer testing service tested whether the average baking time of whole wheat bread in gas ovens was less than the average ba

vichka [17]

Answer:

Part 1) The explanatory variable is the type of oven

It is a categorical variable

Part 2) The response variable is the baking time

It is a quantitative variable

part 3) two-sample z-test for proportions should be used for the test

Step-by-step explanation:

An explanatory variable is an independent variable that is not affected by all other variables. In this experiment, the type of oven is the input variable and it is not affected by any other variable

A categorical variable is one that has two or more categories without any intrinsic ordering of the categories. The type of oven is either gas or electric, so it is categorical.

A response variable is a dependent variable whose variation depends on other variables. The baking time in this experiment depends on the type of oven used

A quantitative variable is one that take on numerical values.

A two proportion z-test allows you to compare two proportions to see if they are the same. The null hypothesis (H0) for the test is that the proportions are the same. The alternate hypothesis (H1) is that the proportions are not the same.

5 0

3 years ago