if cos x ( cos x - 2) = 0 where 90° sxs 180°, then x =​

To verify the inequality without evaluating the integrals, we can use the properties of integrals.

First, we know that the integral of a positive function gives the area under the curve. Therefore, the integral of √(1-x^2) from -1 to 1 gives the area of a semicircle with radius 1. This area is equal to π/2, which is approximately 1.57.
Next, we can use the fact that the integral of a function over an interval is less than or equal to the product of the length of the interval and the maximum value of the function on that interval. Since the function √(1-x^2) is decreasing on the interval [-1,1], its maximum value is at x=-1, which is √2/2.
Using this property, we have:
∫1 -1 √(1-x^2) dx ≤ (1-(-1)) * √2/2 = √2
Finally, we can use a similar argument to show that the integral is greater than or equal to 2. Therefore, we have:
2 ≤ ∫1 -1 √(1-x^2) dx ≤ √2
To verify the inequality 2 ≤ ∫(1, -1) √(1 - x^2) dx ≤ 2√2 using properties of integrals, let's first establish that the integrand is non-negative on the interval [-1, 1]. Since 0 ≤ x^2 ≤ 1, we have 0 ≤ 1 - x^2 ≤ 1, so √(1 - x^2) is non-negative.
Now, consider the areas of two squares: one with side length 2 and the other with side length √2. The area of the first square is 2² = 4, and the area of the second square is (√2)² = 2. Since the integrand lies between 0 and 1, the area under the curve is less than the area of the first square but more than half of it (as it resembles half of the first square).
Therefore, 2 ≤ ∫(1, -1) √(1 - x^2) dx ≤ 2√2, as the area under the curve is between half of the first square's area and the second square's area.

To know more about integrals visit:

https://brainly.com/question/31744185

#SPJ11

Answer:

n =2

Step-by-step explanation:

2= -9n+22-n

Combine like terms

2 = -10n+22

Subtract 22 from each side

2-22 = -10n+22-22

-20 = -10n

Divide by -10

-20/-10 = -10n/-10

2 = n

Answer:

=

2

Step-by-step explanation:

Solve

1

Combine like terms

2=-9n+22-n

2=-10n+22

2

Subtract

22

from both sides of the equation

2=−10+22

2-22=-10n+22-22

3

Simplify

Subtract the numbers

Subtract the numbers

−20=−10

4

Divide both sides of the equation by the same term

-20=-10n

-20/-10=-10n/-10

5

Simplify

Divide the numbers

Cancel terms that are in both the numerator and denominator

Move the variable to the left

=2

Answer:

$55 + $8.50 (x) = $123

:))

The conditions that should be checked to make sure that your linear model is reasonable are: Quantitative Variables Condition, Straight Enough Condition, Outlier Condition.
A. Quantitative Variables Condition: This condition requires that both the explanatory and response variables be quantitative, so that the relationship between them can be modeled with a straight line.
B. Straight Enough Condition: This condition requires that the relationship between the two variables be approximately linear, so that the linear model is a good fit for the data.
D. Outlier Condition: This condition requires that there are no outliers in the data that can significantly affect the linear model.
The "Does the Plot Thicken?" condition is not a valid condition for checking the reasonableness of a linear model.https://brainly.com/question/29665935

Learn more about regression analysis here:

#SPJ11

Number of books that students read ≥ 2x, where x is the number of books that Anders read. Let's use "x" to represent the number of books that Anders read.

According to the statement, the students read at least double the number of books that Anders read, which means they read 2x or more.

To write an equation for this situation, we can use the symbol ">" to represent "greater than":

number of books that students read > 2x

However, since the statement says "at least double", we know that the number of books that students read could be any value greater than or equal to 2x. To represent this, we can use the symbol "≥", which means "greater than or equal to":

number of books that students read ≥ 2x

Therefore, the equation that shows how many books those students read is:

number of books that students read ≥ 2x, where x is the number of books that Anders read.

Learn more about Anders read,

https://brainly.com/question/15069764

#SPJ4

Answer:

6,309,020 in words is "six million, three hundred nine thousand, twenty."

please make me brainalist

six million three hundred nine thousand twenty

Answer:

13.5

Step-by-step explanation:

6 x^2

Let x= 1.5

6 ( 1.5) ^2

6 *2.25

13.5

Answer:

-6

Step-by-step explanation:

-2x - 3 = 9

     + 3     +3

-2x = 12

/ -2     / -2

x = -6

The grape juice does Sarah use for each cup of water is 3/8 cup .

Given :

Sarah dilutes grape juice for her two-year-old sister. She uses 1/4 cup of grape juice for every 2/3 cup of water .

Let x be the grape juice use for each cup of water .

From the given statements :

1 / 4 cup of grape juice = 2 / 3 cup of water

x cup of grape juice = 1 cup of water

1 / 4 / x = 2 / 3 / 1

cross multiplication

1 / 4 * 1 = 2 / 3 * x

1 / 4 = 2x / 3

2x * 4 = 3 * 1

8x = 3

x = 3/8 cup

Learn more about the cup of water here:

https://brainly.com/question/24803403

#SPJ4

Step-by-step explanation:

f(x)=8(5x-2)

interchanging the role of x&y

x=8(5y-2)

f-1(x)=(x+16)/10

The value of \(f^{-1}(x)\) for the given function f(x) = 8(5x - 2) will be  \(f^{-1}(x)\) =(x + 16)/40.

A function's inverse can be thought of as a reverse of the function.

For instance, if y = f(x), then x = f will be the inverse (y).

It implies that we must swap x and y in the inverse function.

As per the given,

f(x)=8(5x-2)

Interchange the variable y and x as,

⇒ x = 8(5y - 2)

⇒ x+16=401y

⇒ y = (x+16)/40

Put y =  \(f^{-1}(x)\)

\(f^{-1}(x)\) =(x + 16)/40

Hence "The value of \(f^{-1}(x)\) for the given function f(x) = 8(5x - 2) will be  \(f^{-1}(x)\) =(x + 16)/40".

For more information about the inverse of a function,

brainly.com/question/2541698

#SPJ2

Answer:

13.994\(cm (5.sf)\)

Step-by-step explanation:

We know that the base of the cylinder is a circular base.

So circumference of base = \(2\pi r\)

Given \(2\pi r=22cm\\\\r=\frac{22}{2\pi } \\r=\frac{11}{\pi } cm\\\)

Volume of a cylinder = \(\pi r^{2} h\) = 539\(cm^{3}\)

Substitute r into the formula for volume of cylinder.

\(\pi (\frac{11}{\pi } )^{2} h=539\\\pi (\frac{121}{\pi ^{2} } )h=539\)

Now, we will cancel \(\pi\) from the numerator and denominator.

\((\frac{121}{\pi } )h=539\\h = \frac{539}{\frac{121}{\pi } } \\h = 539 * \frac{\pi }{121} \\h = 13.994cm(5s.f)\)

Answer:

Aproximated height is:

14 cm

Step-by-step explanation:

volume of a cylinder = л r² h

л = 3.1416 (aprox)

r = radius

h = height

r = circunference/2л

r = 22/(2*3.1416)

r = 3.5    (aprox)

then volume is:

539 = 3.1416 * 3.5² * h

539 = 3.1416 * 12.25 * h

539 = 38.5 * h

h = 539/38.5

h = 14 cm     (aprox)

Answer:

A continuous variable does allow fractional amounts. a discrete variable  does not allow fractional amounts.

Which variables require boundaries, also known as real limits, in their measurement scales?

A researcher must utilize genuine limits, which are boundaries that are exactly halfway between adjacent categories, to specify the units for a continuous variable.

What distinguishes a ratio scale from an ordinal scale?

For continuous data, what kind of data would you use?

Line graphs, skews, and other data analysis techniques are used to measure continuous data. One of the most popular kinds of continuous data analysis is regression analysis.

Learn more about ordinal scale

brainly.com/question/20630243

#SPJ4

the ship is 472 m from the lighthouse

Step-by-step explanation:

from the question, we can know ∠OAS = 90°-23° =67° and AO = 200m

OS = A0 • tan 67°

= 200 m • 236°

= 472 m

Answer:

the answer is c. next time figure it out on your own..

The 99% confidence interval for the population proportion is (0.671, 0.769), using a z-score distribution table.

To find the 99% confidence interval for the population proportion, we can use the following formula:

CI = p ± z x√(p'(1-p')/n)

where CI is the confidence interval, p is the population proportion, p' is the sample proportion, n is the sample size, and z is the z-score associated with the desired confidence level.

In this case, we have p' = 360/500 = 0.72 and n = 500. To find the z-score, we can use a standard normal distribution table or calculator. For a 99% confidence level, the z-score is approximately 2.576.

Substituting these values into the formula, we get:

CI = 0.72 ± 2.576 x √(0.72(1-0.72)/500)

= 0.72 ± 0.049

Therefore, the 99% confidence interval for the population proportion is (0.671, 0.769).

To know more about confidence interval, refer:

https://brainly.com/question/15905481

#SPJ4

Let Xi be the random variable that represents the number of "6"s that turn up when one die is thrown. Since there are six possible outcomes, each with probability 1/6, we have E(Xi) = 1/6.

Let X = X1 + X2 + ... + X72 be the total number of "6"s that turn up when 72 dice are thrown. Then, by the linearity of expectation, we have:

E(X) = E(X1 + X2 + ... + X72)

= E(X1) + E(X2) + ... + E(X72)

= 72 * (1/6)

= 12

Now, let Y = X^2 be the square of the total number of "6"s. We want to find E(Y) = E(X^2).

Using the identity Var(X) = E(X^2) - [E(X)]^2, we can find E(X^2) as follows:

Var(X) = Var(X1 + X2 + ... + X72)

= Var(X1) + Var(X2) + ... + Var(X72) (since the Xi's are independent)

= 72 * Var(X1)

= 72 * [(1/6) * (5/6)]

= 60

Since E(X) = 12, we have:

E(Y) = E(X^2) = Var(X) + [E(X)]^2

= 60 + 12^2

= 204

Therefore, the expected value of X^(2) is 204, which is closest to option (d) 154.

For more questions like dice visit the link below:

https://brainly.com/question/16683529

#SPJ11

Answer:

The cylinder with maximum volume has a radius of √(20 / 3π) and a height of 0. The maximum volume is V = π(20 / 3π)^2(0) = 0

Step-by-step explanation:

Let's assume the height of the cylinder is also variable and denoted by "h", and the radius of the cylinder is denoted by "r". The surface area of the cylinder is given by:

A = 2πrh + 2πr^2

The cost of the packaging is $0.10 per square cm, and the total cost of packaging should not exceed $4. Therefore, we can write:

0.10(2πrh + 2πr^2) ≤ 4

Simplifying this inequality, we get:

πrh + πr^2 ≤ 20

Now, we want to maximize the volume of the cylinder, which is given by:

V = πr^2h

Using the inequality we derived above, we can express h in terms of r:

h ≤ (20 - πr^2) / πr

Substituting this expression for h in the formula for V, we get:

V = πr^2[(20 - πr^2) / πr]

Simplifying this expression, we get:

V = 20r - πr^3

To find the maximum volume, we need to find the value of r that maximizes V. To do this, we take the derivative of V with respect to r and set it equal to zero:

\(dv/dr\)= 20 - 3πr^2 = 0

Solving for r, we get:

r = √(20 / 3π)

Substituting this value of r back into the inequality we derived earlier, we can find the corresponding value of h:

h = (20 - πr^2) / πr

h = (20 - 20) / (√(3π))

h = 0

Therefore, the cylinder with maximum volume has a radius of √(20 / 3π) and a height of 0. The maximum volume is V = π(20 / 3π)^2(0) = 0

Note that this means the cylinder has no volume and therefore cannot be packaged. In other words, it is not possible to design a cylindrical package with a volume greater than zero that costs less than $4.

To know more about height of the cylinder refer here

https://brainly.com/question/20371974#

#SPJ11

In order to test the hypothesis of whether customers are getting fewer ounces of a soft drink than the stated 28 ounces on the label, the inspector should use a hypothesis test.

A hypothesis test is a statistical procedure used to make inferences or draw conclusions about a population based on sample data. In this case, the inspector wants to investigate if the mean number of ounces in the bottles is less than 28 ounces, which implies that customers are receiving fewer ounces than stated on the label.

The inspector should follow the steps of a hypothesis test, which include formulating the null hypothesis (H0) and the alternative hypothesis (Ha), selecting an appropriate significance level, collecting sample data, and conducting the test using statistical methods such as a t-test or z-test.

The null hypothesis (H0) would state that the mean number of ounces in the bottles is equal to 28 ounces, while the alternative hypothesis (Ha) would state that the mean number of ounces is less than 28 ounces.

By analyzing the collected sample data and conducting the hypothesis test, the inspector can assess the evidence and make an informed conclusion regarding whether customers are indeed receiving fewer ounces than stated on the label.

To learn more about hypothesis test visit:

brainly.com/question/17099835

#SPJ11

36 is large a sample should the researcher   by confidence level.

What does "confidence level" mean?

Confidence lavel = 93%

           z = 1.81

        σ = 10

       E = 3

Sample mix n = ( zσ/E)² = ( 1.81 * 10/3)

                         = 36.4

                         ≈ 36

Learn more about confidence level

brainly.com/question/22851322

#SPJ4

\(\rightarrow\sf \sqrt{27} + 7 \sqrt{5} : \sqrt{2 } \\ = \sf \sqrt{9(3)} + 7 \sqrt{5} : \sqrt{2 } \\ = \sf \sqrt{ {3}^{2} } \times 3 + 7 \sqrt{5} : \sqrt{2} \\ \rightarrow \large\boxed{\sf{\red{3 \sqrt{3} + 7 \sqrt{5} : \sqrt{2} }}}\)

\(\large\boxed{\sf{\red{3 \sqrt{3} + 7 \sqrt{5} : \sqrt{2} }}}\)

\(\color{red}{==========================}\)

✍︎ꕥᴍᴀᴛʜᴅᴇᴍᴏɴǫᴜᴇᴇɴꕥ

✍︎ꕥᴄᴀʀʀʏᴏɴʟᴇᴀʀɴɪɴɢꕥ

ꕥᴀʀᴀꕥ

       For C1(Q) = 3 - 2Q.

        For C2(Q) =  4.

     2. The AVC function

           For C1(Q) = 5/Q + 3 + 20/Q - Q.

           For C2(Q) = 3/Q + 4 + 2/Q.

     3. The AFC function

              For C1(Q)= 5/Q - 20/(5 + 3Q + 20/Q - Q)

              For C2(Q) = 0.

     4.  To find the AC function

        For C1(Q) = (5 + 3Q + 202 - Q^2)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q).

         For C2(Q) = (3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q.

    5.To find the ATC function

    For C1(Q)= 5/Q² + 3/Q + 20/Q² - Q/Q + 5/Q - 20/(5Q + 3Q² + 20 - Q²)

     For C2(Q)= 3/Q² + 4/Q + 2/Q² + 3/Q + 4/Q + 2/Q.

1. To find the MC function, we take the derivative of the cost functions with respect to Q.

For C1(Q) = 5 + 3Q + 202 - Q^2, MC1(Q) = 3 - 2Q.

For C2(Q) = 3 + 4Q + 2, MC2(Q) = 4.

2. To find the AVC function, we divide the cost functions by Q.

For C1(Q), AVC1(Q) = (5 + 3Q + 202 - Q^2)/Q = 5/Q + 3 + 20/Q - Q.

For C2(Q), AVC2(Q) = (3 + 4Q + 2)/Q = 3/Q + 4 + 2/Q.

3. To find the AFC function, we subtract the AVC function from the ATC function.

For C1(Q), AFC1(Q) = (5 + 3Q + 202 - Q^2)/Q - (5 + 3Q + 202 - Q^2)/(5 + 3Q + 20/Q - Q)

= 5/Q - 20/(5 + 3Q + 20/Q - Q).

For

C2(Q), AFC2(Q) = (3 + 4Q + 2)/Q - (3 + 4Q + 2)/(3/Q + 4 + 2/Q) = 0.

4. To find the AC function, we add the AVC function to the AFC function.

For

C1(Q), AC1(Q) = (5 + 3Q + 202 - Q^2)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q).

For

C2(Q), AC2(Q) = (3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q.

5. To find the ATC function, we divide the AC function by Q.

For

C1(Q), ATC1(Q) = [(5 + 3Q + 202 - Q²)/Q + 5/Q - 20/(5 + 3Q + 20/Q - Q)]/Q

= 5/Q² + 3/Q + 20/Q² - Q/Q + 5/Q - 20/(5Q + 3Q² + 20 - Q²).

For

C2(Q), ATC2(Q) = [(3 + 4Q + 2)/Q + 3/Q + 4 + 2/Q]/Q

= 3/Q² + 4/Q + 2/Q² + 3/Q + 4/Q + 2/Q.

Learn more about  Average Total Cost

brainly.com/question/29306232

#SPJ11

Answer:

  x ≈ 7.68

Step-by-step explanation:

You want to find the length x of the tangent segment in the given figure.

Drawing an altitude of the triangle to the upper point of tangency, we have the figure shown in the first attachment. All of these right triangles are similar, so ∠CAB ≅ ∠CDA = 52°.

The tangent of the angle 52° is given by ...

  Tan = Opposite/Adjacent

  tan(52°) = BC/BA

The tangents to the circle from point C are the same length, so BC = x and ...

  tan(52°) = x/6

  x = 6·tan(52°) ≈ 7.68 . . . . cm

The value of x cm is about 7.68 cm.

<95141404393>

Answer:

\(x \approx 7.68 \text{ cm}\)

Step-by-step explanation:

We can solve for the length of segment x in this circle diagram by using the principles of tangency and the altitude of a right triangle.

First, we can assume that the hypotenuse of the diagrammed right triangle is tangent to, or parallel with, the circumference of the circle at its point of intersection it. This means that it is perpendicular, or at a right angle, to the radius at the point of intersection with the circumference.

Second, we can see that the altitude of the diagrammed right triangle is the radius of the circle which intersects with the circumference at the hypotenuse's point of tangency (see the attached image).

We can use our knowledge of a right triangle's altitude to make the assertion that the three triangles formed by drawing the altitude are all similar. This means that their angles are the congruent.

We can solve for the length of the horizontal segment \(h\) (the hypotenuse of one of the triangles formed by drawing the altitude) by using the trigonometric ratio cosine.

\(\cos(\theta) = \dfrac{\text{adjacent}}{\text{hypotenuse}}\)

↓ plugging in the known values

\(\cos(52\°) = \dfrac{6}{h}\)

↓ dividing both sides by 6

\(\dfrac{\cos(52\°)}{6} = \dfrac{1}h\)

↓ taking the reciprocal of both sides

\(h = \dfrac{6}{\cos(52\°)}\)

Finally, we can solve for x by constructing another right triangle, assuming that the segment of length x is tangent to the circle's circumference. We know that the sides of the right triangle are: the radius, \(h\), and x. We already know two of these values (the radius and \(h\)), so we can solve for x using the Pythagorean Theorem.

\(a^2 + b^2 = c^2\)

↓ plugging in the known values

\(x^2 + 6^2 = \left(\dfrac{6}{\cos(52\°)}\right)^2\)

↓ subtracting 6² from both sides

\(x^2 = \left(\dfrac{6}{\cos(52\°)}\right)^2 - 6^2\)

↓ taking the square root of both sides

\(x = \sqrt{\left(\dfrac{6}{\cos(52\°)}\right)^2 - 6^2}\)

↓ evaluating using a calculator

\(\boxed{x \approx 7.68\text{ cm}}\)

To solve the quadratic function -3x² + 5x + 9 = 0, the formula that should be used is Option C: x = (-5 ± √133) / -6.

What is a quadratic function?

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.

The quadratic formula is used to solve quadratic equations in the form of ax² + bx + c = 0, where a, b, and c are constants.

To use the quadratic formula to solve the equation -3x² + 5x + 9 = 0, we need to identify the values of a, b, and c.

In this case, a = -3, b = 5, and c = 9.

Therefore, we can use these values to plug into the quadratic formula -

x = (-b ± √(b² - 4ac)) / 2a

So the answer that can be used to find the solutions to the equation using the quadratic formula is -

x = (-5 ± √(5² - 4 × (-3) × 9)) / 2 × (-3)

Solving this equation we get -

x = (-5 ± √(25 + 108)) / -6

x = (-5 ± √133) / -6

Therefore, the solution is obtained by the equation x = (-5 ± √133) / -6.

To learn more about quadratic function from the given link

https://brainly.com/question/25841119

#SPJ1

A diagram and graph that shows this transformation include the following: D. On a coordinate plane, heart 1 is shifted down 3 units to form heart 2.

In Mathematics and Geometry, a transformation can be defined as the movement of a point from its initial position to a new location. This ultimately implies that, when a geometric figure or object is transformed, all of its points would also be transformed.

By critically observing the geometric figures, we can reasonably infer and logically deduce that a vertical translation of heart 1 down by 3 units in order to produce heart 2 is a graph that correctly shows this transformation.

Read more on transformation here: https://brainly.com/question/10754933

#SPJ1

Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The average value of Avogadro's number based on the 4 trials is 6.017 × \(10^{23\) molecules/mole. The percent error for Avogadro's number is 0.0199%.

Let's say the average value of Avogadro's number based on the 4 trials is 6.017 × \(10^{23\) molecules/mole. The accepted value of Avogadro's number is 6.022 × \(10^{23\) molecules/mole.

The percent error can be calculated as follows:

percent error = |(experimental value - accepted value)| / accepted value * 100

In this case, the percent error is:

percent error = |(6.017 × \(10^{23\) - 6.022 × \(10^{23\))| / 6.022 × \(10^{23\) * 100

= 0.012 / 6.022 × \(10^{23\) * 100

= 0.0199%

Therefore, the percent error for Avogadro's number is 0.0199%. This means that the average value of Avogadro's number is very close to the accepted value.

Here are some of the factors that could contribute to the error:

The accuracy of the measuring instruments used.

The precision of the experimental procedure.

The variability of the samples used.

By repeating the experiment multiple times and using more accurate measuring instruments, the percent error can be reduced.

To learn more about percent here:

https://brainly.com/question/31323953

#SPJ4