In a circle with radiu 2. 2, an angle intercept an arc of length 12. 2. Find the angle in radian to the nearet 10th

The value of the indefinite integral [tex]\int [z^2 + \frac{1}{(1-z)^8}]dz[/tex] will be [tex][ \frac{(z)^3}{3} - \frac{1}{7(1-z)^7}] + c[/tex].

Given that:

[tex]\begin{aligned} I &= \int \left [z^2 + \dfrac{1}{(1-z)^8}\right] dz \end{aligned}[/tex]

The indefinite integral, also known as an antiderivative, represents the family of functions whose derivative is equal to the given function. It is denoted by the symbol ∫.

Integration is a way of finding the total by adding or summing the components. It's a reversal of differentiation, in which we break down functions into pieces. This approach is used to calculate the total on a large scale.

Let 1 - z = u, then -dz = du and 1 - u = z. Then we have

[tex]\begin{aligned} I &= -\int \left [(1-u)^2 + \dfrac{1}{u^8}\right] du\\I &= \left [ \dfrac{(1-u)^3}{3} - \dfrac{1}{7u^7}\right] + c \\I &= \left [ \dfrac{(z)^3}{3} - \dfrac{1}{7(1-z)^7}\right ] + c\end{aligned}[/tex]

The value of the indefinite integral [tex]\int [z^2 + \frac{1}{(1-z)^8}]dz[/tex] will be [tex][ \frac{(z)^3}{3} - \frac{1}{7(1-z)^7}] + c[/tex].

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The value of the differential dy when y = x^4 - x^2 + 1 , x = 1 , x = 1, and dx = 0.1 is (D) dy = 0.5.

To find the value of dy, we need to first find the derivative of the function y = x^4 - x^2 + 1. The derivative is given by y' = 4x^3 - 2x. At x = 1, the value of y' is 4(1)^3 - 2(1) = 2. The differential dy is given by dy = y' * dx, where dx = 0.1. So, dy = 2 * 0.1 = 0.2.

Correct Question :

Find the value of the differential dy when y = x^4 - x^2 + 1 , x = 1, and dx = 0.1. ?A. dy = 0.2 B. dy = 0.6 C. dy = 0.12 D. dy = 0.5 E. dy = 6

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The truth values of a compound statement are displayed in a truth table for all feasible combinations of the truth values of its component propositions.

A truth table is a graph that shows the truth value of one or more compound propositions for any two compound propositions that can have the same truth value. It is used to judge whether a logical argument is sound. A truth table is made up of rows and columns, each row having the truth value of the compound proposition for the specified set of truth values, and each column containing the truth value of the individual proposition. The propositions that make up the compound proposition must first be identified, and all potential combinations of truth values for each of those propositions must then be listed in order to produce a truth table. The truth value of the compound proposition can then be calculated for each combination. Applying reasoning to the provided combination will do this. The truth value of the compound proposition will then be shown in the truth table for each combination of truth values. This can assist in determining the viability of a given logical argument.

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The value of tanθ is either 3/2 or -3/2.

We can solve for the value of tanθ by squaring both sides of the equation 2 - cos(2θ) = 3sinθcosθ, then using the identity tan^2(θ) = sin^2(θ)/cos^2(θ).

Starting with the left-hand side:

(2 - cos(2θ))^2 = 9sin^2(θ)cos^2(θ)

Using the identity cos(2θ) = 2cos^2(θ) - 1, we can simplify:

(2 - 2cos^2(θ) + 1)^2 = 9sin^2(θ)cos^2(θ)

Expanding the square and simplifying:

9 = 8sin^2(θ)cos^2(θ)

Finally, dividing both sides by 8cos^2(θ)sin^2(θ) (which is non-zero since sinθ ≠ cosθ) and using the identity tan^2(θ) = sin^2(θ)/cos^2(θ), we get:

tan^2(θ) = 9/8

Taking the square root of both sides, we have:

tan(θ) = ±3/2

So, the value of tanθ is either 3/2 or -3/2.

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The solution is after 3 yrs the populations of the two types of fish be the same.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

let, after t yrs the populations of the two types of fish be the same.

so, we get,

5750-250t = 3500+ 500t

2250=750t

t=3

Hence, The solution is after 3 yrs the populations of the two types of fish be the same.

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By integrating the function f(x,y)=xy with respect to x and y across the specified area, it is possible to determine the solid's volume. This will reveal the solid's overall volume beneath the function's graph.

By integrating the function with respect to both x and y, it is possible to determine the volume of the solid above the specified region and under the graph of the function f(x,y)=xy. This will provide us with the solid's overall volume. We must integrate the function over the specified area in order to determine the volume. The integration will be carried out first with regard to x and subsequently with regard to y. The x integral will have a lower limit of 0 and an upper limit of 4, whereas the y integral will have a lower limit of 0 and an upper limit of 3. We shall obtain the total volume of the solid under the function's graph and above after integrating.

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We obtained the solutions by solving the system via substitution:

x = 2/3, y = 8/3.

We should probably start by solving problem number 5 in the system of equations.

The set of equations is as follows:

y = x + 2

3x + 3y = 6

We must isolate one of the variables from one of the equations before substituting it in the other equation to solve it via substitution.

Since "y" is already isolated in the first equation, for instance, we can utilize it to replace it in the second equation.

3x + 3y = 6

3x + 3*(y = x + 2) = 6

3x + 3*(x + 2) = 6

We now have an equation that depends just on x, allowing us to solve it:

3x + 3x + 2 = 6

6x + 2 = 6

6x = 6 - 2 = 4

x = 4/6 = 2/3.

The value of y can now be determined using the first equation:

y = x + 2 = 2/3 + 2 = 2/3 + 6/3 = 8/3.

The answer is then:

x = 2/3 and y = 8/3.

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The Complete Question

Unit 5: Systems of Equations & Inequalities Homework 2: Solving Systems by Substitution

The height of the next bounce which is on the third bounce will be 12.8 feet.

A series of non-zero integers where every term after the first is obtained by increasing the one before it by a constant, non-zero value known as the scale factor.

Let a₁ be the first term and r be the common ratio.

Then the nth term of the geometric sequence is given as,

aₙ = a₁ · (r)ⁿ⁻¹

Then the common ratio is given as,

r = 80 / 200

r = 0.40

The height of the next bounce will be given as,

a₄ = 200 · (0.4)⁴⁻¹

a₄ = 200 · (0.4)³

a₄ = 200 · 0.064

a₄ = 12.8 feet

The height of the next bounce which is on the third bounce will be 12.8 feet.

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The most likely scientific explanation for improvement after wearing this jewelry was D. Some people may feel improvement after a week because their body is healing naturally, without help from the ions.

The placebo effect is the best scientific explanation for why so many people experience better after donning a particular piece of jewelry.

The placebo effect happens when users of a product claim to be experiencing physical or mental changes as a result of using it, despite the fact that the product itself lacks the ingredients necessary to produce these effects. The jewelry is acting as a placebo in this scenario.

After a week, some people may experience improvement as their bodies begin to recover on their own, without the aid of the ions.

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Answer:

-4/5

Step-by-step explanation:

To find the slope perpendicular to another slope, take the negative reciprocal. All you need to do is switch the numbers and change the sign.

ex.
2/3 becomes -3/2
-4/7 becomes 7/4

Answer:

I don't know. I hope this helps!

Step-by-step explanation:

Answer:

C , B , A

Explanation:

In any triangle, there is a direct relation between the measure of the angle and the length of the opposite side.

This means that:

- The longest side will be the one opposite to the largest angle

- The shortest side will be the one opposite to the smallest angle

In the given triangle:

- The longest side is BC, this means that the largest angle is angle A

- The shortest side is AB, this means that the smallest angle is C

- CA has an intermediate length (AB < CA < BC), this means that measure angle B will be greater than C and less than A

Based on the above, the order from the smallest angle to the largest angle will be as follows:

C < B < A

Step-by-step explanation:

Hope its Helps :]

4min/hr jon can paddle in the water.

consider the velocity formula:

velocity = distance/time

The given information is:

Distance downstream = 5 miles

Distance upstream = 6 miles

Trip time = 3 hours

Time downstream = (5 / 5+6)(3) = 15/11 hours

Time upstream = (6 / 5+6)(3) = 18/11 hours

velocity downstream = 5 / 15/11 = 11/3mi/hr + 1mi/hr

velocity upstream = 6 / 18/11 = 11/3mi/hr - 1mi/hr

average velocity = 11/3 or 3.6667 or 4 mi/hr

This question can also be calculated in another way:

velocity = distance/time

time = distance/velocity

x + 1 for downstream because it is on current and x - 1 for upstream because it is against the current.

3hours = (5 / x + 1) + (6 / x - 1)

3(x + 1)(x - 1) = 5(x - 1) + 6(x + 1)

3x^2 - 3x + 3x - 3 = 5x - 5 + 6x + 6

3x^2 - 3 = 11x + 1

3x^2 - 11x - 4 = 0

using a quadratic equation, we can find the roots of the equation:

The roots are = 4, -1/3

since there is no negative velocity, x = 4 mi/h

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Answer:

[tex]\huge\boxed{\sf Time = 18.5\ minutes}[/tex]

Step-by-step explanation:

Time = Distance / Speed

Using the normal speed and time, we will first find the distance to her friends house.

Here,

Speed = 50 km/h

Time = 24 minutes / 60 = 0.4 hours

So,

Distance = 50 × 0.4

Now, finding time when the speed is 65 km/h.

So,

Time = Distance / Speed

Time = 20 km / 65 km/hr

To convert it into minutes, we multiply it by 60.

So,

Time = 0.31 × 60

[tex]\rule[225]{225}{2}[/tex]

Answer:

160%

Step-by-step explanation:

320 divided by 200, times 100 = 160%

The proof that can be used to show that this is an isosceles triangle has been given below

A cyclic quadrilateral is a quadrilateral whose vertices lie on the same circle. In this case, since ABCD is a cyclic quadrilateral and arc AD = arc DC, it follows that the opposite angles of the quadrilateral are equal. Let's call the equal angles of the quadrilateral "x."

Since AB = CE, we can use the angle-angle criterion for congruent triangles to prove that triangle ABD is congruent to triangle ECD:

ADB and CDE are both right angles, and the equal angles x in triangle ABD and CDE both add up to 90 degrees.

So, by the angle-angle criterion, triangle ABD is congruent to triangle CDE.

Since AB = CE and ABD is congruent to CDE, we can conclude that triangle ABD is isosceles.

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The correct system of inequalities to represents this scenario are,

⇒ x² - 2y ≤ 5,000

⇒ 2x + 5y < 1000

A relation by which we can compare two or more mathematical expression is called an inequality.

We have to given that;

The value of a company’s stock is represented by the expression x²- 2y and the company’s purchases are modeled by 2x + 5y.

Here, The company’s goal is to maintain a stock value of at least $5,000.

Hence, We get;

⇒ x² - 2y ≤ 5000

And, keeping the purchases below $1,000.

Hence, We get;

⇒ 2x + 5y < 1,000

Thus, The correct system of inequalities to represents this scenario are,

⇒ x² - 2y ≤ 5,000

⇒ 2x + 5y < 1000

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Answer:

x2 – 2y ≥ 5000

2x + 5y < 1000

Step-by-step explanation:

I got it right on the test.

The ∆GHI is an isosceles triangle and have the base angles m∠H and m∠G equal to 74° and the angle I is equal to 32°.

An isosceles triangle have the measure of its base angles to be equal, and the sum of the interior angles sum up to 180°.

Given that sides IG ≅ HI, then the triangle ∆GHI has two sides with similar length and base angles so;

angles m∠H and m∠G are the base angles and m∠G = 74°

m∠I = 180° - (74 + 74)° {sum of interior angles of a triangle}

m∠I = 32°

Therefore, the ∆GHI is an isosceles triangle and have the base angles m∠H and m∠G equal to 74° and the angle I is equal to 32°.

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For the equation y=mx+b, we need to identify "b" (the y-intercept).

For the equation y=mx+b, we need to identify "b" (the y-intercept).

If you are familiar with the slope (m), you can utilize any of the given points by replacing the Y value with y and the X value with x.

Find the solution to b = Y-mX.

The quantity m is known as the line's slope in the equation for a straight line, y = mx + b.

If x is set to 0, then y will equal b because it will equal m • 0 + b.

The graph's y-axis crossing point, designated by the number b, is located there.

To determine the y-intercept, use the slope and a single point (b).

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A cone is a three-dimensional geometric form with a flat base and a smooth tapering apex or vertex.

A cone is made up of a collection of line segments, half-lines, or lines that connect the apex—the common point—to every point on a base that is in a plane other than the apex.

A sphere is a geometrical object that resembles a two-dimensional circle in three dimensions.

In three-dimensional space, a sphere is a collection of points that are all located at the same r-distance from a single point. The radius of the sphere is equal to r, and the provided point is its center.

The three-dimensional shape of a cylinder is made up of two parallel circular bases connected by a curved surface.

The right cylinder is created when the centers of the circular bases cross each other. The axis, which represents the height of the cylinder, is the line segment that connects the two centers.

A three-sided polyhedron consisting of a triangle base, a translated copy, and three faces connecting equivalent sides is known as a triangular prism in geometry. If the sides of a right triangle are not rectangular, the prism is oblique.

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Define the following solids:

(a) cone, (b) sphere, (c) cylinder, (d) prism.

The unsigned decimal equivalent of the following unsigned binary integer value

(11011100)₂ will be (220)₁₀.

An integer variable that can only be either zero or one is referred to as a binary integer variable, often known as a 0/1 variable.

Start with the integer in question and divide it by 2 keeping track of the quotient and remainder to convert it to binary. Divide the quotient by 2 again until you reach zero. The remainders should then be written out in reverse order.

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What is the unsigned decimal equivalent of the following unsigned binary integer value?

11011100

The equation of the plane passing through the three points (1,3,1), (2,8,8), and (11,8,2) is 7x - 17y + 10z = -34

An equation is a mathematical statement that shows the equality or balance of two expressions. It is represented by an equal sign (=) and consists of variables, numbers, and mathematical operations. Equations are used to describe relationships between different quantities and can be solved to find unknown values. For example, the equation 2x + 3 = 7 can be solved for x by subtracting 3 from both sides, giving 2x = 4, and then dividing both sides by 2, giving x = 2.

We can find the equation of a plane passing through three points using the cross product of the vectors connecting two of the points.

Let's first find two vectors that lie on the plane:

v1 = (2,8,8) - (1,3,1) = (1,5,7)

v2 = (11,8,2) - (1,3,1) = (10,5,1)

Next, we can find the normal vector to the plane using the cross product of v1 and v2:

n = v1 x v2 = <7, -17, 10>

The equation of a plane is given by Ax + By + Cz = D, where A, B, and C are the coefficients of the normal vector n = <A, B, C> and D is the constant determined by the coordinates of any point on the plane.

Let's use the point (1,3,1) to find D:

D = A * 1 + B * 3 + C * 1 = 7 - 51 + 10 = -34

Therefore, the equation of the plane passing through the three points (1,3,1), (2,8,8), and (11,8,2) is:

7x - 17y + 10z = -34

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The point a shows -2.9, b shows -2 5/8 and c shows -7/3.

A number line is a visual depiction of numbers on a straight line in mathematics. A number line's numerals are arranged in a sequential manner at equal intervals along its length. It is often displayed horizontally and can extend indefinitely in any direction.

Given:

We have first -7/3 which can be written as -2.33

and, -2 5/8 can be written as -21/8 or -2.625

and, the third is -2.9

So, the point a shows - 2.9.

and point b shows -2.625 or -2 5/8.

an point c shows -2.33 or -7/3.

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Answer:

Step-by-step explanation:

The system of equations is:

y = -8x - 4

y = -x + 3

And the solution is (-1, 4).

Remember that a general linear equation is:

y = a*x + b

Where a is the slope and b is the y-intercept.

First we can see that one of the equations has an y-intercept of y = 3, then we can write:

y = a*x + 3

And that line also passes through (1, 2), replacing these values we will get:

2 = a*1 + 3

2 - 3 = a

-1 = a

So the line is:

y = -x + 3

The other line has an y-intercept of y = -4

Then we can write:

y = a*x - 4

And that line also passes through (-1, 4), replacing that:

4 = a*-1 - 4

4 = -a - 4

4 + 4 = -a

-8 = a

So that line is:

y = -8x - 4

Then the system of equations is:

y = -8x - 4

y = -x + 3

And the solution is the point where the lines intercept, which is (-1, 4)

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Answer:

Below

Step-by-step explanation:

y= 1/4 x + 1

The graph has a y-axis intercept of +1     (y = mx + b form)

 last one looks correct....at x = 4   the value is 2 which is correct

T symbol in statistics means Test statistic for t-test ( t-score )

What is  t-statistic ?

The t-statistic in statistics measures how far an estimated value of a parameter deviates from its hypothesised value in relation to its standard error.

T symbol in statistics mean Test statistic for t-test (  t-score )

Through the Student's t-test, it is utilised for testing hypotheses. To decide whether to accept or reject the null hypothesis in a t-test, the t-statistic is used.

It is quite comparable to the z-score, but when the sample size is small or the population standard deviation is unknown, the t-statistic is employed instead.

For instance, if the population standard deviation is unknown, the population mean can be estimated using the t-statistic from a sampling distribution of sample means.

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The expression if a = -2/7 than -a = 1/2 is a false statement.

The opposite of a number is obtained exchanging just the signal of the number.

The number for this problem is given as follows:

a = -2/7.

The signal is negative, hence the opposite of the number is given as follows:

-a = -(-2/7)

-a = 2/7. (two negatives become a positive).

As the problem states that the opposite is of -a = 1/2, the statement is false.

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The root of the quadratic equation we get x=1

A quadratic equation can be written in the standard form as ax2 + bx + c = 0, where a, b, c are constants and x is the variable. The values of x that satisfy the equation are called solutions of the equation, and a quadratic equation has at most two solutions.

Given here: The quadratic equation x²+6x=7

now, x²+6x=7

        x²+6x+9=16

         (x+3)²=16

          x+3=4

            x=1

Hence, The root of the quadratic equation we get x=1

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The Correct statement about Standardized units is (c) Standardized units are units that have the same meaning for everyone who uses them. When using standardized​ units, people can communicate measurements and know  they mean same thing to both people.

The Standardized Units are a set of units of measurement that have been universally recognized and adopted for specific quantities.

The International System of Units (SI) is the most widely used system of standardized units, and includes units for measuring length, mass, time, electric current, temperature, and other physical quantities.

The Standardized Units play a crucial role in scientific experiments, as well as in manufacturing processes, and in providing precise information on medication dosages, food labeling, and other important areas.

Therefore , standardized units ensure uniformity and comparability of measurements across different fields and geographic locations.

What is meant by standardized units and why are they​ useful?

Choose the correct answer below.

(a) Standardized units are the units that were once standard but have since been phased out for more precise definitions of measurements. They are useful for historical​ reason, as knowledge of these older units allows people to translate the measurements of the past into the units of today.

(b) Standardized units are the units that have been determined by a monarchy. They allow educated peoples who use them to distinguish themselves from the common folk who do not.

(c) Standardized units are units that have the same meaning for everyone who uses them. When using standardized​ units, people can communicate measurements and know that they mean the same thing to both people.

(d) Standardized units are units that are about the same for each person. For example the length of a​ person's foot is a foot. These units are useful​ because, for​ example, anyone with a foot can use their own to get a measurement.

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