complete the following table: (do not round net price equivalent rate and single equivalent discount rate. round the dollar amounts to the nearest cent.)
item list price chain discount net price equivalent rate (in decimals) single equivalent discount rate (in decimals) trade discount net price. LG Blu-Ray player $207 $7/5/3

The antiderivative of the function is [tex][sec\theta]-3[e^{\theta}]+c\\[/tex] and the constant acceleration is required to increase the speed of a car from 30 mi/h to 57 mi/h in 3 seconds is 13.20 ft/s².

Functions' antiderivative is often referred to as their integral. The original function is derived by differentiating the antiderivative of a function. The term "anti" derivatives refers to the process of integration, which is the opposite of differentiation.

Indefinite integrals are the standard name for antiderivatives. Nevertheless, antiderivatives can also be connected to definite integrals by applying the Basic Theorem of Calculus.

1) r(θ) = secθtanθ - 3[tex]e^{\theta}[/tex]

Anti derivative,

[tex]\int {r(\theta)} \, d\theta=\int {sec\theta tan\theta \ d\theta } - 3\inte^{\theta}[/tex]

[tex]= [sec\theta]-3[e^{\theta}]+c\\[/tex]

2) 1hr = 3600 sec

1 minute  = 5280 feet

The required formula to calculate acceleration

[tex]a=\frac{v_2-v_1}{t}[/tex]

v1 = 30mi/h = 44 ft/sec

v2 = 57 mi/h = 83.6 ft/sec

time t = 3 sec

[tex]a=\frac{v_2-v_1}{t}[/tex]

= [tex]\frac{83.6-44}{3}[/tex]

= 39.6/3

= 13.20 ft/s².

Therefore, acceleration is required to increase the speed is 13.20 ft/s².

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The correct expression in 1-notation for the statement "12 2 177 17 n(8n - 7) for every integer n > 3 7" is "n(8n - 7) ∈ Θ(n²)".

This notation represents that the function n(8n - 7) is bounded above and below by a constant multiple of n², which means it grows at the same rate as n².

The condition "n > 3" is not included in the 1-notation expression because it only affects a finite number of values and does not change the overall growth rate of the function.

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Answer:

The experimental probability of drawing a diamond is 0.15.

Step-by-step explanation:

The student drew cards from a standard deck of 52 cards, 20 times. The outcome shows that the diamond card was drawn 3 times.

The experimental probability of drawing a diamond card can be calculated as the number of times a diamond was drawn divided by the total number of draws:

Experimental probability of drawing a diamond = Number of times a diamond was drawn / Total number of draws Experimental probability of drawing a diamond = 3 / 20 Experimental probability of drawing a diamond = 0.15

Therefore, the experimental probability of drawing a diamond is 0.15.

A homogeneous linear system of 6 equations with 3 variables may have 0, 1, or infinitely many solutions depending on the properties of the equations.

A homogeneous linear system is a system of linear equations where the constant terms are all equal to zero. In general, the number of solutions depends on the relationship between the number of equations and the number of variables, as well as the properties of the equations themselves.

In your case, you have 6 equations with 3 variables. If the system is consistent, it will always have at least one solution, which is the trivial solution (all variables equal to zero). If the system is also linearly dependent, meaning some of the equations are multiples or linear combinations of others, then the system will have infinitely many solutions. However, if the system is inconsistent, meaning there is a contradiction among the equations, then there will be no solution.

To summarize, a homogeneous linear system of 6 equations with 3 variables may have 0, 1, or infinitely many solutions depending on the properties of the equations.

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Using the point-normal form of a plane, the tangent plane equation is -2x + 4y + z + 1 = 0 or equivalently z = -2x - 4y + 3.

To find the equation of the tangent plane to the surface z=-x^2-2y^2 at the point (1,1,-3), we need to find the partial derivatives of the surface with respect to x and y.

∂z/∂x = -2x
∂z/∂y = -4y

At the point (1,1,-3), these partial derivatives are:

∂z/∂x = -2(1) = -2
∂z/∂y = -4(1) = -4

Using the point-normal form of a plane, the equation of the tangent plane is:

-2(x-1) -4(y-1) + (z+3) = 0

Simplifying:

-2x + 4y + z + 1 = 0

Therefore, the equation of the tangent plane to the surface z=-x^2-2y^2 at the point (1,1,-3) is -2x + 4y + z + 1 = 0.

To find the equation of the tangent plane to the surface z = -x^2 - 2y^2 at the point (1,1,-3), we first need to find the partial derivatives of the function with respect to x and y.

∂z/∂x = -2x
∂z/∂y = -4y

Now, we evaluate these partial derivatives at the point (1,1,-3):

∂z/∂x(1,1) = -2(1) = -2
∂z/∂y(1,1) = -4(1) = -4

The gradient of the function at the point (1,1,-3) is given by the vector <-2, -4, 1>. Using the point-slope form of a plane, we can write the equation of the tangent plane as:

z - (-3) = -2(x - 1) - 4(y - 1)

Simplifying the equation gives:

z + 3 = -2x + 2 - 4y + 4

z = -2x - 4y + 3

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If 5^a = y, then we can rewrite 25 as 5^2. Therefore, we have:

25^a = (5^2)^a

= 5^(2a)

Now, we can substitute y for 5^a to get:

25^a = 5^(2a)

= (5^a)^2

= y^2

Therefore, 25^a is equal to y^2.

The solution to the initial-value problem is y = 4(x^2 + 1)^(3/2) + 1.

To solve the initial-value problem (x^2 + 1) dy/dx = 3x(y - 1) with y(0) = 5, follow these steps:
Separate variables.
Divide both sides of the equation by (x^2 + 1) and (y - 1):
dy/(y - 1) = (3x dx)/(x^2 + 1)
Integrate both sides.
∫(1/(y - 1)) dy = ∫(3x/(x^2 + 1)) dx
Let's first integrate the left side:
ln|y - 1| = ∫(3x/(x^2 + 1)) dx + C₁
Now, integrate the right side using substitution: let u = x^2 + 1, so du = 2x dx
ln|y - 1| = (3/2) ∫(u^-1 du) + C₁
ln|y - 1| = (3/2) ln|u| + C₁
ln|y - 1| = (3/2) ln|x^2 + 1| + C₁
Combine constants.
ln|y - 1| - (3/2) ln|x^2 + 1| = C₂
where C₂ = C₁ - (3/2) ln|x^2 + 1|
Apply the initial condition.
y(0) = 5, so ln|5 - 1| - (3/2) ln|0^2 + 1| = C₂
ln|4| - (3/2) ln|1| = C₂
C₂ = ln|4|
Solve for y.
ln|y - 1| - (3/2) ln|x^2 + 1| = ln|4|
ln|(y - 1)/(x^2 + 1)^(3/2)| = ln|4|
(y - 1)/(x^2 + 1)^(3/2) = 4
Now, isolate y:
y = 4(x^2 + 1)^(3/2) + 1
So the solution to the initial-value problem is y = 4(x^2 + 1)^(3/2) + 1.

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Answer: Part A: The two factors in this expression are 5 and (6 + 4x).

Part B: There is only one term in the first factor (5), and two terms in the second factor (6 and 4x).

Part C: The coefficient of the variable term is 4, since it is the coefficient of the term 4x.

Step-by-step explanation:

When mixing a quantity of electrolyte for a storage battery, the electrician uses a ratio of 2 parts of acid and 3 parts of water. This means that for every 5 parts of the mixture, 2 parts are acid and 3 parts are water.

To find the percentage of acid in the mixture, we can use the formula:

% acid = (parts of acid / total parts of mixture) x 100

In this case, we have 2 parts of acid and 3 parts of water, for a total of 5 parts. So:

% acid = (2 / 5) x 100
% acid = 40

Therefore, the percentage of acid in the mixture is 40%.
Hi! When mixing an electrolyte for a storage battery, the electrician uses 2 parts of acid and 3 parts of water. To find the percentage of acid, you can follow this formula:

Percentage of acid = (Parts of acid / Total parts) * 100

Total parts = 2 (acid) + 3 (water) = 5

Percentage of acid = (2 / 5) * 100 = 40%

So, the mixture consists of 40% acid.

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The equation 3x + 2 Cos X + 5 = 0 has exactly one real root.

Why the equation exactly one real root?

To show that the equation 3x + 2 Cos X + 5 = 0 has exactly one real root, follow these steps:

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70.4 g of water are contained in 75.0 g of 6.10 aqueous solution of K3PO4. Therefore option D is correct.

To find the mass of water in the solution, we need to first find the mass of K3PO4 in the solution.

We can do this using the concentration of the solution, which is given as 6.10.

This means that there are 6.10 grams of K3PO4 for every 100 grams of solution.
To find the mass of K3PO4 in 75.0 grams of solution, we can use a proportion:
6.10 g K3PO4 / 100 g solution = x g K3PO4 / 75.0 g solution
Cross-multiplying gives:
(6.10 g K3PO4) * (75.0 g solution) = (100 g solution) * (x g K3PO4)
Solving for x gives:
x = (6.10 g K3PO4) * (75.0 g solution) / (100 g solution) = 4.575 g K3PO4

Now we can find the mass of water in the solution by subtracting the mass of K3PO4 from the total mass of the solution:
Mass of water = Total mass of solution - Mass of K3PO4
Mass of water = 75.0 g - 4.575 g = 70.425 g
Therefore, the answer is (d) 70.4 g of water are contained in 75.0 g of a 6.10 aqueous solution of K3PO4.

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The geometric series is convergent, and its sum is equal to 17.17.which was calculated by dividing the two successive terms and using the formula S = a / (1 - r), then reducing the sum by multiplying it with the common ratio.

Identify the common ratio's value by:

Any two successive terms in the sum can be divided to obtain the common ratio, r:

r = 0.73 = 0.73¹

Calculate the series' sum:

The following formula can be used to calculate the sum of the geometric series:

S = a / (1 - r)

Where a stands for the series' initial term and r for its common ratio.

Therefore:

S = 12 / (1 - 0.73)

S = 12 / 0.27

S = 44.44

Reduce the sum: The sum can be made simpler by multiplying it by the common ratio because the series is convergent.

S = 44.44×0.73

S = 17.17

Hence, the sum of this geometric series is 17.17.

Complete Question:

Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum.

\sum_1{ }_{12(0.73)^{n-1}}

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Answer:5345

Step-by-step explanation:son i used to the apple

Answer:

11.3

Step-by-step explanation:

Because if you add the 4.6 miles from her house to school and the 6.7 miles to her friends house it would equal 11.3. This is because she is already 4.6 miles away from her home and she rides her bike another 6.7 miles away from her house.

the completely factored form of the expression is: [tex]10x^2 + 28x - 6 = 2x(5x + 14) - 6 = (5x + 14)(x - 3/5)[/tex]

What is quadratic equation?

it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x2 is a prerequisite for an equation to be a quadratic equation. The x2 term is written first, then the x term, and finally the constant term is written when constructing a quadratic equation in standard form. In most cases, the numerical values of letters a, b, and c are expressed as integral values rather than fractions or decimals.

The expression inside the parentheses is now in the form of ax + b, where a = 5/2 and b = 7. To factor this, we can use the product-sum method:

a = 5/2

b = 7

Find two numbers whose product is equal to a times b:

(5/2) * 7 = 35/2

Find two numbers whose sum is equal to the coefficient of x:

(5/2) + 2(7) = 19/2

Using these two numbers, we can rewrite the expression as:

2x(5x/2 + 7) - 6

= 2x(2.5x + 7) - 6

= (5x + 14)(x - 3/5)

Therefore, the completely factored form of the expression is: [tex]10x^2 + 28x - 6 = 2x(5x + 14) - 6 = (5x + 14)(x - 3/5)[/tex]

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The subtended arc along the circle is 79/360 of the circle's circumference. Therefore, the subtended arc is approximately 0.2194 times as long as 1/360 of the circle's circumference.


To find the length of the subtended arc along the circle, we need to know what fraction of the circle's circumference it represents.

The angle measures 79 degrees, which is a little over 1/5 of a full circle (which measures 360 degrees). Therefore, the subtended arc represents a little over 1/5 of the circle's circumference. More precisely, it represents 79/360 of the circle's circumference.

To find out how many times as long the subtended arc is as 1/360 of the circle's circumference, we can divide the length of the subtended arc by the length of 1/360 of the circle's circumference. This gives us:

(79/360) / (1/360) = 79

So the subtended arc is 79 times as long as 1/360 of the circle's circumference. Alternatively, we can express this as a decimal by dividing the subtended arc by 1/360:

(79/360) ÷ (1/360) = 0.2194

So the subtended arc is approximately 0.2194 times as long as 1/360 of the circle's circumference.

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Answer:

[tex]c = \sqrt{ {2.2}^{2} + {.6}^{2} } = \sqrt{5.2} = 2.28[/tex]

So the hypotenuse is about 2.3 millimeters.

To find the volume of the solid generated by rotating the region in the first quadrant enclosed by the coordinate axes, the line x=pi, and the curve y=cos(cosx) about the x-axis, we can use the disk method.

Let's consider a small slice of the solid at a given value of x. The slice is a disk with radius y=cos(cosx) and thickness dx. The volume of the slice is then given by:

dV = pi * (cos(cosx))^2 * dx

Integrating this expression from x=0 to x=pi, we obtain the total volume of the solid:

V = integral from 0 to pi of pi * (cos(cosx))^2 dx

Unfortunately, this integral does not have an elementary closed form solution. We can approximate the value using numerical methods, such as Simpson's rule or the trapezoidal rule. Using Simpson's rule with 1000 intervals, we obtain:

V ≈ 0.6347 cubic units

Therefore, the volume of the solid generated by rotating the region in the first quadrant enclosed by the coordinate axes, the line x=pi, and the curve y=cos(cosx) about the x-axis is approximately 0.6347 cubic units.

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Special right triangles are right-angled triangles whose interior angles are fixed and sides are always in a defined ratio.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

To define the term Special right triangles.

We know that;

Special right triangles are right-angled triangles whose interior angles are fixed and sides are always in a defined ratio.

And, There are two types of special right triangles,

One which has angles that measure 45°, 45°, 90°;

And, the other which has angles that measure 30°, 60°, 90°.

Thus, Special right triangles are right-angled triangles whose interior angles are fixed and sides are always in a defined ratio.

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The expression "log6 e" means the logarithm of e with base 6. Using a calculator, we can evaluate this expression to be approximately 0.82. Rounding to two decimal places, our final answer is 0.82.
To evaluate the expression log₆e (log base 6 of e), we can use the change of base formula. The formula is:

logₐb = logₓb / logₓa

In our case, a = 6, b = e (Euler's number), and we can choose x = 10 (common logarithm) for simplicity.

log₆e = log₁₀e / log₁₀6

Using a calculator or online tool to find the values of log₁₀e and log₁₀6:

log₁₀e ≈ 0.43429
log₁₀6 ≈ 0.77815

Now, divide the two values:

log₆e = 0.43429 / 0.77815 ≈ 0.55811

Therefore, log₆e ≈ 0.56 (rounded to two decimal places).

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Answer:

thw answer is 0.56 is the closest answer

The number of elements in the intersection of sets a and b, n(a ∩ b), is 8.

To get n(a ∩ b), you can use the formula for the union of two sets: n(a ∪ b) = n(a) + n(b) - n(a ∩ b). You are given n(a) = 16, n(b) = 45, and n(a ∪ b) = 53. Let's solve for n(a ∩ b):
Plug in the given values into the formula:
53 = 16 + 45 - n(a ∩ b)
Simplify the equation:
53 = 61 - n(a ∩ b)
Solve for n(a ∩ b) by subtracting 61 from both sides:
-8 = -n(a ∩ b)
Multiply both sides by -1 to find n(a ∩ b):
8 = n(a ∩ b)
So, the number of elements in the intersection of sets a and b, n(a ∩ b), is 8.

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Answer:

-3

Step-by-step explanation:

Replace x with the given value (8) in the function:

[tex] f(8) = \frac{1}{2} \times 8 - 7 = 4 - 7 = - 3 [/tex]

Answer:

f(8) = -3

Step-by-step explanation:

Now we have to,

→ Find the required value of f(8).

Given function,

→ f(x) = (1/2)x - 7

Then the value of f(8) will be,

→ f(x) = (1/2)x - 7

→ f(8) = (1/2)(8) - 7

→ f(8) = (8/2) - 7

→ f(8) = 4 - 7

→ [ f(8) = -3 ]

Hence, the value of f(8) is -3.

Aphrodite will have $56 293.2 in 20 years if she invests $12,345 in a mutual fund that grows at a rate of 7.89% per year

To calculate the future value of Aphrodite's investment, we can use the formula for compound interest:

FV = PV x (1 + r)ⁿ

where FV is the future value, PV is the present value, r is the annual interest rate expressed as a decimal, and n is the number of years.

7.89% is the rate of interest

Substituting the given values, we get:

FV = $12,345 x (1 + 0.0789)²⁰

FV = $12,345 x 4.56

FV = $56,293.2

Therefore, Aphrodite will have $56 293.2 in 20 years if she invests $12,345 in a mutual fund that grows at a rate of 7.89% per year.

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The percent error in the small angle approximation depends on the specific angle being used. In this approximation, it is assumed that sin(θ) ≈ θ and cos(θ) ≈ 1 for small angles θ, where θ is measured in radians. The percent error can be calculated using the formula:

Percent Error = (|(Approximate Value - Exact Value)| / Exact Value) x 100%

As the angle θ increases, the percent error in the small angle approximation also increases. For very small angles, the percent error is relatively low, making the approximation useful in certain applications such as physics and engineering.

The small angle approximation is a method used to estimate the value of trigonometric functions when the angle is small. It is based on the assumption that the sine and tangent of a small angle are approximately equal to the angle itself, and the cosine of a small angle is approximately equal to 1.

The percent error in the small angle approximation depends on how small the angle is and how accurate you need the estimate to be. Generally, the smaller the angle, the smaller the percent error. However, as the angle approaches zero, the percent error approaches infinity, since the approximation becomes less and less accurate. Therefore, it is important to use the small angle approximation only when the angle is sufficiently small and the required accuracy is achievable.

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To include aspects such as how much variability or spread we see (A), where the values tend to be centered (C), and the shape and unusual values, such as outliers (D).

When describing the behavior in a distribution of a quantitative variable, you should include the following aspects:
A. How much variability or spread we see.
C. Where the values tend to be centered.
D. The shape and unusual values (outliers).
When describing the behavior in a distribution of a quantitative variable, we should be sure to include aspects such as how much variability or spread we see (A), where the values tend to be centered (C), and the shape and unusual values, such as outliers (D).

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The residual be for an observed value of (3, 510) is option a. -2.

To find the residual, we need to first plug in the given observed value of (3, 510) into the equation for the least squares regression line:

ý = 500 + 4x
ý = 500 + 4(3)
ý = 512

So the predicted value for this observation is 512. To find the residual, we subtract the predicted value from the actual observed value:

Residual = Observed value - Predicted value
Residual = 510 - 512
Residual = -2

Therefore, the residual for an observed value of (3, 510) is -2. Answer choice (a) is correct.

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The value of z is a complex number with both a real and imaginary part. Letter B represents this.

To find the value of z, we can start by expressing the given equation in polar form.

Let's first find the modulus of z, denoted by |z|:

|z³| = |3 + i√3|

Using the modulus property of complex numbers, we can simplify this to:

|z|³ = √(3² + (√3)²)

|z|³ = √12

|z|³ = 2√3

Taking the cube root of both sides, we get:

|z| = ∛(2√3)

Now, let's find the argument of z, denoted by arg(z):

z³ = 3 + i√3

We can rewrite the right-hand side in polar form:

3 + i√3 = 2(cosπ/6 + isinπ/6)

Therefore,

z³ = 2(cosπ/6 + isinπ/6)

Using De Moivre's theorem, we can take the cube root of both sides:

z = 2^(1/3) [cos(π/18 + 2πn/3) + isin(π/18 + 2πn/3)], where n = 0, 1, or 2.

Therefore, the three possible values of z are:

z₁ = 2^(1/3) [cos(π/18) + isin(π/18)]

z₂ = 2^(1/3) [cos(11π/18) + isin(11π/18)]

z₃ = 2^(1/3) [cos(19π/18) + isin(19π/18)]

The value of z depends on which of the three possible values we choose.

So, in general, the value of z is a complex number with both a real and imaginary part. Letter B represents this.

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Answer: I believe the answer is A

Happy homeworking y'all :]

For the equilibrium system of Ni(H2O)6(aq) + 6NH3(aq) + HCl, adding more HCl will shift the equilibrium to the right, resulting in more Ni(NH3)2(aq) and H2O(l) being formed.

For the equilibrium system of Cu(H2O)4(aq) + 4Br-(aq) + heat, adding more heat (or increasing temperature) will shift the equilibrium to the left, resulting in less CuBr2(aq) and H2O(l) being formed.

For the equilibrium system of SO3(g) + 120(g) ↔ SO2(g) + O2(g), removing heat (or decreasing temperature) will shift the equilibrium to the right, resulting in more SO2(g) and O2(g) being formed.

For the equilibrium system of Ag2CO3(s) + 2Ag+(aq) + CO32-(aq), adding HCl(aq) will shift the equilibrium to the left, resulting in less Ag2CO3(s) and more Ag+(aq) and CO32-(aq) being formed.

For the equilibrium system of CaCO3(s) ↔ Ca2+(aq) + CO32-(aq), adding rainwater (which is typically slightly acidic) will shift the equilibrium to the left, resulting in less Ca2+(aq) and CO32-(aq) and more CaCO3(s) being formed.

For the equilibrium system of CH3COOH(aq) ↔ CH3COO-(aq) + H+(aq), adding CH3COONa(aq) will shift the equilibrium to the left, resulting in less CH3COO-(aq) and more CH3COOH(aq) being formed

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For the given problem the required value of x is 12°.

An angle is a geometric figure formed by two rays or line segments that share a common endpoint, called the vertex. The two rays or line segments are called the arms of the angle.

The measure of an angle is determined by the amount of rotation needed to bring one arm of the angle to coincide with the other arm.

There can be types of Angles on the basis of their size, shape, and location. The most common classification is based on the size of the angle. An acute angle is an angle that measures less than 90 degrees, while a right angle measures exactly 90 degrees.

An obtuse angle measures more than 90 degrees but less than 180 degrees, and a straight angle measures exactly 180 degrees. An angle that measures more than 180 degrees but less than 360 degrees is called a reflex angle, while an angle that measures exactly 360 degrees is a full angle.

Here from the given figure it is clear that sum of angles 2x° and (4x+108)° are making angle 180°.

Because they are form a straight angle.

So, 2x°+ (4x+108)° = 180°

2x°+4x° = 180°-108°

6x° = 72°

x° = 12°

Therefore, the value of 'x' is 12°.

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Answer:

Step-by-step explanation:

You want the displacement and the distance traveled on the interval [-2, 6] by a particle whose velocity is v(t) = -t² +5t -4.

The particle's displacement (s) will be given by the integral of velocity. We can integrate from t=-2 so that the integral gives the net displacement after that time.

  [tex]\displaystyle s(t)=\int_{-2}^t{v(t)}\,dt=\left[\dfrac{-t^3}{3}+\dfrac{5t^2}{2}-4t\right]_{-2}^t\\\\s(t)=\left(\left(-\dfrac{t}{3}+\dfrac{5}{2}\right)t-4\right)t-\left(\dfrac{8}{3}+10+8\right)\\\\s(t)=\left(\left(-\dfrac{t}{3}+\dfrac{5}{2}\right)t-4\right)t-20\dfrac{2}{3}[/tex]

The displacement at t=6 relative to that at t=-2 is ...

  s(6) = ((-6/3 +5/2)t -4)6 -(20 2/3) = -80/3 = -26 2/3

The displacement is -26 2/3 on the interval [-2, 6].

The distance the particle travels can be found by integrating the absolute value of the velocity over the interval. Here, we see the velocity is only positive on the interval (1, 4), so we need to negate the displacement outside that interval.

  d(6) = -s(1) +(s(4) -s(1)) -(s(6) -s(4))

This rearranges to ...

  d(6) = 2(s(4) -s(1)) -s(6)

  d(6) = 2(-18 -(-45/2)) -(-26 2/3) = 2(4 1/2) +(26 2/3) = 35 2/3

The distance traveled is 35 2/3 on the interval [-2, 6].

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Additional comment

We designed s(t) so that s(-2) = 0, so we don't need to subtract that value in any of the calculations.

We find it very convenient to use a suitable calculator for the integration, especially where numerical values are desired.