3a + 4 = 2a + 7 and justify your steps

Given the function f(x)=sin(2πx), with x = 0.3, f(x) = 0.951057. The objective is to approximate the value of f(0.2) using the first two terms in the Taylor series and Vx=0.1.

We know that the Taylor series for a function f(x) can be written as:f(x)=f(a)+f′(a)(x−a)+f′′(a)2(x−a)2+…+f(n)(a)n!(x−a)n+…The first two terms of the Taylor series are given by:f(x)=f(a)+f′(a)(x−a)The first derivative of f(x) is given by:f′(x)=2πcos(2πx)On substituting x = a = 0.1, we get:f′(0.1) = 2πcos(2π * 0.1) = 5.03118603447The value of f(x) at a=0.1 is given by:f(0.1) = sin(2π * 0.1) = 0.587785252292With a=0.1, the first two terms of the Taylor series become:f(x)=0.587785252292+5.03118603447(x−0.1) = 0.587785252292+0.503118603447x−0.503118603447×0.1Using x=0.2 and substituting the values of a and f(a) in the equation above, we get:f(0.2)=0.587785252292+0.503118603447*0.2−0.503118603447×0.1=0.712261After approximating the value of f(0.2) using the first two terms in the Taylor series,

we can conclude that the value of f(0.2) = 0.712261 with a = 0.1, with an error of approximately 0.012796.

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When a side in polygon P is 6 the corresponding side in polygon Q is 4.5

the scale factor is 4/3

From the question it can be deduced that

The polygon is four sided

1 side in polygon P is 4 and it corresponding side in Q is 3

let the scale factor be k

4 * k = 3

k = 3/4

When a side in polygon P is 6 the corresponding side in polygon Q is solved using the scale factor

the side in polygon Q = 6 * k

the side in polygon Q = 6 * 3/4

the side in polygon Q = 4.5

complete question

Polygon P is a scaled copy of Polygon Q. the 2 are 4-sided polygon, P and Q. 1 side in polygon P is 4 and it's correponding side in Q is 3. Another side in polygon P is x, and it correponding side in Q is y. The value of x is 6, what is the value of y?

What is the scale factor?

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Answer:

the numbers are 10 and 8

Answer:-4c^2+4c+6

Step-by-step explanation:

Hope that’s what ur looking for:)

Answer:

2 + 7c – 4c2 – 3c + 4

4c∧2 + 4c + 6

Step-by-step explanation:

There are several statistics that are robust to outliers: Median, Interquartile range, Winsorized mean and Trimmed mean.

These statistics are more suitable for datasets that contain outliers as they are less influenced by the extreme values and provide more accurate information about the central tendency and variability of the data.

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Answer:

Hope that helps! :)

-Aphrodite

Step-by-step explanation:

Answer:

D)

hope this helped

Step-by-step explanation:

Answer:

The owners' cost of the candy bar is $1

Step-by-step explanation:

Assume that the owners' cost of the candy bar is 100%

∵ The owners' cost of the candy bar is 100%

∵ The candy store uses a 50% markup on cost

∵ The selling cost = owners' cost + markup

∴ The selling cost = 100% + 50% = 150%

∵ The candy bar sells for $1.50

→ That means 1.50 is 150% of the owners' cost

∴ 1.50 = 150% × owners' cost

→ Change 150% to decimal by divide it by 100

∵ 150% = 150 ÷ 100 = 1.50

∴ 1.50 = 1.50 × owners' cost

→ Divide both sides by 1.50

∴ 1 = owners' cost

∴ The owners' costs = $1

∴ The owners' cost of the candy bar is $1

Answer:

We found, based on beach strandings, that more than 1,000 turtles are dying a year, after becoming tangled up, but this is almost certainly a gross underestimate. Young turtles and hatchings are particularly vulnerable to entanglement.” In recent years, global turtle population numbers have been falling.

Answer:

If a = -1/2 is a root of the quadratic equation 8x² - bx - 3, then we know that when x = -1/2, the equation is equal to 0. We can use this information to solve for b.

Substituting x = -1/2 into the equation, we get:

8(-1/2)² - b(-1/2) - 3 = 0

Simplifying and solving for b, we get:

2 - (b/2) - 3 = 0

b/2 = -1

b = -2

Therefore, b = -2 is the value we are looking for.

To find the other root, we can use the fact that the product of the roots of a quadratic equation is equal to the constant term divided by the leading coefficient. In this case, the constant term is -3 and the leading coefficient is 8. Therefore, the product of the roots is:

(-1/2) times the other root = -3/8

Solving for the other root, we get:

(-1/2) times the other root = -3/8

other root = (-3/8) / (-1/2)

other root = (3/8) * 2

other root = 3/4

Therefore, the other root is 3/4.

Finally, to find (1/a - 1/b)², we can substitute a = -1/2 and b = -2 into the expression:

(1/a - 1/b)² = (1/(-1/2) - 1/(-2))²

= (-2 - 1/2)²

= (-5/2)²

= 25/4

Therefore, (1/a - 1/b)² is equal to 25/4.

Answer:

\(b=2\)

\(\textsf{Other root} = \dfrac{3}{4}\)

\(\left(\dfrac{1}{a}-\dfrac{1}{b}\right)^2=\dfrac{25}{4}\)

Step-by-step explanation:

Roots are also called x-intercepts or zeros.  They are the x-values of the points at which the function crosses the x-axis, so the values of x when f(x) = 0.

If x = α is a root of a polynomial f(x), then f(α) = 0.

Therefore, given that a = -1/2 is a root of the quadratic equation 8x² - bx - 3, substitute x = -1/2 into the equation and set it to zero:

\(\implies 8\left(-\dfrac{1}{2}\right)^2-b\left(-\dfrac{1}{2}\right)-3=0\)

Solve for b:

\(\implies 8\left(\dfrac{1}{4}\right)+\dfrac{1}{2}b-3=0\)

\(\implies \dfrac{8}{4}+\dfrac{1}{2}b-3=0\)

\(\implies 2+\dfrac{1}{2}b-3=0\)

\(\implies \dfrac{1}{2}b-1=0\)

\(\implies \dfrac{1}{2}b=1\)

\(\implies b=2\)

Therefore, the quadratic equation is:

\(\boxed{8x^2-2x-3}\)

The product of the roots of a quadratic equation is equal to the constant term divided by the leading coefficient.  

The constant term of the quadratic equation is -3 and the leading coefficient is 8.  Let the other root be "r". Therefore:

\(\implies a \cdot r=\dfrac{-3}{8}\)

Substitute the known value of a = -1/2 and solve for r:

\(\implies -\dfrac{1}{2} \cdot r=\dfrac{-3}{8}\)

\(\implies r=\dfrac{3}{4}\)

Therefore, the other root of the quadratic equation is 3/4.

To find the value of (1/a - 1/b)²​, substitute the given value of a and the found value of b into the equation and solve:

\(\implies \left(\dfrac{1}{a}-\dfrac{1}{b}\right)^2\)

\(\implies \left(\dfrac{1}{-\frac{1}{2}}-\dfrac{1}{2}\right)^2\)

\(\implies \left(-2-\dfrac{1}{2}\right)^2\)

\(\implies \left(-\dfrac{5}{2}\right)^2\)

\(\implies \dfrac{25}{4}\)

Answer:

See below.

Step-by-step explanation:

First, notice that this is a composition of functions. For instance, let's let \(f(x)=\sqrt{x}\) and \(g(x)=7x^2+4x+1\). Then, the given equation is essentially \(f(g(x))=\sqrt{7x^2+4x+1}\). Thus, we can use the chain rule.

Recall the chain rule: \(\frac{d}{dx}[f(g(x))]=f'(g(x))\cdot g'(x)\). So, let's find the derivative of each function:

\(f(x)=\sqrt{x}=x^\frac{1}{2}\)

We can use the Power Rule here:

\(f'(x)=(x^\frac{1}{2})'=\frac{1}{2}(x^{-\frac{1}{2} })=\frac{1}{2\sqrt{x}}\)

Now:

\(g(x)=7x^2+4x+1\)

Again, use the Power Rule and Sum Rule

\(g'(x)=(7x^2+4x+1)'=(7x^2)'+(4x)'+(1)'=14x+4\)

Now, we can put them together:

\(y'=f'(g(x))\cdot g'(x)=\frac{1}{2\sqrt{g(x)}} \cdot (14x+4)\)

\(y'=\frac{14x+4}{2\sqrt{7x^2+4x+1} } =\frac{7x+2}{\sqrt{7x^2+4x+1} }\)

Answer:

pick any two points

im going to chose (1,3) and (3,7)

so the equation y2-y1/x2-x1

1 = x1

3=y1

3=x2

7=y2

so 7-3/3-1 is 4/2

which is 2

We can conclude that there are no nontrivial clean pulsations for the given left-mounted beam with a simple support on the right.

To find the equation of clean pulsations for a left-mounted beam with a simple support on the right, we can use the differential equation that describes the deflection of the beam. Assuming the beam is subject to a distributed load and has certain boundary conditions, the equation governing the deflection can be written as:

d^2y/dx^2 + (chx)^2 * y = 0

Where:

y(x) is the deflection of the beam at position x,

d^2y/dx^2 is the second derivative of y with respect to x,

ch(x) is the hyperbolic cosine function.

To solve this differential equation, we can assume a solution in the form of y(x) = A * cosh(kx) + B * sinh(kx), where A and B are constants, and k is a constant to be determined.

Substituting this assumed solution into the differential equation, we get:

k^2 * (A * cosh(kx) + B * sinh(kx)) + (chx)^2 * (A * cosh(kx) + B * sinh(kx)) = 0

Simplifying the equation and applying the given identity (chx)^2 - (shx)^2 = 1, we have:

(A + A * chx^2) * cosh(kx) + (B + B * chx^2) * sinh(kx) = 0

For this equation to hold for all values of x, the coefficients of cosh(kx) and sinh(kx) must be zero. Therefore, we get the following equations:

A + A * chx^2 = 0

B + B * chx^2 = 0

Simplifying these equations, we have:

A * (1 + chx^2) = 0

B * (1 + chx^2) = 0

Since we are looking for nontrivial solutions (A and B not equal to zero), the expressions in parentheses must be zero:

1 + chx^2 = 0

Using the identity (sinx)^2 + (cosx)^2 = 1, we can rewrite this equation as:

1 + (1 - (sinx)^2) = 0

Simplifying further, we get:

2 - (sinx)^2 = 0

Solving for (sinx)^2, we find:

(sin x)^2 = 2

Since the square of the sine function cannot be negative, there are no real solutions to this equation. Therefore, we can conclude that there are no nontrivial clean pulsations for the given left-mounted beam with a simple support on the right.

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The value of c in the right triangle using Pythagoras theorem is c = √113.

An equation is an expression that shows the relationship between two or more numbers and variables.

Pythagoras theorem shows the relationship between the sides of a right triangle. Hence:

c² = 8² + 7²

c = √113

The value of c in the right triangle using Pythagoras theorem is c = √113.

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The average annual return on this investment from 2011 to 2015 is approximately 0.8%.

To calculate the value of a $1 investment made at the beginning of 2011 and its average annual return by the end of 2015, we need to multiply the successive annual returns and calculate the cumulative value.

The successive annual returns on small U.S. stocks from 2011 to 2015 are:

-3.80%, 19.15%, 45.91%, 3.26%, and -3.80%.

To calculate the cumulative value, we multiply the successive returns by the initial investment value of $1:

(1 + (-3.80%/100)) * (1 + (19.15%/100)) * (1 + (45.91%/100)) * (1 + (3.26%/100)) * (1 + (-3.80%/100))

Calculating this expression, we find that the cumulative value is approximately $1.044, rounded to three decimal places.

Therefore, a $1 investment made at the beginning of 2011 would have been worth approximately $1.044 at the end of 2015.

To calculate the average annual return, we need to find the geometric mean of the annual returns. We can use the following formula:

Average annual return = (Cumulative value)^(1/number of years) - 1

In this case, the number of years is 5 (from 2011 to 2015).

Average annual return = (1.044)^(1/5) - 1

Calculating this expression, we find that the average annual return is approximately 0.008 or 0.8% per year, rounded to two decimal places.

Therefore, the average annual return on this investment from 2011 to 2015 is approximately 0.8%.

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The amount needed in the account is 182,713.25 dollars then the correct option is B.

The term loan refers to a sort of credit vehicle in which a sum of money is lent to another party in exchange for the value or principal amount being repaid in the future.

Then the formula of monthly payment (MP) will be

\(\rm MP = P \times \dfrac{r(1+r)^n}{(1+r)^n - 1}\\\)

The formula can be written as

\(\rm P = MP \times \dfrac{(1+r)^n-1}{r(1+r)^n}\\\)

You plan on supplementing your income. you would like to withdraw a semiannual salary of $6,951.20 from an account paying 1.75% interest, compounded semiannually.

The amount needed in the account is such that you can withdraw the needed amount at the end of each period for 15 years will be

MP = $6951.20

r = 0.00875

n = 30

Then we have

\(\rm P = 6951.20 \times \dfrac{(1+0.00875)^{30}-1}{0.00875(1+0.00875)^{30}}\\\\P = \$182713.25\)

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Two equations that represent the graph shown below as sine function y = 0.909x−3 and as cosine function y = −0.416x −3.

The sine graph or sinusoidal graph is an up-down graph and repeats every 360 degrees i.e. at 2π.

The general form of a cosine function is:

y = a cosb (θ±c) ± d

Here, amplitude, a  is = 1

For b, period is = π

2π/b = π

b = 2

c = 0

vertical shift = D = -3

Putting the value into formula

y = 1 cos2 (θ + 0) - 3

y = 1 ×−0.416(θ + 0) - 3

y = −0.416θ−3  

y = −0.416x −3  (cosine function)

y = 1 sin2 (θ + 0) - 3

y = 1 ×0.909(θ + 0) - 3

y = 0.909θ−3

y = 0.909x−3 (sine function)

Thus, two equations that represent the graph shown below as sine function y = 0.909x−3 and as cosine function y = −0.416x −3.

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Answer:

(x-7)²+(y+5)²=25

Step-by-step explanation:

The standard form of a circle is (x-h)²+(y-k)²=r²

(h,k) is the center

r is the radius

h=7

k=-5

r=5

(x-7)²+(y--5)²=5²

(x-7)²+(y+5)²=25

The z-score is a standardized score that measures how many standard deviations the score is from the mean of the population. By transforming data into z-scores, we can compare and rank scores from different populations with different means and standard deviations.

Using z-scores to compare the given values, we have; The z-score for the male is;  z = (1600 - 3247.5) / 580.3 = -1.88. The z-score for the female is; z = (1600 - 3078.8) / 692.7 = -2.36. The z-score is a standard score that can be used to compare values from different populations, with different means and standard deviations. We can use z-scores to determine which value is more extreme relative to the population from which it was drawn. Based on sample data, newborn males have weights with a mean of 3247.5 g and a standard deviation of 580.3 g, while newborn females have weights with a mean of 3078.8 g and a standard deviation of 692.7 g. The z-score for a male who weighs 1600 g is z = (1600 - 3247.5) / 580.3 = -1.88. Similarly, the z-score for a female who weighs 1600 g is z = (1600 - 3078.8) / 692.7 = -2.36. Since the z-score for the female is more negative, the female has a weight that is more extreme relative to the group from which they came. This means that the female weight of 1600 g is farther from the mean of the female population than the male weight of 1600 g is from the mean of the male population.

Using z-scores to compare the weights of newborn males and females, we found that a female who weighs 1600 g has a more extreme weight relative to the group from which she came than a male who weighs 1600 g. The z-score for the female was -2.36, while the z-score for the male was -1.88. The z-score is a useful tool for comparing values from different populations with different means and standard deviations.

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By using the quadratic formula, the solution to this quadratic equation is equal to -0.5251 or -3.8081.

In Mathematics, a quadratic equation can be defined as a mathematical expression that can be used to define and represent the relationship that exists between two or more variable on a graph. In Mathematics, the standard form of a quadratic equation is given by;

ax² + bx + c = 0

Mathematically, the quadratic formula is modeled or represented by this mathematical expression:

\(x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}\)

From the information provided, we have the following values;

3x² + 13x + 4 = 0

Where:

a = 3

b = 13

c = 4

Substituting the values into the quadratic formula, we have the following;

\(x = \frac{-(13)\; \pm \;\sqrt{(13)^2 - 4(3)(13)}}{2(3)}\\\\x = \frac{-13\; \pm \;\sqrt{169 - 72}}{6}\)

x = (-13 + √97)/6

x = -0.5251 or -3.8081.

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Answer:

176

Step-by-step explanation:

Answer:Holly drank 12 bottles in a week.

Step-by-step explanation:

First change the fraction 1 2/5 litre into a decimal, by doing this, we can know how many litres are there in 2/5.

So= 1 2/5

= 2 ÷5 = 0.4

= 1 + 0.4 = 1.4 liters

1.4 liters is the amount of water in a bottle.

Next, also change the fraction 2 2/5 litres into a decimal.

So=2 2/5

= 2÷5 = 0.4

= 2 + 0.4 = 2.4 liters

She drinks 2.4 liters a day.

To find how many bottles she drank in 1 week, we must multiply the amount of water she drinks in a day to the days in a week.

So= 1 week= 7 days

= 1 day= 2.4 liters

So= 2.4 × 7 = 16.8

She drinks 16.8 in a week.

To find how much bottles she drank in a week, we must divide the amount of liters she drank in one week to the amount of liters are there in a bottle.

So= 16.8 ÷ 1.4= 12 bottles

Holly drinks 12 bottles in a week.

I hope this helps! I'm sorry if it's wrong and complicated.

In exercise 10(b) of Chapter 10, Section 5, the question asks whether it is possible to cross all the bridges shown in a given map exactly once and return to the starting point.

This problem is known as the "Seven Bridges of Königsberg" puzzle, famously solved by Leonhard Euler in the 18th century. The solution involves applying graph theory principles to analyze the connectivity and degree of the bridges. The Seven Bridges of Königsberg problem is a well-known mathematical puzzle that involves a network of bridges and islands. The goal is to determine whether it is possible to cross each bridge exactly once and return to the starting point. This problem was originally posed by the Swiss mathematician Leonhard Euler in 1736 and played a significant role in the development of graph theory.

To solve this problem, we can represent the bridges and islands as a graph. Each island is represented as a vertex, and each bridge is represented as an edge connecting two vertices. By analyzing the connectivity and degree of the vertices in the graph, we can determine whether a solution exists.

In the given map, we would analyze the graph formed by the bridges and islands. If each island has an even degree (an even number of bridges connected to it), then it is possible to find a path that crosses each bridge exactly once and returns to the starting point. This can be proved using Euler's theorem, which states that in a connected graph, if the number of vertices with an odd degree is either 0 or 2, then there exists an Eulerian path or an Eulerian circuit respectively. However, if any island has an odd degree, it is not possible to find a path that satisfies the conditions of crossing each bridge exactly once and returning to the starting point.

Without further information or a specific map, it is not possible to determine the exact solution to exercise 10(b) in Chapter 10, Section 5. The solution would require analyzing the connectivity and degree of the bridges and islands in the given map and applying graph theory principles to determine the possibility of crossing all the bridges exactly once and returning to the starting point.

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Answer:

Below

Step-by-step explanation:

sin(2x) = 2 ×cos(x)× sin(x)

● sin(x) = 2 × cos(x) × sin(x)

● 2 × cos(x) = 1

● cos (x) = 1/2

So we can deduce that:

● x = Pi/3 + 2*k*Pi

● or x = -Pi/3 + 2*k*Pi

K is an integer

The Solution of x:

x = π/3 + 2πn, where n is an integer.

x = 2π/3 + 2πn, where n is an integer.

In degrees:

x = 60° + 360°n, where n is an integer.

x = 120° + 360°n, where n is an integer.

To solve the equation sin(2x) = sin(x), we can use the properties of trigonometric functions.

First, let's simplify the equation using the double angle identity for sine:

sin(2x) = 2sin(x)cos(x).

Now we can rewrite the equation as:

2sin(x)cos(x) = sin(x).

2cos(x) = 1.

Dividing both sides of the equation by cos(x), we get:

2 = 1/cos(x).

Now, we can find the value of cos(x) by taking the reciprocal of both sides:

cos(x) = 1/2.

From the unit circle or trigonometric values,

we know that cos(x) = 1/2 corresponds to angles of π/3 or 2π/3 (in radians) or 60° or 120° .

So, the solutions for x are:

x = π/3 + 2πn, where n is an integer.

or

x = 2π/3 + 2πn, where n is an integer.

In degrees:

x = 60° + 360°n, where n is an integer.

or

x = 120° + 360°n, where n is an integer.

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The border line is so much shaded below the inequality symbol (shown in purple).

A relationship among two expresses or values that is neither equal in mathematics is referred to by the term inequality. Thus, unequal results from imbalance. In arithmetic, an inequality explains the links between two non-equal numbers. Egality nor disparities are not the same. Were using the not equal symbol most usually when two values are just not equal (). Values of any size can be contrast using a variety of discrepancies. By changing the two sides till only the variables are left, many straightforward inequalities can be solved. However, a variety of factors support injustice: Both sides' negative values are split or added. Change the left and the right.

given

Gold costs $25 a gram, therefore y grams would cost $25. Because silver costs $0.40 per gram, x grams will cost you $0.0040. If the entire cost of the ring must be less than $90, then 25y+0.40x90, making the cost of the ring (25y+0.40x) dollars. For y, resolve this inequality: 25+0.40<90/25−0.40+90

Take 0.40 off of both sides.

<−0.016+3.6

25y+0.40x y900.40x+900.016x+3.6 = 25y+0.40x y900.40x+903.6

Remove 0.40x from both sides.

Add 25 to both sides.

The boundary line is therefore defined as =0.016+3.6 y=0.016x+3.6, which has a y-intercept of 3.6 and a slope of 0.016 0.016.

The border line is so much shaded below the inequality symbol (shown in purple).

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The equilibrium point for the supply and demand equations p² + 4q = 253 and 183p² + 6q = 0 is (q, p) = (3, 10).

To find the equilibrium point, we need to solve the system of equations formed by the supply and demand equations. By substituting the value of q = 3 into the first equation, we get p² + 4(3) = 253, which simplifies to p² + 12 = 253.

Solving this equation gives us p = 10. Substituting the values of q = 3 and p = 10 into the second equation, we get 183(10)² + 6(3) = 0, which simplifies to 18300 + 18 = 0.

Since this equation holds true, we have found the equilibrium point to be (q, p) = (3, 10), where the equilibrium quantity is q = 3 and the equilibrium price is p = 10.

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Answer:

Area = 45 units²

Perimeter = 29.4 units

Step-by-step explanation:

We can find the area of the shape in two parts.

The first part is the rectangle,

w × l

7 × 5 = 35 units²

The second part is the triangle,

\( \frac{1}{2} \times b \times h\)

\( \frac{1}{2} \times 5 \times 4 = 10 \: \: {units}^{2} \)

To find the area of the whole shape, add both parts up:

35 units² + 10 units² = 45 units²

9 + 7 + 5 + 2 + 6.4 = 29.4 units