MATH HELP. ( please answer both questions ) thank you !

The difference quotient for the given function is 9 -2/h.

The difference quotient for the given function can be calculated as:

[f(x+h) - f(x)]/h

= [(3(x+h)² - 2(x+h) + 5) - (3x² - 2x + 5)]/h

= (3x² + 6xh + 3h² - 2x - 2h + 5 - 3x² + 2x - 5)/h

= (6xh + 3h² - 2h)/h

= (6x + 3h -2)/h

Simplifying the expression further, we get:

(6x + 3h -2)/h = 6 + 3h/h -2/h

= 6 + 3 -2/h

= 9-2/h

Therefore, the difference quotient for the given function is 9 -2/h.

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"Your question is incomplete, probably the complete question/missing part is:"

Find the difference quotient [f(x+h)-f(x)]/h, where h≠0, for the function below.

f(x)=3x² -2x+5. Simplify your answer as much as possible.

The exact length of the polar curve r = 5cos(theta) over the interval 0 ≤ theta ≤ pi/2 is 5π/2 units

To find the length of the polar curve r = 5cos(theta) over the interval 0 ≤ theta ≤ pi/2, we can use the following formula:

L = ∫[a,b] sqrt[r^2 + (dr/dθ)^2] dθ

where a and b are the initial and final values of theta over the interval, and r and (dr/dθ) are the polar equation and its derivative with respect to theta.

First, we need to find the derivative of r with respect to theta:

dr/dθ = -5sin(theta)

Then, we can substitute r and (dr/dθ) into the formula:

L = ∫[0,π/2] sqrt[(5cos(theta))^2 + (-5sin(theta))^2] dθ

Simplifying under the square root:

L = ∫[0,π/2] sqrt[25(cos^2(theta) + sin^2(theta))] dθ

L = ∫[0,π/2] 5 dθ

L = 5θ ∣ [0,π/2]

L = 5(π/2 - 0)

L = 5π/2

Therefore, the exact length of the polar curve r = 5cos(theta) over the interval 0 ≤ theta ≤ pi/2 is 5π/2 units.

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Answer:

a. A si C

b. A

Step-by-step explanation:

Aici, vrem să cunoaștem seturile la care aparțin elementele;

a) Elementul

a putem vedea elementul a în mulțimea A și C

b) Elementul b

putem vedea elementul b numai în mulțimea A

Answer:

Square

Step-by-step explanation:

the quadrilateral obtained by joining the mid points of adjacent sides of a square is a square.

Answer:

The formula for the area of a circle is:

A = πr^2

where A is the area and r is the radius.

In this case, we are given that the area is 4π cm². Solving for the radius, we get:

4π = πr^2

r^2 = 4

r = 2

So the radius of the circle is 2 cm.

The formula for the circumference of a circle is:

C = 2πr

Plugging in the value for the radius, we get:

C = 2π(2) = 4π

Therefore, the circumference of the circle is 4π cm.

Answer:

40

Step-by-step explanation:

i minus

There are four degrees of freedom for the chi-square goodness-of-fit test in this study. So, correct option is B.

For a chi-square goodness-of-fit test in the context of testing the fairness of a spinner with five sections, the number of degrees of freedom can be determined by subtracting 1 from the number of categories being tested.

In this case, since the spinner has five sections, there are five categories. Therefore, the degrees of freedom for the chi-square goodness-of-fit test would be:

Degrees of freedom = Number of categories - 1

= 5 - 1

= 4

Degrees of freedom represent the number of values in the final calculation of the chi-square test statistic that are free to vary. It determines the critical values and the distribution of the test statistic.

In the case of the chi-square goodness-of-fit test, the test compares the observed frequencies in each category with the expected frequencies under the assumption of fairness. By comparing these frequencies, the test determines if there is a significant deviation from the expected distribution, indicating unfairness in the spinner.

So, correct option is B.

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The simplified form of the given expression is option c 1 1/2x - 1 3/4

Given,

The expression; 1/4 (3x - 7) + 3/4x

We have to simplify this expression;

Simplification of expressions;

To simplify a phrase, create an equivalent expression without any terms that are identical. The expression will then be rewritten using the fewest terms feasible.

Then,

1/4 (3x - 7) + 3/4x

= 1/4 × 3x - 1/4 × 7 + 3/4x

= 3/4x - 7/4x + 3/4x

= 6x/4 - 7/4

= 3x/2 - 7/4

= 1 1/2x - 1 3/4

Therefore,

The simplified form of the given expression is option c 1 1/2x - 1 3/4

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Answer:

2 times 2 is 4

Step-by-step explanation:

okay so i have 2 cookies right, my big brother gave me 2 more. how many do  i have ? i should have 4 because 1 plus 1 plus 1 plus 1 is 4.

The first term on the left-hand side represents the flux of the quantity D(pu δ) across the cell boundaries, and the second term represents the change of this flux within the cell.

To integrate the 1D steady-state convection-diffusion equation over a typical cell, we can start with the given equation:

D/dx(pu δ) = d/dx (rd δ/dx)

Here, D is the diffusion coefficient, p is the velocity, r is the reaction term, u is the concentration, and δ represents the Dirac delta function.

To integrate this equation over a typical cell, we need to define the limits of the cell. Let's assume the cell extends from x_i to x_i+1, where x_i and x_i+1 are the boundaries of the cell.

Integrating the left-hand side of the equation over the cell, we have:

∫[x_i to x_i+1] D/dx(pu δ) dx = D∫[x_i to x_i+1] d(pu δ)/dx dx

Using the integration by parts technique, the integral can be written as:

= [D(pu δ)]_[x_i to x_i+1] - ∫[x_i to x_i+1] d(D(pu δ))/dx dx

Similarly, integrating the right-hand side of the equation over the cell, we have:

∫[x_i to x_i+1] d/dx (rd δ/dx) dx = [rd δ/dx]_[x_i to x_i+1]

Combining the integrals, we get:

[D(pu δ)][x_i to x_i+1] - ∫[x_i to x_i+1] d(D(pu δ))/dx dx = [rd δ/dx][x_i to x_i+1]

This equation can be further simplified and manipulated using appropriate boundary conditions and assumptions based on the specific problem at hand.

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Answer:

100

Step-by-step explanation:

Just add

Hi!

The minimum is the lowest possibility on the graph, and the maximum is the highest.

In this graph, the highest point (the maximum) is (10,11) and the lowest point (the minimum) is (3, 1).

Hope this helps! :D

Answer:

that was when I was in 1st grade. I was quite confused and didn't know what to do. We rehearsed first. I made a lot of mistakes but everything was fine until I got on stage. I think when I finished performing, it was my proudest time

i dont know is there a picture

Step-by-step explanation:

\( \frac{12}{6} \times \frac{12}{1} = 24\)

That is the answer

The given expression is a simplified algebraic equation: (1/2) * a^2 - 3b + 2c. It represents a combination of variables a, b, and c with their respective coefficients.

Utilizing symbols and operations, an algebraic equation illustrates the equivalence or inequivalence of two expressions. These generated expressions may hold variables that have varying values.

The premise centered around calculus is to arrive at a solution by acquiring the correct value(s) of these variable(s), ultimately fulfilling the outlined specification in the problem. Algebraic equations can range from uncomplicated linear problems to elaborate polynomials and trigonometric functions.

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The amount of total cost at q* is 1.

To determine the production level that minimizes total cost, we need to find the value of q (production level) at which the derivative of the total cost function TC(q) is equal to zero. Let's begin by finding the derivative of TC(q):

TC(q) = 10 - 6q + q^2

To find the minimum point, we differentiate TC(q) with respect to q:

d(TC(q))/dq = -6 + 2q

Setting the derivative equal to zero and solving for q:

-6 + 2q = 0

2q = 6

q = 3

So the production level q* that minimizes the total cost is 3.

To find the amount of total cost at q*, we substitute q = 3 into the total cost function TC(q):

TC(q*) = 10 - 6(3) + (3)^2

TC(q*) = 10 - 18 + 9

TC(q*) = 1

Therefore, the amount of total cost at q* is 1.

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The slope is of m = 7 and the y-intercept is of b = 10.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

From the table, when x increases by one, y increases by 7, hence the slope m is given as follows:

m = 7.

Hence:

y = 7x + b.

When x = 1, y = 17, hence the intercept b is given as follows:

7 + b = 17

b = 10.

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Explanation:

8 people picked comedy out of 14+8+2+4 = 28 people total.

8/28 = (4*2)/(4*7) = 2/7 is the probability of randomly selecting someone who picked comedy as their favorite.

Answer:

3

Step-by-step explanation:

Given information: Mass of dolphin, m = 1800 N; Height of jump, h = 2.10 m.

The gravitational potential energy of the dolphin can be calculated as follows: Gravitational potential energy = mgh where, m is the mass of the dolphin, g is the acceleration due to gravity, and h is the height of the jump.

Given that the dolphin jumps from the water, its initial potential energy is zero. Hence, the total energy of the dolphin is equal to the potential energy at the highest point. At this point, the kinetic energy of the dolphin is also zero. Therefore, the energy conservation equation can be written as follows: mg h = (1/2)mv²where, v is the velocity of the dolphin just before it jumps out of the water.  

Solving for v, we get v = sqrt(2gh)where sqrt denotes the square root, g is the acceleration due to gravity, and h is the height of the jump. Substituting the given values, we get v = sqrt(2 x 9.8 x 2.10)v = 6.22 m/s Therefore, the dolphin must be moving at a speed of 6.22 m/s as it leaves the water in order to jump to a height of 2.10 m.

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the statement is true

this is

We can use the following theorem:

From the problem:

The normal price of the car is given as follows:

£9000.

The normal price of the car is obtained applying the proportions in the context of this problem.

In a sale, the normal price of a car has been reduced by 30%. The new price is £6300, meaning that 70% of the price x is equivalent to 6300.

Thus the equation used to obtain the value of x is given as follows:

0.7x = 6300

x = 6300/0.7

x = £9000.

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Answer: That made no sense

Step-by-step explanation:

To transform the regression equation, you would divide both sides of the equation by the square root of Var(ut), which is σ√(zt). This transformation helps in obtaining the transformed regression coefficients and standard errors that account for the heteroscedasticity in the error term.

When the variance of the error term (ut) is related to a known variable (zt), it implies the presence of heteroscedasticity in the regression model. Heteroscedasticity means that the variability of the error term is not constant across different levels of the independent variables.

To address this issue, we can transform the regression equation by dividing both sides by the square root of the variance of the error term, which is σ√(zt). This transformation is known as the weighted least squares (WLS) estimation.

By dividing both sides of the equation, we can obtain the transformed regression equation with the error term divided by its standard deviation. This transformation accounts for the heteroscedasticity by giving different weights to the observations based on the variability of the error term. It allows for a more appropriate estimation of the regression coefficients and standard errors, as it gives more weight to observations with smaller error variances and less weight to observations with larger error variances.

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The parametric equations of a line can be determined using a point on the line and a direction vector. To find the parametric equation of a line that passes through a point A and is parallel to a direction vector b, we can use the following formula:

x = x0 + tbx

y = y0 + tby

z = z0 + tbz

where (x0, y0, z0) is the position vector of point A, (bx, by, bz) is the direction vector, and t is the parameter that varies along the line.

An algebraic equation, also known as a polynomial equation, is a mathematical equation of the form P=0, where P is a polynomial with coefficients in some field, most commonly the field of rational numbers. An algebraic equation is a mathematical statement that sets two expressions equal to each other. An algebraic equation is typically made up of a variable, coefficients, and constants.

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Let's take a look at the graph of the polynomial:

Now, notice that those three turning points tell us that the function changes from decreasing to increasing, or viceversa, right at that point.

This way, the decreasing intervals are:

And the increasing intervals are:

Thus, the standard form equation of the ellipse that has vertices \((\pm 12,0) and foci (\pm 9,0) is x^2/1008 + y^2/504 = 1.\)

The given vertices are\((\pm 12,0) and foci are (\pm 9,0)\). We know that for the ellipse, \(c^2=a^2-b^2\), where c is the distance from the center to the foci, a is the distance from the center to the vertices, and b is the distance from the center to the co-vertices. Here, the center is at the origin (0, 0).

So, the value of 'a' is 12 and 'c' is 9. Thus, we can find the value of 'b' as follows:\(b=√(a^2-c^2)b=√(12^2-9^2)b=√(144-81)b=√63 =3√7\)

Now we can write the standard equation of the ellipse: \(x^2/a^2 + y^2/b^2 = 1\)

Substitute the given values, a=12 and b=3

√\(7: x^2/12^2 + y^2/(3√7)^2 = 1x^2/144 + y^2/63 = 1\)

Multiply both sides by \(144: x^2 + 144y^2/63 = 144 Divide by 144/63: x^2/144/63 + y^2/144/63 = 1\)

The above equation is the standard form of the ellipse.

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Answer:

x-10

Step-by-step explanation: