what is the difference between integrationg by ordinary substitution and integrating by trigonometric substiti

The activation energy of the reaction is approximately 126.8 kJ/mol. The calculation was done using the Arrhenius equation and the natural logarithm of the rate constants at the two temperatures.

To calculate the activation energy of a reaction, we can use the Arrhenius equation:

k = A * e⁽⁻ᴱᵃ/ᴿᵀ⁾

where k is the rate constant, A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin.

We have two rate constants at different temperatures, so we can set up two equations:

k₁ = A * e⁽⁻ᴱᵃ/ᴿᵀ₁⁾

k₂ = A * e⁽⁻ᴱᵃ/ᴿᵀ₂⁾

We want to solve for Ea, so we can take the natural logarithm of both sides of each equation:

ln(k₁) = ln(A) - Ea/RT₁

ln(k₂) = ln(A) - Ea/RT₂

We can subtract the second equation from the first to eliminate ln(A):

ln(k₁) - ln(k₂) = Ea/R * (1/T₂ - 1/T₁)

Now we can solve for Ea:

Ea = -R * (ln(k₁) - ln(k₂)) / (1/T₂ - 1/T₁)

Plugging in the given values, we get:

Ea = -8.314 J/mol/K * (ln(6.20 x 10⁻⁴) - ln(2.39 x 10⁻²)) / (1/760 K - 1/700 K)

Ea ≈ 126.8 kJ/mol

Therefore, the activation energy of the reaction is approximately 126.8 kJ/mol.

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A leaking faucet in the S&E building lab, dripping at a rate of one drop per second, will result in a water loss of approximately 4,725 liters in one year.

To calculate the amount of water lost in one year, we need to determine the number of drops per year and then convert it to liters. Since the faucet drips at a rate of one drop per second, there are 60 drops in a minute (60 seconds), which totals to 3,600 drops in an hour (60 minutes).

In a day, there would be 86,400 drops (24 hours * 3,600 drops). Considering a year of 365 days, the total number of drops would be approximately 31,536,000 drops (86,400 drops * 365 days). To convert the number of drops to liters, we need to multiply the total number of drops by the volume of each drop.

Given that each drop contains 0.150 milliliters, we convert it to liters by dividing by 1,000, resulting in 0.00015 liters per drop. Multiplying the total number of drops by the volume per drop, we find that the total water loss is approximately 4,725 liters (31,536,000 drops * 0.00015 liters/drop).

Therefore, in one year, the leaking faucet in the S&E building lab would result in a water loss of approximately 4,725 liters.

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Answer:

There are 13 blue pens in a package.

Explanation:

total blue pens: 45 - 6 = 39 blue pens in 3 packages

3 package → 39 blue pens

1 package → (39/3) blue pens

1 package → 13 blue pens

Answer:

13 blue pens

Step-by-step explanation:

6 red pens + 3 packages of blue pens = 45

3 packages of blue pens = 39

\(\hookrightarrow\) Divide by 3

1 package of blue pens = 13

-Chetan K

Step-by-step explanation:

The factors of -3 are -1, -3.

Answer:

Step-by-step explanation:

If the sum of three consecutive odd integers is 255, then the three integers are 83, 85, and 87.

The solution:

Given:

cosine function has an amplitude of 4, a vertical shift of 1, and a period of 3.

Required:

To write out the equation of the graph in terms of cosine.

So, the required equation is:

Therefore, the correct answer is:

Answer:

since speed is miles per hour it would be s=1/1/2 so it would be 2mph

At point, the parametric curve cross (4, 1, 32).

t functions expressed as x = f(y) = y = f(x) = (some function of the variable x) (some function of the variable y).

It is frequently more easier to view functions of two or more variables (although we'll keep it at two here) as parametric functions, particularly in physical science.

The introduction of the idea of time makes parametric functions the most simple to understand.

Imagine tracing a parabola-like function from left to right as time passes.

Then, it is simple to begin considering how the x-coordinate and the y-coordinate change as a function of time: x = f(t), y = g. (t). In this sense, time is actually referred to as the parameter.

We will investigate functions for which a point exists in this section.

Hence, At point, the parametric curves cross (4, 1, 32).

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time to get your Unit Circle, if you don't have one, this will  be a good time to get one, you can get many online.

\(cos(x)=\cfrac{sin(30^o)}{tan(30^o)}\implies cos(x)=\cfrac{~~ \frac{1}{2}~~}{\frac{1}{\sqrt{3}}}\implies cos(x)=\cfrac{1}{2}\cdot \cfrac{\sqrt{3}}{1} \\\\\\ cos(x)=\cfrac{\sqrt{3}}{2}\implies \measuredangle x=cos^{-1}\left( \cfrac{\sqrt{3}}{2} \right)\implies \measuredangle x=30^o\)

You can male 40 muffins with 5 cups of flour.

Step-by-step explanation:

24÷3=8

8×5=40

To determine Km from a double-reciprocal plot, you would choose option (A) which is to multiply the reciprocal of the x-axis intercept by -1.

In the double-reciprocal plot equation, the x-axis intercept is -1/Km, and the y-axis intercept is 1/Vmax. Therefore, if you take the reciprocal of the x-axis intercept, you get -Km, and multiplying it by -1 gives you Km.

This method is preferred because it is more accurate than estimating Km based on the position of the curve on the plot or by taking the x-axis intercept where V0 = 1/2 Vmax, which can be influenced by experimental error.

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Answer:

5y=9x-2

y=mx-b

m=slope

y=9/5x-2/5

m=9/5=1.8 slope of pArallel

slope of pARALLEL=-1/M SLOPE OF A LINE PERPENDICULAR

m=-5/9 slope of a line perpendiculr

Step-by-step explanation:

area of the trapezoid = area of the 2 triangles +

area of the rectangle

i) area of triangle on left:

a = ½ bh

a = ½ × 2 × 9

a = 9 in²

ii) area of triangle on right:

a = ½ bh

a = ½ × 2 × 9

a = 9 in²

iii) area of rectangle = length × width

a = l × w

a = 12 × 9

a = 108 in²

iv) area of trapezoid = 9 + 9 + 108

= 126 in²

hope this helps you!

-s.

Answer

Step-by-step explanation:

8^-5/8^-2

=8^5-(-2)

=8^5+2

=8^7

=2097152

Note in division if the base the base are same then u can subtract their exponent but in multiplication bases are same u should add their exponent.

When Trevor graduated high school, he put his pirating CDs behind him and got a job at a clothing store to save money for college. Saving money is an essential part of financing college.

A student can achieve their dream of attending college by following the steps below.

Step 1: Create a budget. Creating a budget is the first step in saving for college. The budget should include all expenses, such as tuition, room and board, books, and other fees.

Step 2: Find ways to save money. Save money by finding ways to reduce spending on non-essentials such as entertainment, dining out, and shopping. Every little bit counts, and the savings can be put toward college.

Step 3: Explore scholarships and financial aid. Apply for financial aid and scholarships to help pay for college. Grants, loans, and scholarships are available from federal, state, and private sources.

Step 4: Consider community college or online education. Consider community college or online education as an affordable way to earn college credit and save money.

Step 5: Work and save Continue working and saving money during college. A part-time job or paid internship can help cover expenses and reduce student loan debt.

These are the essential steps for saving money for college. A student can explore these options and make smart financial decisions to achieve their dream of attending college.

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Answer:

Given a function f, a new function g ( x ) = f ( x − h ) \displaystyle g\left(x\right)=f\left(x-h\right) g(x)=f(x−h), where h is a constant, is a horizontal shift of the function f. If h is positive, the graph will shift right. If h is negative, the graph will shift left.

Step-by-step explanation:

Answer:

b = 12 ft; h = 8 ft

Step-by-step explanation:

Area of Triangle:

A = base × height / 2

The base and height are both unknown.

Let the height = h

The base is 4 more than the height, so the base is h + 4.

A = base × height / 2

48 = (h + 4)(h)/2

96 = (h + 4)h

h² + 4h - 96 = 0

(h - 8)(h + 12) = 0

h - 8 = 0  or h + 12 = 0

h = 8 or h = -12

The height cannot be a negative number, so discard the solution h = -12.

h = 8

base = h + 4 = 8 + 4 = 12

Answer: b = 12 ft; h = 8 ft

Answer:

1 a) 20202

Ans. 20000+0+200+0+2

b)220202

Ans. 200000+20000+0+20+0+2

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Answer:

6 workers have to be on the team to finish the project A in 72 days

Step-by-step explanation:

Hi, I will help you with this question

In any project, if x employees work for y days to finish the project, then

Project = x y

x and y are variables but the project is constant, so

In the same job, if z employees work for m days to finish it, then

Project = z m

∵ Project = Project

∴ x y = z m

Very important note:

Let us use this rule in the question

∵ 18 workers will take 95 days to finish the project

∴ Project = 18 (95) = 1710

∵ x workers take 72 days to finish the same project

∴ Project = x (72)

→ Substitute the project by 1710

∴ 1710 = 72 x

Divide both sides by 72 to find x

∴ x = 23.75 ≈ 24

∵ x represents the number of workers

∴ 24 workers can finish the project in 72 days

∵ There are 18 workers already

∴ The number of workers needed = 24 - 18 = 6

∴ 6 workers have to be on the team to finish the project A in 72 days

The claim that two situations are similar, despite major differences being ignored and only minor similarities being emphasized, is a fallacy known as false analogy.

False analogy is a logical fallacy that occurs when two situations are compared based on minor similarities while ignoring significant differences. It involves drawing an invalid or weak comparison between two unrelated or dissimilar things. In this fallacy, the person making the claim assumes that because two situations share some superficial similarities, they must be similar in all aspects. However, this overlooks the fundamental differences that make the situations distinct.

For example, if someone argues that banning the use of plastic bags in a city is similar to banning the use of cars, based solely on the fact that both involve restricting a common item, they would be committing a false analogy. While there may be minor similarities between the two situations, such as the concept of imposing restrictions, there are major differences in terms of environmental impact, necessity, and alternatives. Ignoring these significant differences leads to an invalid comparison and can result in flawed reasoning.

In conclusion, false analogy occurs when two situations are deemed similar based on minor similarities while disregarding major differences. It is essential to carefully evaluate the relevant factors and understand the nuances of each situation before drawing comparisons to ensure logical and valid arguments.

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Answer:

150min

Step-by-step explanation:

a. U'(ct) = β(1 + r)U'(ct+1). This equation is known as the Euler equation, which represents the intertemporal marginal rate of substitution between consumption at time t and consumption at time t+1.

b. U'(c1) = β(1 + r)^2U'(c3). This relationship shows that the marginal utility of consumption at time 1 is equal to the discounted marginal utility of consumption at time 3.

c. C0 = ∑t=0[infinity]​(β(1 + r))^tct. This equation represents the sum of the discounted values of consumption at each period, where the discount factor β(1 + r) accounts for the diminishing value of future consumption.

d.  U0 = ∑t=0[infinity]​(β(1 + r))^tln(ct). This equation represents the sum of the discounted values of utility at each period, where the discount factor β(1 + r) reflects the time preference and the logarithmic utility function captures the agent's preference for consumption.

Y0 = y0 + (1 + γ)y1 + (1 + γ)^2y2 + ..., where γ represents the growth rate of income.

a. The optimization problem of the representative agent involves maximizing the present discounted value of utility subject to the period-by-period budget constraint. The Euler equation is derived as follows:

At each period t, the agent maximizes the utility function U(ct) = ln(ct) subject to the budget constraint ct = (1 + r)wt + yt, where wt is the agent's wealth at time t. Taking the derivative of U(ct) with respect to ct and applying the chain rule, we obtain: U'(ct) = β(1 + r)U'(ct+1). This equation is known as the Euler equation, which represents the intertemporal marginal rate of substitution between consumption at time t and consumption at time t+1.

b. The Euler equation between time 1 and time 3 can be written as U'(c1) = β(1 + r)U'(c2), where c1 and c2 represent consumption at time 1 and time 2, respectively.

Similarly, we can write the Euler equation between time 2 and time 3 as U'(c2) = β(1 + r)U'(c3). Combining these two equations, we fin

d U'(c1) = β(1 + r)^2U'(c3). This relationship shows that the marginal utility of consumption at time 1 is equal to the discounted marginal utility of consumption at time 3.

c. The present discounted value of optimal lifetime consumption can be written as C0 = ∑t=0[infinity]​(β(1 + r))^tct. This equation represents the sum of the discounted values of consumption at each period, where the discount factor β(1 + r) accounts for the diminishing value of future consumption.

d. The present discounted value of optimal lifetime utility can be written as U0 = ∑t=0[infinity]​(β(1 + r))^tln(ct).

This equation represents the sum of the discounted values of utility at each period, where the discount factor β(1 + r) reflects the time preference and the logarithmic utility function captures the agent's preference for consumption.

e. The present discounted value of lifetime income, denoted as Y0, can be expressed as Y0 = y0 + (1 + γ)y1 + (1 + γ)^2y2 + ..., where γ represents the growth rate of income. The income in each period is multiplied by (1 + γ) to account for the increasing income over time.

This assumption of income growth allows for a more realistic representation of the agent's economic environment, where income tends to increase over time due to factors such as productivity growth or wage increases.

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Answer:

\(\frac{5}{24}\)

Step-by-step explanation:

\(\frac{5x^3}{6}\) × \(\frac{1}{4x^3}\) ( cancel x³ on numerator/ denominator )

= \(\frac{5}{6}\) × \(\frac{1}{4}\)

= \(\frac{5(1)}{6(4)}\)

= \(\frac{5}{24}\)

Answer:

\( \frac{5}{3} {a}^{2} b + \frac{3}{4} abc + 5 \\ \\ \frac{5}{3} ( { - 2)}^{2} (1) + \frac{3}{4} ( - 2)(1)(2) \\ \\ \frac{5}{3} (4) + \frac{3}{4} ( - 4) \\ \\ = \frac{20}{3} - 3 \\ \frac{20 - 9}{3} = \frac{11}{3} = 3.666\)

3x²y+5xy²+2xyz = 3(-1)²(2) + 5(-1)(2)² + 2(-1)(2)(-2) = 3(1)(2) + 5(-1)(4) + 2(4) = 6 – 20 + 8 = – 6

I hope I helped you^_^

Answer:

66 sweets

Step-by-step explanation:

all you need to do is multiply 11 by 6 to get your answer seeing that ⅙ of the jar is 11

Answer:

9.6 days

Step-by-step explanation:

100 chickens, 12 days

find the days for 10 chickens: 1.2 days (to get 10 you have to divide 100 by ten, so divide 12 by ten too)

times by 8 to get the days for 80 chickens: 9.6 days

Answer: Let's assume that the bag of corn contains "C" units of corn. We know that this amount of corn can feed 100 chickens for 12 days.

To determine how long the same bag of corn would feed 80 chickens, we can use the following proportion:

(Corn units)/(chickens * days) = (Corn units)/(chickens * days)

We can set up two ratios, one for the original situation and one for the new situation, and then cross-multiply to solve for the unknown value:

C/100 * 12 = C/80 * d

where "d" is the number of days that the same bag of corn would feed 80 chickens.

Simplifying the equation, we get:

C/10 = C/80 * d

Multiplying both sides by 80, we get:

8C = Cd

Dividing both sides by "C", we get:

8 = d

Therefore, the same bag of corn would feed 80 chickens for 8 days.

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Answer:

y = 4x - 25

Step-by-step explanation:

y = 4x + b

-1 = 4(6) + b

-1 = 24 + b

-25 = b

The first order differential equation y' + xy² = 0 is both Linear & Separable.

The given first order differential equation is y' + xy² = 0.

In differential equations, a differential equation that is separable if it can be written in the form

g(y)dy = f(x)dx.

Separable equations have the advantage that they can be solved using straightforward integration.

In other words, a differential equation that can be solved by separating the variables and integrating each side is known as a separable differential equation.

For the given equation, y' + xy² = 0, we can separate the variables as follows:

y' = -xy²dy/dx

= -xy²dy/y²

= -xdx

Integrating both sides, we have,

∫ dy/y² = -∫ xdx-y⁻¹

= (-1/2)x² + C

Where C is the constant of integration.

The integral 3x e4x dx can be solved using integration by parts with

u = 3x,

v' = e4x

The given integral is ∫ 3xe⁴xdx.To solve this, we use integration by parts, where

u = 3x and

dv/dx = e⁴x.

Integrating by parts formula

∫ udv = uv - ∫ vdu

Using this formula, we get

∫ 3x e⁴x dx = 3x (1/4) e⁴x - (3/4) ∫ e⁴x dx

= (3/4) e⁴x - (9/16) e⁴x + C

= (3/16) e⁴x + C

Therefore, the correct options are:C Both Linear & Separable B neither of these

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Answer:

11

Step-by-step explanation:

6 is 1/3 of 18

so, 6% is 1/3 of 18%