Which of terms could be added to √5?

Answers

Answer 1

Answer: 10 is the correct answer

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The rate of change of the temperature T(t) of a body is still governed bydT
/dt
= âk(T â A), T(0) = T0,

when the ambient temperature A(t) varies with time. Suppose the body is known to have

k = 0.2

and initially is at 32Â°C; suppose also that

A(t) = 20eât.

Find the temperature T(t).

Answers

Answer:

$T(t)=5e^(-t)+27e^(-0.2t)$

Step-by-step explanation:

QUESTION

The rate of change of the temperature T(t) of a body is still governed by

$(dT)/(dt)=-k(T-A), T(0)=T_0$ when the ambient temperature A(t) varies with time. Suppose the body is known to have k = 0.2 and initially is at 32°C; suppose also that $A(t) = 20e^(-t)$ . Find the temperature T(t).

SOLUTION

$(dT)/(dt)=-k(T-A), T(0)=T_0, A(t) = 20e^(-t), k=0.2$

$(dT)/(dt)=-0.2T+20(0.2)e^(-t)\n(dT)/(dt)+0.2T=4e^(-t)\n\text{Integrating factor}=e^(0.2t)\n(dTe^(0.2t))/(dt)=4e^(-t)e^(0.2t)\ndTe^(0.2t)=4e^(-t)e^(0.2t)dt\n\int d[Te^(0.2t)]=4\int e^(-t(1-0.2))dt\nTe^(0.2t)=4\int e^(-0.8t)dt\nTe^(0.2t)=(4)/(-0.8) e^(-0.8t)+C, \text{C a constant of integration}\nTe^(0.2t)=-5 e^(-0.8t)+C\nT(t)=5 e^(-0.8t)e^(-0.2t)+Ce^(-0.2t)\nT(t)=5e^(-t)+Ce^(-0.2t)\nWhen t=0, T_0=32\n32=5+C\nC=27$

Therefore:

$T(t)=5e^(-t)+27e^(-0.2t)$

A certain city's population is 120,000 and decreases 1.4% per year for 15 years.Is this exponential growth or decay? Growth
What is the rate of growth or decay?
What was the initial amount? 120000
What is the function?
What is the population after 10 years? Round to the nearest whole number.

Answers

Answer:

Decay Problem.

Decay rate, r = 0.014
Initial Amount =120,000

$P(t)=120000(0.986)^t$
P(10)=104,220

Step-by-step explanation:

The exponential function for growth/decay is given as:

$P(t)=P_0(1 \pm r)^t, where:\nP_0$ is the Initial Population\nr is the growth/decay rate\nt is time$

In this problem:

The city's initial population is 120,000 and it decreases by 1.4% per year.

Since the population decreases, it is a Decay Problem.

Decay rate, r=1.4% =0.014
Initial Amount =120,000

Therefore, the function is:

$P(t)=120000(1 - 0.014)^t\nP(t)=120000(0.986)^t$

When t=10 years

$P(10)=120000(0.986)^10\n=104219.8\n\approx 104220 $ (to the nearest whole number)$

Find the slope using the formula.
(4, 19) and (2, 11)

Answers

Answer:

$m=4$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Slope Formula: $m=(y_2-y_1)/(x_2-x_1)$

Step-by-step explanation:

Step 1: Define

(4, 19)

(2, 11)

Step 2: Find slope m

Substitute: $m=(11-19)/(2-4)$
Subtract: $m=(-8)/(-2)$
Divide: $m=4$

Wendi is 6 years older than Zaviel. The sum of their ages is 30. Which of these systems of equations can be used to find Wendi's age (w) and Zaviel's age (z)?

Answers

The system of equations for the ages of Wendi and Zaviel can be obtained as x = y + 6 and x + y = 30 respectively.

What is a system of linear equations?

A system of linear equations is a group of equations having same number of variables and degree.

For the n number of variables n number of equations are required.

On the basis of number of solutions a system of equations can be classified as consistent and inconsistent.

Suppose the age of Wendi and Zaviel be x and y respectively.

Then, the equation for their age can be written as,

x = y + 6

And, the equation for the sum of ages is given as,

x + y = 30

Hence, the equations that represent the given case are x = y + 6 and x + y = 30 respectively.

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For Wendy’s age you can’t do 30-6=24 and then for Zaviel’s you can do 24-6=18 so Wendy is 24 years old and Zaviel is 18 years old.
30-6=w
W-6=z
30-6=24(w)
24-6=18(z)

Given that a 90% confidence interval for the mean height of all adult males in Idaho measured in inches was [62.532, 76.478]. Use this to answer all parts. What was the point estimate used to estimate the mean height of all adult males in Idaho?

Answers

The point estimate used to estimate the mean height of all adult males in Idaho was 69.505 inches.

Calculation of the estimation of the point

Since Given that a 90% confidence interval for the mean height of all adult males in Idaho measured in inches was [62.532, 76.478].

So, the estimation of the point is

$= (62.532 + 76.478) / 2$

= 69.505 inches

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Answer:

The point estimate used to estimate the mean height of all adult males in Idaho was 69.505 inches.

Step-by-step explanation:

The point estimate is the halfway point of the confidence interval, that is, the lower bound added to the upper bound, and then this sum is divided by 2. So

Lower bound: 62.535

Upper bound: 76.478

Point estimate:

$P_(e) = (62.535 + 76.478)/(2) = 69.505$

The point estimate used to estimate the mean height of all adult males in Idaho was 69.505 inches.

Kent Co. manufactures a product that sells for $60.00. Fixed costs are $285,000 and variable costs are $35.00 per unit. Kent can buy a new production machine that will increase fixed costs by $15,900 per year, but will decrease variable costs by $4.50 per unit. What effect would the purchase of the new machine have on Kent's break-even point in units?

Answers

0riginal break even point:

285000/ 60/35 = $166,250

New break even point = new fixed costs / ( selling price - variable cost/ selling price)

New break even point = 285,000 + 15,900. / ( 60-( 35-4.50)/60

300,900 / 60-30.50/60 = $612,000

The new break even point increases.

Final answer:

With the new machine, Kent Co.'s break-even point in units would decrease, from 11,400 to 10,200 units. Despite increasing fixed costs, the new machine drives down variable costs, effectively lowering the total number of units needed to cover costs.

Explanation:

The concept under consideration here is the break-even point calculation in unit terms. The break-even point (units) is calculated by dividing the total fixed costs by the contribution margin per unit, which is sales price per unit minus variable cost per unit.

Currently, Kent Co.'s break-even point can be found using its original costs:

Fixed costs: $285,000
Sales price per unit: $60
Variable cost per unit: $35
Contribution margin per unit: $60 - $35 = $25
Break-even point (units): $285,000 / $25 = 11,400 units

If Kent were to purchase the new machine, its costs would alter as follows:

New fixed costs: $285,000 + $15,900 = $300,900
New variable cost per unit: $35 - $4.50 = $30.50
New contribution margin per unit: $60 - $30.50 = $29.50
New break-even point (units): $300,900 / $29.50 = 10,200 units

Thus, purchasing the new machine would in fact lower Kent Co.'s break-even point to 10,200 units, thereby improving its cost efficiency.

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