The average rate of change for the function below is f(x)=x2−6x+8 when x2=1 and x1=3

Answer: First one is A, 2nd one is B, 3rd one is C

Step-by-step explanation:

The Marginal Rate of Substitution (MRS) for each utility function is:

(a) MRS = xb/xa

(b) MRS = 3y/x

(c) MRS = xa/xb

(d) MRS = y/x

(e) MRS = 2

To locate the Marginal Rate of Substitution (MRS) for every software function, we want to calculate the partial derivatives with recognition to the variables concerned. Let's decide the MRS for each feature:

(a) u(xa, xb) = \(xa^(1/2) * xb^(1/2)\)

MRS = ∂u/∂xa / ∂u/∂xb

= (∂/∂xa \((xa^(1/2) * xb^(1/2))\)) / (∂/∂xb \((xa^(1/2) * xb^(1/2))\))

= \((1/2 * xa^(-1/2) * xb^(1/2)) / (1/2 * xa^(1/2) * xb^(-1/2))\)

= xb/xa

(b) u(x, y) = \(x^(3/4) * y^(1/4)\)

MRS = ∂u/∂x / ∂u/∂y

= (∂/∂x \((x^(3/4) * y^(1/4)))\) / (∂/∂y \((x^(3/4) * y^(1/4))\))

=\((3/4 * x^(-1/4) * y^(1/4)) / (1/4 * x^(3/4) * y^(-3/4))\)

= 3y/x

(c) u(xa, xb) = (1/2) * ln(xa) + (1/2) * ln(xb)

MRS = ∂u/∂xa / ∂u/∂xb

= (∂/∂xa [(1/2) * ln(xa) + (1/2) * ln(xb)]) / (∂/∂xb [(1/2) * ln(xa) + (1/2) * ln(xb)])

= (1/2) * (1/xa) / (1/2) * (1/xb)

= xa/xb

(d) u(x, y) = (4/3) * ln(x) + (4/1) * ln(y)

MRS = ∂u/∂x / ∂u/∂y

= (∂/∂x [(4/3) * ln(x) + (4/1) * ln(y)]) / (∂/∂y [(4/3) * ln(x) + (4/1) * ln(y)])

= (4/3) * (1/x) / (4/1) * (1/y)

= y/x

(e) u(xa, xb) = 2 * xa + xb

MRS = ∂u/∂xa / ∂u/∂xb

= (∂/∂xa (2 * xa + xb)) / (∂/∂xb (2 * xa + xb))

= 2 / 1

= 2

Therefore, the Marginal Rate of Substitution (MRS) for every utility characteristic is:

(a) MRS = xb/xa

(b) MRS = 3y/x

(c) MRS = xa/xb

(d) MRS = y/x

(e) MRS = 2

To know more about MRS,

https://brainly.com/question/33034222

#SPJ4

(a) The MRS for this utility function is √(xb / xa).

(b) The MRS for this utility function is 3 *\((y / x)^(0.25).\)

(c) The MRS for this utility function is xb / xa.

(d) The MRS for this utility function is y / x.

(e) The MRS for this utility function is 2.

To find the Marginal Rate of Substitution (MRS) for each utility function, we need to calculate the ratio of the marginal utilities of the two goods.

The MRS represents the rate at which a consumer is willing to trade one good for another while maintaining the same level of utility.

(a) \(u(xa, xb) = xa^(1/2) * xb^(1/2)\)

To find the MRS, we calculate the partial derivatives of the utility function with respect to each good and take the ratio:

MRS = (d(u(xa, xb))/d(xa)) / (d(u(xa, xb))/d(xb))

= \((0.5 * xb^0.5 * xa^(-0.5)) / (0.5 * xa^0.5 * xb^(-0.5))\)

=\((xb^0.5) / (xa^0.5)\)

= √(xb / xa)

Therefore, the MRS for this utility function is √(xb / xa).

(b) u(x, y) = \(x^(3/4) * y^(1/4)\)

MRS = (d(u(x, y))/d(x)) / (d(u(x, y))/d(y))

= \((0.75 * x^(-0.25) * y^(0.25)) / (0.25 * x^(0.75) * y^(-0.75))\)

= \((3 * y^(0.25)) / (x^(0.25) * y^(-0.75))\)

= \(3 * (y / x)^(0.25)\)

Therefore, the MRS for this utility function is 3 * \((y / x)^(0.25).\)

(c) u(xa, xb) = (1/2) * ln(xa) + (1/2) * ln(xb)

MRS = (d(u(xa, xb))/d(xa)) / (d(u(xa, xb))/d(xb))

= [(1/2) * (1/xa)] / [(1/2) * (1/xb)]

= xb / xa

Therefore, the MRS for this utility function is xb / xa.

(d) u(x, y) = (4/3) * ln(x) + (4/1) * ln(y)

MRS = (d(u(x, y))/d(x)) / (d(u(x, y))/d(y))

= [(4/3) * (1/x)] / [(4/1) * (1/y)]

= y / x

Therefore, the MRS for this utility function is y / x.

(e) u(xa, xb) = 2 * xa + xb

MRS = (d(u(xa, xb))/d(xa)) / (d(u(xa, xb))/d(xb))

= 2 / 1

= 2

Therefore, the MRS for this utility function is 2.

Learn more about Marginal Rate of Substitution from this link:

https://brainly.com/question/14390716

#SPJ11

d=?

d=12.5×9

=112.5

c=?

8*8

=64

b=?

10×7

Area of base:

3 * 9 = 27

So, 243 is the answer.

Answer:

slope: -1/2

y intercept: -1

Answer:

cylinder A is 141.3 meters

cylinder b is 245.5 meters

Step-by-step explanation:

Cylinder a: 3x3x5x3.14

cylinder B : 5x5x3x3.14

This question is incomplete

Complete Question

Leah would like to earn at least $120 per month. She babysits for $5 per hour and works at an ice cream shop for $10 per hour. Leah cannot work more than a total of 20 hours per month. Let x represent the number of hours Leah babysits and let y

represent the number of hours Leah works at the ice cream shop.

Answer:

The inequalities to solve this question is given as:

x + y ≤ 20

5x + 10y ≥ 120

Leah must spend: 16 hours babysitting and 4 hours working at the ice cream shop to earn at least $120

Step-by-step explanation:

Let x represent the hours she number of hours she babysits and y represent the hours she works at the ice cream shop. Leah cannot work more than a total of 20 hours per month.

Hence:

x + y ≤ 20 ...... Equation 1

Leah would like to earn at least $120 per month.

She babysits for $5 an hour and works at an ice cream shop for $10 per hour.

Hence, out Equation is given as:

x × $5 + y × $10 = $120

5x + 10y ≥ 120..... Equation 2

The inequalities to solve this question is given as:

x + y ≤ 20

5x + 10y ≥ 120

To find x and y:

x + y = 20

x = 20 - y

5x + 10y = 120

Substitute: 20 - y for x

5(20 - y) + 10y = 120

100 - 5y + 10y = 120

Collect like terms

- 5y + 10y = 120 - 100

5y = 20

y = 20/5

y = 4 hours

Note:

x = 20 - y

x = 20 - 4

x = 16 hours

Hence:

Leah must spend: 16 hours babysitting and 4 hours working at the ice cream shop to earn at least $120

Answer:

The distance between the boats after 1 minute is 17 ft

Step-by-step explanation:

Here, we want to calculate the distance between the boats after 1 minute

The distance covered by the first boat after 1 minute is 2 feet while for the second it is 1 foot

So for the first boat, it has 8 ft ahead, for the second boat, it has 9 ft ahead

So the distance between the two after 1 minute will be 9 ft + 8 ft = 17 ft

Answer:

   Simplify each side of the equation by removing parentheses and combining like terms.

   Use addition or subtraction to isolate the variable term on one side of the equation.

   Use multiplication or division to solve for the variable.

Step-by-step explanation:

Answer:

Solution

= −7

Step-by-step explanation:

3 + 9 = − 12

3 + 9 − 9 = − 12 − 9

Subtract the numbers

Subtract the numbers

3 = − 21

Divide both sides of the equation by the same term

3 = − 21

3/3 = −21/3

Solution

= −7

Answer:

\(y=\frac{2}{3}x+3\)

Step-by-step explanation:

Perpendicular Bisector

It's defined as a line that divides another line into two equal parts. The bisector passes through the midpoint of the line forming any angle, but if that angle is exactly 90°, then the bisector is also perpendicular.

We need to find the equation of the line that divides into equal parts the line with endpoints (-1, -2) and (-5,4) and is perpendicular to it.

First, let's find the slope of the line segment. The slope can be calculated with the formula:

\(\displaystyle m=\frac{y_2-y_1}{x_2-x_1}\)

\(\displaystyle m=\frac{4-(-2)}{-5-(-1)}=\frac{6}{-4}=-\frac{3}{2}\)

The line for the perpendicular bisector has a slope m2. Two perpendicular lines with slopes m1 and m2 must comply:

\(m_1.m_2=-1\)

Solving for m2:

\(\displaystyle m_2=-\frac{1}{m_1}\)

\(\displaystyle m_2=-\frac{1}{-\frac{3}{2}}=\frac{2}{3}\)

The equation of the perpendicular bisector has the form:

\(y=\frac{2}{3}x+b\)

Now we find the coordinates of the midpoint of the segment:

\(\displaystyle \bar x=\frac{-1-5}{2}=-3\)

\(\displaystyle \bar y=\frac{4-2}{2}=1\)

The midpoint is (-3,1). Using this point will allow us to find the value of b:

\(1=\frac{2}{3}(-3)+b\)

\(b=1+2=3\)

Thus, the equation for the perpendicular bisector is

\(\boxed{y=\frac{2}{3}x+3}\)

Answer:

5\(\sqrt{3}\)

Step-by-step explanation:

Perimeter = 3 sides add up= 10+10+10

so the bottom of the half triangle is 5

a^2+b^2=c^2

10^2=a^2+5^2

100=a^2+25

a^2 = 75

a = \(\sqrt{75}\)

simplify

a = \(\sqrt{25*3}\)

a = \(5\sqrt{3}\)

a. The length of the adjacent side to the given angle is 13.40.

b. The length of the hypotenuse is 51.78.

c. The other acute angle is 15°.

Given that,

In the picture we can see the triangle which is right angle triangle with one side as 50 cm and one acute angle as 75°.

a. We have to find the length of the adjacent side to the given angle.

By using trigonometric ratio,

tan75° = \(\frac{opp}{adj}\)

tan75° = \(\frac{50}{adj}\)

3.7321 = \(\frac{50}{adj}\)

Adjacent side = 13.40

Therefore, The length of the adjacent side to the given angle is 13.40.

b. We have to find the length of the hypothenuse.

sin75° = \(\frac{50}{h}\)

0.9659 = \(\frac{50}{h}\)

h = \(\frac{50}{0.9659}\)

h = 51.78

Therefore, the length of the hypotenuse is 51.78.

c. We have to find the measure of the other acute angle

By adding of the angles in the triangle is 180°

The measure of the other acute angle = 180° - (90+75) °

= 180°- 165°

= 15°

Therefore, The other acute angle is 15°.

To know more about length visit:

https://brainly.com/question/27791593

#SPJ4

The complete question is :

The triangle which is right angle triangle with one side as 50 cm and one acute angle as 75°.

a. Find the length of the adjacent side.

b. Find the hypothenuse.

c. Find the other acute angle

First, we need to subtract the last payment from the last month's balance.

Then, apply the interest:

The Values of (a+b)ab are undefined.

Given that, a = 3an and db = -2We need to find the values of (a+b)

Now, we have a = 3an... equation (1)Also, we have db = -2... equation (2)From equation (1), we get: n = 1/3... equation (3)Putting equation (3) in equation (1), we get: a = a/3a = 3... equation (4)Now, putting equation (4) in equation (1), we get: a = 3an... 3 = 3(1/3)n = 1

From equation (2), we have: db = -2=> d = -2/b... equation (5)Multiplying equation (1) and equation (2), we get: a*db = 3an * -2=> ab = -6n... equation (6)Putting values of n and a in equation (6), we get: ab = -6*1=> ab = -6... equation (7)Now, we need to find the value of (a+b).For this, we add equations (1) and (5),

we get a + d = 3an - 2/b=> a + (-2/b) = 3a(1) - 2/b=> a - 3a + 2/b = -2/b=> -2a + 2/b = -2/b=> -2a = 0=> a = 0From equation (1), we have a = 3an=> 0 = 3(1/3)n=> n = 0

Therefore, from equation (5), we have:d = -2/b=> 0 = -2/b=> b = ∞Now, we know that (a+b)ab = (0+∞)(0*∞) = undefined

Therefore, the values of (a+b)ab are undefined.

For more questions on Values .

https://brainly.com/question/843074

#SPJ8

The values of a and b such that W X is perpendicular to  Y Z .

a = 8

b = 54

If two geometric objects overlap at a right angle, they are perpendicular. The perpendicular sign, can be used to express the condition of perpendicularity graphically '⟂' . It can be defined across two lines, a line and a plane, or two planes.

∠WVY = 4a+58

∠XVY = 2b-18

Determining the value of a ,b

Because WX and YZ are perpendicular to one another and intersect at point V, both WVY and XVY are valid 90°.

So,

4a+58  = 90

4a = 90 - 58

     = 32

a = 32/4

  = 8

And now:

2b-18 = 90

2b = 108

b = 108/2

 = 54

The value of the 'a' and 'b' are as follows:

a = 8

b = 54

To know more about perpendicular visit:

https://brainly.com/question/2096532

#SPJ1

Answer:

12.5 pints is the correct answer

Answer:

7

Step-by-step explanation:

2x2 - 5

= (2x3x2)-5

= 12-5

= 7

The statement that is false with respect to the diagram given where angle FEA is stated to be supplementary to angle HGD, is:

A. measure of angle FEB + measure of angle HGD = 180°

By definition, supplementary angles are two angles that have a sum of 180 degrees when added together, that is, one is a supplement of the other.

Given the image below, we know the following:

Since angle FEA is supplementary to angle FEA would be congruent to angle HGC, and angle HGD is congruent to angle FEB. This is because, the supplement of angle

angle FEA + angle FEB - angle FEA + angle HGD = 180° - 180°. Therefore,

angle FEB = angle HGD.

In summary, from the options given, the statement that is false with respect to the diagram given where angle FEA is stated to be supplementary to angle HGD, is:

A. measure of angle FEB + measure of angle HGD = 180°

Learn more about supplementary angles on:

https://brainly.com/question/8992900

#SPJ1

The circumference of the circle is 26.38 inches and the area of the circle is 55.39 square inches, both rounded to the nearest hundredth.

The diameter of a circle is the distance across the circle passing through its center. In this problem, the diameter of the circle is given as 8.4 inches. We can use the formula for the circumference and the area of a circle in terms of its diameter to find the solutions.

First, we can find the radius of the circle by dividing the diameter by 2. So, the radius is 8.4/2 = 4.2 inches.

To find the circumference of the circle, we can use the formula:

C = πd

where d is the diameter. Substituting the value of d = 8.4 inches and π = 3.14, we get:

C = 3.14 x 8.4 = 26.376

Therefore, the circumference of the circle is 26.38 inches (rounded to the nearest hundredth).

To find the area of the circle, we can use the formula:

A = πr²

where r is the radius. Substituting the value of r = 4.2 inches and π = 3.14, we get:

A = 3.14 x (4.2)² = 55.3896

Therefore, the area of the circle is 55.39 square inches (rounded to the nearest hundredth).

Learn more about the circumference and area at

https://brainly.com/question/17130827

#SPJ4

We have two right-angled triangles that share a common side, with side lengths 6 and 10. Let's label the sides of the triangles as follows:

Triangle 1:

Side adjacent to the right angle: 6 (let's call it 'a')

Side opposite to the right angle: x (let's call it 'b')

Triangle 2:

Side adjacent to the right angle: x (let's call it 'c')

Side opposite to the right angle: 10 (let's call it 'd')

Using the Pythagorean theorem, we can write the following equations for each triangle:

Triangle 1:\(a^2 + b^2 = 6^2\)

Triangle 2: \(c^2 + d^2 = 10^2\)

Since the triangles share a common side, we know that b = c. Therefore, we can rewrite the equations as:

\(a^2 + b^2 = 6^2\\b^2 + d^2 = 10^2\)

Substituting b = c, we get:

\(a^2 + c^2 = 6^2\\c^2 + d^2 = 10^2\)

Now, let's add these two equations together:

\(a^2 + c^2 + c^2 + d^2 = 6^2 + 10^2\\a^2 + 2c^2 + d^2 = 36 + 100\\a^2 + 2c^2 + d^2 = 136\)

Since a^2 + 2c^2 + d^2 is equal to 136, we can conclude that x (b or c) is between 11 and 12

For more such questions on right angled triangle.

https://brainly.com/question/64787

#SPJ8

Answer:

\(\huge\boxed{\cot\dfrac{3\pi}{2}=0}\)

Step-by-step explanation:

\(\text{We know}\ \cot x=\cot(x\pm\pi)\ \text{and}\ \cot(-x)=-\cot x.\\\\\text{We have}\ \cot\dfrac{3\pi}{2}=\cot\dfrac{\pi+2\pi}{2}=\cot\bigg(\dfrac{\pi}{2}+\dfrac{2\pi}{2}\bigg)=\cot\bigg(\dfrac{\pi}{2}+\pi\bigg)=\cot\dfrac{\pi}{2}\\\\\cot\bigg(\dfrac{\pi}{2}\bigg)=0\\\\\text{Therefore}\ \cot\dfrac{3\pi}{2}=0.\)

Answer:

The number of sunny days this year = 0.75x

where,  x is the sunny days in last years.

Step-by-step explanation:

Given - This year there was 25% fewer sunny days than last year.

To find - What is the number of sunny days this year?

Proof -

Let us assume that,

The total number of sunny days last year = x

Given that,

This year there was 25% fewer sunny days than last year.

i.e this year total sunny days = 100 - 25 = 75 %

So,

we get

If there were x sunny days last year,

Then,

This year Total sunny days = 0.75x

Product of b and 256 means multiplication

Plus 17 means addition

Now combine to firm expression

Lets solve it out

Answer:

£95

Step-by-step explanation:

Given that:

Whitney's initial amount = £265

Nancy's initial amount = £180

Let amount each spent = x (amount is the same)

After spending Whitney has twice as much money as Nancy.

Amount spent by each?

(Whitney's initial amount - x) = 2(Nancy's initial amount - x)

265 - x = 2(180 - x)

265 - x = 360 - 2x

-x + 2x = 360 - 265

x = £95

Hence, they both spent £95

The probability that the mean number of daily emergency admissions is between 75 and 95 is approximately 0.8990.

To find the probability that the mean number of daily emergency admissions is between 75 and 95, we can use the Z-score formula for sample means: Z = (X - μ) / (σ / √n), where X is the sample mean, μ is the population mean, σ is the standard deviation, and n is the sample size.

First, calculate the Z-scores for both 75 and 95:
Z_75 = (75 - 85) / (37 / √30) ≈ -1.62
Z_95 = (95 - 85) / (37 / √30) ≈ 1.62

Now, use a Z-table to find the probabilities corresponding to these Z-scores. P(Z ≤ 1.62) ≈ 0.9474 and P(Z ≤ -1.62) ≈ 0.0526.

Finally, subtract the probabilities to find the probability between the two Z-scores:
P(-1.62 ≤ Z ≤ 1.62) = P(Z ≤ 1.62) - P(Z ≤ -1.62) ≈ 0.9474 - 0.0526 ≈ 0.8948

Among the given answer choices, the closest value is 0.8990.

Therefore, the probability that the mean number of daily emergency admissions is between 75 and 95 is approximately 0.8990.

To learn more about probability here:

brainly.com/question/30034780#

#SPJ11

Answer:

house

Step-by-step explanation:

I think,look I am just a little kid I am a  10 year old  kid in 5 th grade I am at school I am trying to cheat so sorry if it’s wrong

Answer: Greater than 10.

Answer:

Step-by-step explanation:

To find the mean, we need to calculate the sum of all the values and divide by the number of data values. Using the stem and leaf plot and the key, we can determine the following data values:

12, 15, 17, 22, 25, 26, 28, 32, 33, 34, 36, 37, 39, 42, 44, 45, 46, 47, 48, 49, 52, 53, 55, 57, 57, 59, 62, 65, 68, 72, 73, 75, 75, 77, 79, 82, 85, 88, 92, 95

There are 37 data values in total. To find the sum of the data, we can add up all the individual values:

12 + 15 + 17 + 22 + 25 + 26 + 28 + 32 + 33 + 34 + 36 + 37 + 39 + 42 + 44 + 45 + 46 + 47 + 48 + 49 + 52 + 53 + 55 + 57 + 57 + 59 + 62 + 65 + 68 + 72 + 73 + 75 + 75 + 77 + 79 + 82 + 85 + 88 + 92 + 95 = 2098

So the sum of the data is 2098. To find the mean, we divide the sum by the number of data values:

MEAN = sum of data / number of data values

MEAN = 2098 / 37

MEAN = 56.7568

Rounded to the nearest hundredth, the mean of the data is 56.76. Therefore, the answer is closest to option A) 57.