A whole wall is split in half and we painted half of the wall 3 colors what fraction of the wall does each color occupy?

a) To express ∂z/∂u and ∂z/∂v as functions of u and v, we first need to express z directly in terms of u and v. We are given that:

z = tan^-1(x/y)

And that:

x = ucosv
y = usinv

Substituting these expressions for x and y into the equation for z, we get:

z = tan^-1((ucosv)/(usinv))
z = tan^-1(cotv)

Now we can use the chain rule to find ∂z/∂u and ∂z/∂v:

∂z/∂u = ∂z/∂cotv * ∂cotv/∂u
∂z/∂v = ∂z/∂cotv * ∂cotv/∂v

To find ∂cotv/∂u and ∂cotv/∂v, we use the quotient rule:

∂cotv/∂u = -cosv/u^2
∂cotv/∂v = -csc^2v

Substituting these into the chain rule expressions, we get:

∂z/∂u = (-cosv/u^2) * (1/(1+cot^2v))
∂z/∂v = (-csc^2v) * (1/(1+cot^2v))

Simplifying these expressions using trig identities, we get:

∂z/∂u = (-cosv/u^2) * (1/(1+(cosv/usinv)^2))
∂z/∂v = (-1/sinv^2) * (1/(1+(cosv/usinv)^2))

b) To evaluate ∂z/∂u and ∂z/∂v at (u,v) = (1.3, pi/6), we simply plug in these values into the expressions we derived in part (a):

∂z/∂u = (-cos(pi/6)/(1.3)^2) * (1/(1+(cos(pi/6)/(1.3*sin(pi/6)))^2))
∂z/∂v = (-1/sin(pi/6)^2) * (1/(1+(cos(pi/6)/(1.3*sin(pi/6)))^2))

Simplifying these expressions using trig functions, we get:

∂z/∂u = (-sqrt(3)/1.69^2) * (1/(1+(sqrt(3)/1.3)^2))
∂z/∂v = (-4) * (1/(1+(sqrt(3)/1.3)^2))

Plugging in the values and evaluating, we get:

∂z/∂u ≈ -0.5167
∂z/∂v ≈ -1.5045
To answer this question, we'll first express z directly in terms of u and v, and then apply the chain rule to find the partial derivatives ∂z/∂u and ∂z/∂v.

Given:
z = tan^(-1)(x/y)
x = u*cos(v)
y = u*sin(v)

First, let's express z in terms of u and v:
z = tan^(-1)((u*cos(v))/(u*sin(v)))

Now, we can simplify the expression:
z = tan^(-1)(cot(v))

Next, we'll find the partial derivatives using the chain rule:

a) ∂z/∂u:
Since z doesn't have a direct dependence on u, we have:
∂z/∂u = 0

b) ∂z/∂v:
∂z/∂v = -csc^2(v)

Now let's evaluate the partial derivatives at the given point (u,v) = (1.3, π/6):

∂z/∂u(1.3, π/6) = 0
∂z/∂v(1.3, π/6) = -csc^2(π/6) = -4

So, the partial derivatives at the given point are:
∂z/∂u = 0 and ∂z/∂v = -4.

To learn more about derivatives visit;

/brainly.com/question/30365299

#SPJ11

(a) To find the peak concentration of the drug, we need to find the maximum value of c(t). Since c(t) is an exponential function, its maximum value occurs at its maximum point, which is where its derivative is equal to zero. We can find this point by taking the derivative of c(t) and setting it equal to zero:c'(t) = 53.2e^{-0.26} - 13.832te^{-0.26} = 0Solving for t, we get t = 3.870 hours. Therefore, the peak concentration of the drug is c(3.870) = 109.2 ng/ml.(b) To find when the drug reaches peak concentration, we have already found that it occurs at t = 3.870 hours. Therefore, the drug reaches peak concentration 3.870 hours after it is administered.

For more similar questions on topic

https://brainly.com/app/ask?q=

#SPJ11

The peak concentration of the drug is approximately 42.83 ng/ml, and it occurs around 3.85 hours after the drug is administered.

To find the peak concentration of the drug and when it reaches that peak, we'll need to consider the given function c(t) = 53.2te^(-0.26t), where t is the time in hours.

a) To find the peak concentration, we need to determine the maximum value of c(t). We can do this by taking the first derivative of c(t) with respect to t and setting it equal to 0.

c'(t) = 53.2(-0.26)e^(-0.26t) + 53.2e^(-0.26t) = 0

Now, solve for t:

t ≈ 3.85 hours

b) Plug the value of t back into the c(t) function to find the peak concentration:

c(3.85) = 53.2(3.85)e^(-0.26(3.85)) ≈ 42.83 ng/ml

So, the peak concentration of the drug is approximately 42.83 ng/ml, and it occurs around 3.85 hours after the drug is administered.

To learn more about concentration, refer below:

https://brainly.com/question/10725862

#SPJ11

We can start by integrating both sides of the differential equation to obtain:

∫f '(x) dx = ∫([tex]5x^2 - x^2/5[/tex]) dx

f(x) = (5/3)[tex]x^3[/tex] - (1/15) [tex]x^5[/tex] + C

where C is the constant of integration.

To find the value of C, we can use the initial condition f(1) = 0:

f(1) = (5/3)[tex](1)^3[/tex] - (1/15) [tex](1)^5[/tex] + C = 0

Simplifying this equation gives:

C = (1/15) - (5/3)

C = -2/9

Therefore, the solution to the initial value problem f '(x) = 5[tex]x^2[/tex] − [tex]x^2[/tex]/5 , f(1) = 0 is:

f(x) = (5/3) [tex]x^3[/tex] - (1/15) [tex]x^5[/tex] - (2/9)

Learn more about initial value problem

https://brainly.com/question/30547172

#SPJ4

So the equivalent expression that matches one of the answer choices is option C, 100c/3d.

In mathematics, an expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, division, exponentiation, and so on) that can be evaluated to produce a value. An expression can represent a single number or a more complex calculation, and it can be written using symbols, variables, and/or numbers.

Here,

To simplify the given expression, we need to multiply the two binomials using the distributive property:

(10c6d - 5)(2c - 5d/4)

= 10c * 2c + 10c * (-5d/4) - 5 * 2c - 5 * (-5d/4)

= 20c² - 25cd + 10c + 25/4 d

None of the answer choices match this expression exactly, but we can simplify it further. Factoring out a common factor of 5 from the last two terms, we get:

20c² - 25cd + 10c + 25/4 d

= 5(4c² - 5cd + 2c + 5/4

20c/3 * 5d/4

= 100c/3d

To know more about expression,

https://brainly.com/question/30091997

#SPJ1

The Lagrange error bound for the fourth-degree Taylor polynomial of [tex]e^x[/tex] about 0 for 0 ≤ x ≤ 0.9 is approximately 0.000129.

To find the Lagrange error bound for the fourth-degree Taylor polynomial of [tex]e^x[/tex] about 0, we need to find the maximum value of the fifth derivative of [tex]e^x[/tex] on the interval [0, 0.9].

Since the nth derivative of [tex]e^x[/tex] is [tex]e^x[/tex] for all n, the fifth derivative is also [tex]e^x[/tex]. To find the maximum value of[tex]e^x[/tex]on the interval [0, 0.9].

We evaluate [tex]e^x[/tex] at the endpoints and at the critical point x = 0.45, which is the midpoint of the interval:

[tex]e^0[/tex] = 1

[tex]e^0.9[/tex]≈ 2.4596

[tex]e^0.45[/tex] ≈ 1.5684

The maximum value of [tex]e^x[/tex] on the interval [0, 0.9] is approximately 2.4596.

The Lagrange error bound for the fourth-degree Taylor polynomial of [tex]e^x[/tex] about 0 is given by:

E₄(x) ≤ (M/5!)[tex]|x-0|^5[/tex]

where M is the maximum value of the fifth derivative of [tex]e^x[/tex] on the interval [0, 0.9].

So, we have:

E₄(x) ≤ (2.4596/5!) [tex]|x|^5[/tex] for 0 ≤ x ≤ 0.9

Substituting x = 0.9 into this inequality, we get:

E₄(0.9) ≤ (2.4596/5!)[tex](0.9)^5[/tex] ≈ 0.000129

Therefore, the Lagrange error bound for the fourth-degree Taylor polynomial of [tex]e^x[/tex] about 0 for 0 ≤ x ≤ 0.9 is approximately 0.000129.

Learn more about Lagrange Error Bound

brainly.com/question/30758051

#SPJ11

Answer:

Step-by-step explanation:

To prove that lines a and b are parallel lines cut by transversal f, we need to show that the alternate interior angles are congruent. According to the given information, angle 2 and angle 3 are corresponding angles, and angle 1 and angle 4 are corresponding angles.

Therefore, the set of equations that is enough information to prove that lines a and b are parallel lines cut by transversal f is:

angle 2 = angle 3 (corresponding angles)

angle 1 = angle 4 (corresponding angles)

Herbert will earn $63,417 for his tenth year of work which is calculated using compound interest formula.

After graduating from college, Herbert decided to join a new company. He agreed to a salary which will increase by 4.5% each year. This means that every year, Herbert's salary will increase by 4.5% of his previous year's salary. For example, if his salary in the first year is $50,000, his salary in the second year will be $52,250, and so on.

To find out Herbert's salary for his tenth year of work, we need to use compound interest formula. The formula is:

A = P(1 + r)ⁿ

Where:
A = Final amount (salary in the tenth year)
P = Initial amount (salary in the first year)
r = Annual interest rate (4.5%)
n = Number of years (10)

Substituting the values in the formula, we get:

A = $50,000(1 + 0.045)¹⁰
A = $63,417

Therefore, Herbert will earn $63,417 for his tenth year of work. It is important to note that the increase in salary is a result of compound interest, which means that the salary growth rate accelerates over time. This is a good incentive for Herbert to stay with the company and work hard.

Know more about compound interest here:

https://brainly.com/question/14295570

#SPJ11

The value of the tangent segment b is 20.15.

The secant-tangent power theorem, also known as the tangent-secant theorem, states that if a tangent and a secant are drawn from a common external point to a circle, then the product of the length of the secant segment and its external part is equal to the square of the length of the tangent segment.

It is expressed as:

( tangent segment )² = External part of the secant segment + Secant segment.

From the diagram:

Tangent segment = WX = b

External part of the secant segment = YX = 14

Secant segment = ZX = 15 + 14 = 29

Plug these values into the above formula and solve for b.

( tangent segment )² = External part of the secant segment + Secant segment.

b² = 14 × 29

b² = 406

b = √406

b = 20.15

Therefore, the value of b is 20.15.

Learn more about secant tangent power theorem here: https://brainly.com/question/26407978

#SPJ1

The dilation is (x, y) → (2x, 2y). So, the correct answer is D).

Let the coordinates of point C be (x, y). Then, the distance from the origin to point C is given by the distance formula

OC = √(x² + y²)

The corresponding side lengths are

CG = 16 - x

CD = √((x - 0)² + (y - 0)²)

The scale factor is the ratio of corresponding side lengths

CG/CD = 2

Therefore,

16 - x = 2*√(x² + y²)

Solving for y, we get

y = √(13x² - 64x + 256)

If we assume that point G corresponds to point C, then the center of dilation is the origin and the rule that represents the dilation is

(x, y) → (2x, 2y)

Therefore, the answer is

(x, y) → (2x, 2y)

So, the correct answer is D).

To know more about dilation:

https://brainly.com/question/936148

#SPJ4

--The given question is incomplete, the complete question is given

" Quadrilateral ABCD is dilated about the origin into quadrilateral EFGH so that point G is located at (16,8). scale factor is 2.

Which rule represents the dilation?

Select one

(x, y) → (18x, 18y)

(x, y) → (x+8, y+4)

(x, y) → (12x, 12y)

(x, y) → (2x, 2y) "--

To find the annual rate at which the car depreciated, we need to use the formula for exponential decay:

A(t) = P(1 - r)^t

where A(t) is the current value of the car after t years, P is the initial value of the car, and r is the annual rate of depreciation.

We know that P = $15,500 and A(t) = $8,400, so we can plug in these values to solve for r:

$8,400 = $15,500(1 - r)^t

Divide both sides by $15,500:

0.54 = (1 - r)^t

Take the logarithm of both sides:

log(0.54) = t*log(1 - r)

Solve for r:

log(0.54)/t = log(1 - r)

1 - r = 10^(log(0.54)/t)

r = 1 - 10^(log(0.54)/t)

Plugging in t = 7 (since the car has depreciated for 7 years), we get:

r = 1 - 10^(log(0.54)/7) ≈ 9.35%

Therefore, the car depreciated at an annual rate of approximately 9.35%.

To know more about depreciation, refer here :

https://brainly.com/question/17827672#

#SPJ11

Answer:

  (C)  Neither

Step-by-step explanation:

You want to know if the function values in the table represent an even function, and odd function, or neither.

An Even function is symmetrical about the y-axis:

  f(-x) = f(x)

An Odd function is symmetrical about the origin:

  f(-x) = -f(x)

The attached graph of the given points shows the function has no symmetry at all.

The table represents neither an even nor odd function.

Answer:

Neither

Step-by-step explanation:

In an even function, f(x) = f(-x).

Look at x = 2 and x = -2.

f(2) = -4; f(-2) = 2

Since f(2) ≠ f(-2), the function is not even.

In an odd function, f(x) = -f(-x).

Look at f(2) and f(-2).

f(2) = -4; f(-2) = 2

Since f(2) ≠ -f(-2), the function is not odd.

Answer: C  Neither

There are several transformations that can be applied to a pentagon in order to map it onto itself. One such transformation is a rotation of 72 degrees, which can be performed by rotating the pentagon about its center point by 72 degrees clockwise. This will result in the pentagon appearing exactly as it did before the rotation, but in a different orientation.

Another transformation that will map a pentagon onto itself is a reflection along one of its symmetry lines. A pentagon has five symmetry lines, which are lines that divide the shape into two congruent halves. Reflecting the pentagon along any of these lines will result in the same shape being produced, but in a mirror image orientation.

Finally, a translation can also be used to map a pentagon onto itself. This involves moving the pentagon a certain distance in a particular direction, such as shifting it 2 units to the right or 3 units upwards. As long as the distance and direction of the translation are such that the pentagon ends up exactly where it started, it will be a valid transformation.

Overall, there are several transformations that can be applied to a pentagon in order to map it onto itself, including rotations, reflections, and translations.

To know more about transformations refer here

https://brainly.in/question/15660713#

#SPJ11

The scale factor from A to B is 5 / 4.

The value of t in the diagram is 5.6 cm.

Scale factor is the ratio between corresponding measurements of an object and a representation of that object.

Therefore, let's find the scale factor from the shape A to the shape B as follows:

5 / 4 = 15 / 12

Therefore, the scale factor is 5 / 4.

Hence, let's find the value of t in the diagram as follows:

Therefore, using the proportionality,

7 / t = 5 / 4

cross multiply

28 = 5t

divide both sides by 5

t = 28 / 5

t = 5.6 cm

learn more on scale factor here: brainly.com/question/16609931

#SPJ1

Candace is flipping the coin 5 times.

The probability of an event occurring is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn out.

The theoretical probability of flipping tails on any single flip of a fair coin is 1/2, since there are two equally likely outcomes (heads or tails) on each flip.

If Candace is flipping the coin a certain number of times and the theoretical probability of flipping tails on all flips is 1/32, we can set up the equation:

[tex](1/2)^n[/tex] = 1/32

where n is the number of times Candace is flipping the coin.

We can simplify this equation by taking the logarithm of both sides:

[tex]log((1/2)^n) = log(1/32)[/tex]

Using the property of logarithms that [tex]log(a^b) = b*log(a)[/tex], we can rewrite the left-hand side as:

n*log(1/2) = log(1/32)

We can simplify the logarithms using the fact that log(1/a) = -log(a), so:

n*(-log(2)) = -log(32)

Dividing both sides by -log(2), we get:

n = -log(32) / log(2)

Using a calculator, we find:

n ≈ 5

Therefore, Candace is flipping the coin 5 times.

Learn more about probability on:

https://brainly.com/question/13604758

#SPJ4

To add one number to each column of the table and make it show a function, we need the specific table or information about the columns to provide a precise answer.

To transform the given table into a function, we need to add a column that represents the output values corresponding to each input value. A function relates each input value to a unique output value.

Here is an example of how the table could be modified to represent a function:

Input (x) Output (y)

1             3

2               5

3             7

4            9

In this modified table, the output values (y) are obtained by adding 2 to each input value (x). This ensures that each input value is associated with a unique output value, satisfying the definition of a function.

Learn more about function

brainly.com/question/28925980

#SPJ11

Answer:107

Step-by-step explanation:8*17-29=107 so our answer is 107

To find the population at any given term n, continue to apply the recursive rule.
Pₙ = Pₙ₋₁ + 50
Using this recursive rule and the initial population, you can find the population at any given term n.

We are given a population growth model with a recursive rule and an initial population. Let's break down the information and find the population at any given term n.

Recursive rule: Pₙ = Pₙ₋₁ + 50
Initial population: P₀ = 30

Now let's find the population at any term n, using the recursive rule:

Step 1: Determine the base case, which is the initial population.
P₀ = 30

Step 2: Apply the recursive rule to find the next few terms.
P₁ = P₀ + 50 = 30 + 50 = 80
P₂ = P₁ + 50 = 80 + 50 = 130
P₃ = P₂ + 50 = 130 + 50 = 180

Step 3: To find the population at any given term n, continue to apply the recursive rule.
Pₙ = Pₙ₋₁ + 50

Using this recursive rule and the initial population, you can find the population at any given term n.

Learn more about recursive rule,

https://brainly.com/question/29508048

#SPJ11

From the calculation, you are 100 m away from the plateau.

The angle of elevation is the angle between a horizontal line of sight and a line of sight that is directed upwards, or the angle between the horizontal and the line of sight when an observer is looking upward.

We know that;

Angle of elevation = 35°

Height of the Plateau = 70 m

Thus;

Tan 35 =70/x

x = Your distance from the plateau.

x = 70/Tan 35

x = 100m

In trigonometry and geometry, the angle of elevation—which can be expressed in degrees, radians, or other angular units—is frequently employed to address issues with heights and distances.

Learn more about angle of elevation:https://brainly.com/question/21137209

#SPJ1

Possible options for z could be:

1) z = -6

2) z = -7

These are two possible options for z that satisfy the given inequality.

Given that the opposite of z is greater than 5, we can write this as an inequality:

-z > 5

To find the possible options for z, we can follow these steps:

Step 1: Multiply both sides of the inequality by -1 to solve for z. Remember to flip the inequality sign when multiplying by a negative number:

z < -5

Step 2: Choose two values for z that satisfy the inequality z < -5.

Possible options for z could be:

1) z = -6
2) z = -7

These are two possible options for z that satisfy the given inequality.

Learn more about inequality,

https://brainly.com/question/30681777

#SPJ11

Answer:

Let's start by assigning some variables to the unknowns:

Let's call the price of one taco "t".

Let's call the price of one burrito "b".

With these variables, we can write two equations based on the information given in the problem:

5t + 2b = 13.25 (equation 1)

3t + 2b = 10.75 (equation 2)

We now have two equations and two variables. We can use algebra to solve for t and b. One way to do this is to eliminate b by subtracting equation 2 from equation 1:

(5t + 2b) - (3t + 2b) = 13.25 - 10.75

Simplifying this equation, we get:

2t = 2.5

Dividing both sides by 2, we get:

t = 1.25

So the price of one taco is $1.25.

Now that we know the price of one taco, we can substitute this value into one of the equations to solve for b. Let's use equation 1:

5t + 2b = 13.25

Substituting t = 1.25, we get:

5(1.25) + 2b = 13.25

Simplifying this equation, we get:

6.25 + 2b = 13.25

Subtracting 6.25 from both sides, we get:

2b = 7

Dividing both sides by 2, we get:

b = 3.5

So the price of one burrito is $3.5.

Therefore, the price of one taco is $1.25 and the price of one burrito is $3.5.

To know more about variables refer here

https://brainly.com/question/17344045#

#SPJ11

The length of BC rounded to 3 significant figures is 6.98.

Since ∠cab = 90°, we can use the Pythagorean Theorem to find the length of AB.

Let's call BC = x, then we have:

sin(65°) = AB/BC

AB = sin(65°) * BC

In right triangle ABC, we have:

AB^2 + BC^2 = AC^2

(sin(65°) * BC)^2 + BC^2 = 8.9^2

Solving for BC, we get:

BC = 8.9 / sqrt(sin^2(65°) + 1)

BC ≈ 6.98

Therefore, the length of BC rounded to 3 significant figures is 6.98.

To know more about length, visit:

https://brainly.com/question/9842733#

#SPJ11

The math fact that 4 x 6 = 24 helps Matt remember that 6 x 4 = 24, and Sadie arrived at the answer 10 for 6 + 4 by incorrectly adding the numbers in reverse order.

Matt knows that 6 x 4 = 24. This helps him remember that 4 x 6 and 6 x 4 are both equal to 24.

The math fact that Matt can remember based on 4 x 6 = 24 is that multiplication is commutative. This means that the order of the numbers being multiplied doesn't affect the result. So, if 4 multiplied by 6 equals 24, it also implies that 6 multiplied by 4 would give the same result of 24.

Sadie arrived at the answer 10 for 6 + 4 by mistakenly swapping the order of the numbers and performing the addition incorrectly. The correct sum for 6 + 4 is indeed 10. Sadie's error demonstrates the importance of following the correct order of operations, where addition should be performed after ensuring the numbers are in the correct order.

As for Sadie's answer of 6 + 4 = 10, it is not directly related to the multiplication fact that Matt knows.

It is possible that Sadie used a different math fact or strategy to arrive at that answer.

To know more about math facts refer here:

https://brainly.com/question/5539039

#SPJ11

The value of x and y is 11 and 4 respectively

A cyclic quadrilateral is a quadrilateral which has all its four vertices lying on a circle. It is also sometimes called inscribed quadrilateral.

A theorem in circle geometry states that the sum of opposite angles in a cyclic quadrilateral are supplementary. i.e they sum up to give 180.

10x + 16y+6 = 180

10x+16y = 174... eqn1

4+18y +10x-6 = 180

18y +10x = 182... eqn2

subtract equation 1 from 2

2y = 8

y = 8/2 = 4

Subtitle 4 for y in equation 1

10x+ 16(4)= 174

10x= 174-64

10x = 110

x= 110/10

x = 11

learn more about cyclic quadrilateral from

https://brainly.com/question/26690979

#SPJ1

The circumference of the circle is 6.28 kilometers if the diameter of the circle is 2 kilometers and assuming the value of π is 3.14 kilometers.

The diameter of the circle = 2 kilometers

The circumference of a circle is calculated by using the formula,

C = π *d

where,

C = circumference of a circle

d = diameter of the circle

π = Constant value = 3. 14 Km

Substituting the above-given values into the equation, we get:

C = π*d

C = 3.14 x 2 km

C = 6.28 km

Therefore, we can conclude that the circumference of the circle is 6.28 kilometers.

To learn more about the circumference of the circle

https://brainly.com/question/25945520

#SPJ4

Answer:is 230

Step-by-step explanation:

230 i hoped i helped

Answer:

2*Ab    Or AC

Step-by-step explanation:

No detail in question

Answer:

34.65 mi²

Step-by-step explanation:

Area of parallelogramam = b · h

b = 6.3 mi

h = 5.5 mi

Let's solve

6.3 · 5.5 = 34.65 mi²

So, the area of the shape is 34.65 mi²

Approximate amount of dough that is remaining. Is  (length - 2r)(width - 3r) - 6πr^2.

Without the size of the original sheet of dough or the size of the circles cut from it, it's not possible to give an exact expression. However, assuming that each circle has the same radius of 'r' and the original sheet of dough was a rectangle, we can write an expression in factored form for the remaining area of the dough:

Remaining area of dough = (Area of original rectangle) - 6(Area of circle)

= (length x width) - 6(πr^2)

= (length - 2r)(width - 3r) - 6πr^2

Whether there is enough dough for another circle would depend on the size of the circles and the original sheet of dough.

To learn more about expression visit:

https://brainly.com/question/1859113

#SPJ11

Answer:

f(-2) = 9

Step-by-step explanation:

f(x) = -3x + 3                       Solve for f(-2)

f(-2) = -3(-2) + 3

f(-2) = 6 + 3

f(-2) = 9