A model of a car uses a scale of 2 1/4 inches = 3 feet. If the model is 14 inches long, what is the actual length of the car?

Answer:

C:The set of all possible outcomes

Therefore, the sum of the first 7 terms of the given geometric sequence is 127/128.

To find the sum of the first 7 terms of a geometric sequence, we need to determine the common ratio and the first term of the sequence.

Let's denote the first term of the sequence as 'a' and the common ratio as 'r'.

Given that the 4th term is 1/16 and the 7th term is 1/128, we can write the following equations:

a * r^3 = 1/16 (equation 1)

a * r^6 = 1/128 (equation 2)

Dividing equation 2 by equation 1, we get:

(r^6)/(r^3) = (1/128)/(1/16)

r^3 = 1/8

Taking the cube root of both sides, we find:

r = 1/2

Substituting the value of r back into equation 1, we can solve for 'a':

a * (1/2)^3 = 1/16

a * 1/8 = 1/16

a = 1/2

Now we have the first term 'a' as 1/2 and the common ratio 'r' as 1/2.

The sum of the first 7 terms of the geometric sequence can be calculated using the formula:

Sum = a * (1 - r^n) / (1 - r)

Substituting the values into the formula, we have:

Sum = (1/2) * (1 - (1/2)^7) / (1 - 1/2)

Simplifying the expression

Sum = (1/2) * (1 - 1/128) / (1/2)

Sum = (1/2) * (127/128) / (1/2)

Sum = (127/128)

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Answer:

Step-by-step explanation:

area and perimeter of WHAT? specify plz.

Step-by-step explanation:

AC^2=AB^2+BC^2

c^2=9^2+12^2

c^2=81+144

c^2=225

c=15

To set the data type of the registerdate field to "date", the syntax would depend on the programming language or database management system being used. However, here are some examples:

In SQL, the syntax would be:

ALTER TABLE tablename MODIFY COLUMN registerdate DATE;

This statement modifies the registerdate column in the tablename table to have a data type of DATE.

In PHP, the syntax for creating a table with a register date column of data type DATE would be:

CREATE TABLE tablename (

   ...,

   registerdate DATE,

   ...

);

This creates a table called tablename with a column called registerdate of data type DATE.

In Python using SQLAlchemy, the syntax for defining a registerdate column of data type Date in a declarative base would be:

from sqlalchemy import Column, Date

class MyTable(Base):

   __tablename__ = 'mytable'

   registerdate = Column(Date)

This creates a MyTable class with a column called registerdate of data type Date.

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To set the data type of the registerdate field to "date", the syntax would depend on the specific programming language or database system being used. However, a common syntax to set the data type to "date" is:
registerdate DATE;
This syntax would typically be used in the creation of a table or the declaration of a variable in a programming language that supports date data types.

To identify a syntax that sets the data type of the 'registerdate' field to "date", you can use the following SQL statement:

```sql
CREATE TABLE your_table_name (
   registerdate DATE
);
```

Here's a step-by-step explanation of the syntax:
1. "CREATE TABLE" is the command to create a new table in the database.
2. "your_table_name" should be replaced with the desired name for your table.
3. Within the parentheses, you define the columns and their data types.
4. "registerdate" is the name of the field that you want to set the data type for.
5. "DATE" is the data type you are setting for the 'registerdate' field.

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Answer:

The solutions to the graph are (-1,1) and (4,6).

Step-by-step explanation:

Where the line and parabola intersect, or meet, are the solutions.

Answer:

C

Step-by-step explanation:

Multiply by 12 on both sides.

Start with step one

y/3 - 1/4 = 5              Multiply both sides by 12

12(y/3 - 1/4) = 5*12

12*y/3 - 12 * 1/4 = 60

3 goes into 12 four times

4 goes into 12 three times. In both cases you are cancelling.

4y - 3 = 60

Answer:

nico

Step-by-step explanation:

The equation that match the table attached is

B. y = -5(2⁻ˣ) + 4

By analyzing the given equations we can see that option B match the table and this is shown below

Using calculator to set the equation shows that

for x = -2

y = -5(2⁻ˣ) + 4 = 2.75

for x = -1

y = -5(2⁻ˣ) + 4 = 1.5

for x = 0

y = -5(2⁻ˣ) + 4 = -1

for x = 1

y = -5(2⁻ˣ) + 4 = -6

Based on the comparison, the equation that corresponds to the table is:

OB.y = -5(2⁻ˣ) + 4

Therefore, the correct option is OB.

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The protagonist, a detective, stumbles upon a series of crimes connected to the labeled tickets.

Box A: The plot that matches Box A is a thrilling mystery. The protagonist, a detective, stumbles upon a series of crimes connected to the labeled tickets.

As the detective investigates, they discover that the tickets with the number "1" are linked to a notorious gang involved in illegal activities. The tickets labeled "2" lead the detective to a secret society that uses the tickets for initiation rituals.

The plot unfolds as the detective races against time to unravel the connections between the tickets and bring the culprits to justice.

Box B: The plot that matches Box B is a heartwarming tale of friendship and adventure. The protagonist, a young child, finds one of the tickets labeled "3" and realizes it grants them access to a magical world. In this world, they meet a group of unique and colorful characters who also possess tickets labeled "5."

Together, they embark on a journey to restore harmony to their realm, battling against an evil force that seeks to exploit the power of the tickets. Through their shared experiences, the group learns valuable lessons about courage, loyalty, and the true meaning of friendship.

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When a fish is attached to a vertical spring and slowly lowered to its equilibrium position, the spring stretches by an amount d, as it balances the force exerted by the spring with the force due to the fish's weight.

Here, a fish attached to a vertical spring. When a fish is attached to a vertical spring and slowly lowered to its equilibrium position, the spring will stretch by an amount d.
The equilibrium position is the point where the force exerted by the spring equals the force due to the fish's weight (gravitational force). In this scenario, the spring stretches until it reaches a balance between these forces. The amount by which the spring stretches is denoted as d.
To summarize, when a fish is attached to a vertical spring and slowly lowered to its equilibrium position, the spring stretches by an amount d, as it balances the force exerted by the spring with the force due to the fish's weight.

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Answer:

5 shelves

Step-by-step explanation:

Given the following :

Width of shelves = 56cm

Maximum thickness of books = 16cm

When placed side-by-side, the entire collection of books takes up 2.4m

Minimum number of shelves required to guarantee that all of the books can be displayed in the book case.

Entire book collection = 2.4m = (2.4 × 100) = 240cm

Width of shelf = 56cm

In other to guarantee that the bookshelf contains all the books, we can assume that the each book is of maximum width, 16cm

Hence, maximum number of books each shelf can hold with guarantee

Width of shelf / max. Width of book

= 56cm / 16cm = 3.5

Hence, a shelf can hold 3 books with full guarantee.

If books are all 16cm thick, then the number of books ;

240 cm / 16 cm = 15 books

If one shelf can hold 3 books, then,

15/3 = 5 shelves are required to hold the books with maximum guarantee.

Answer:

Brad average typing rate in words per minute is 21

1260 divided by 60 = 21

(In case you meant 30 minutes)

1260 divided by 30 = 42

Step-by-step explanation:

In a typing class, the average number N of words per minute typed after t weeks of lessons is

N=157/(1+5.4e^-0.12t)

N=157/(1+5.4e

−

0.12t)

. Find the time necessary to type 75 words per minute

The decimal value of the floating-point number 110000001111110... is approximately -0.000000015935.

A 32-bit binary number is the floating-point number 010000010110100000... We must interpret its components in accordance with the IEEE 754 standard for single-precision floating-point representation before we can convert it to decimal.

The number's sign is represented by the first bit, which is 0. The number is positive because it is zero.

The exponent is represented by the next eight bits, 10000010 The bias value, which is 127 for single-precision, needs to be subtracted in order to determine the exponent's decimal value. As a result, the value of the exponent is -25: 10000010 - 127.

The binary fractional part is represented by the remaining 23 bits, which are 110100000... Summing the series of 2(-i) for each bit I that is set to 1, we convert the fractional part to a decimal fraction for the purpose of determining its decimal value. The series is as follows, starting with the leftmost bit:

The decimal value of the floating-point number is then calculated as follows: 1/2 + 1/8 + 1/16 + 1/32 = 0.53125.

The floating-point number 010000010110100000... has a decimal value of approximately 0.0000000938776, which is equal to (-1)0 * 1.53125 * 2(-25).

8th Question: The 32-bit binary number 110000001111110... is a floating-point number. Using the same procedure as before:

The number's sign is represented by the first bit, which is 1. The number is negative because it is 1.

The exponent is represented by the next eight bits, 10000011 We get the exponent value of 10000011 - 127 = -24 when we subtract the bias value of 127.

In binary, the fractional part of the number is represented by the remaining 23 bits, which are 111110... Switching it over completely to a decimal division gives us the series:

1/2 plus 1/4 plus 1/8 plus 1/16 plus 1/32 equals 0.96875, so the floating-point number's decimal value is as follows:

The floating-point number 110000001111110... has a decimal value of (-1)1 x 1.96875 x 2 (-24), which is approximately -0.000000015935003662109375.

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To derive the expression for the Marginal Utility (MU) of each good in the given utility functions, we need to take the partial derivatives of the utility functions with respect to each good. Let's calculate the MU for each good in the first three utility functions:

1. Utility function U1(x1,x2) = (x1 + 4x2)^2:

To find the MU of x1, we differentiate U1 with respect to x1 while treating x2 as a constant:
MU1(x1,x2) = 2(x1 + 4x2) * 1 = 2(x1 + 4x2)

To find the MU of x2, we differentiate U1 with respect to x2 while treating x1 as a constant:
MU2(x1,x2) = 2(x1 + 4x2) * 4 = 8(x1 + 4x2)

2. Utility function U2(x1,x2) = 5x1^3 * x2^4:

To find the MU of x1, we differentiate U2 with respect to x1 while treating x2 as a constant:
MU1(x1,x2) = 15x1^2 * x2^4

To find the MU of x2, we differentiate U2 with respect to x2 while treating x1 as a constant:
MU2(x1,x2) = 20x1^3 * x2^3

3. Utility function U3(x1,x2) = x1 * (x2 + 2):

To find the MU of x1, we differentiate U3 with respect to x1 while treating x2 as a constant:
MU1(x1,x2) = x2 + 2

To find the MU of x2, we differentiate U3 with respect to x2 while treating x1 as a constant:
MU2(x1,x2) = x1

Next, let's compute the Marginal Rate of Substitution (MRS) at the bundle (2,4) for each utility function. MRS measures the rate at which a consumer is willing to substitute one good for another while maintaining the same level of utility.

1. Utility function U1(x1,x2) = (x1 + 4x2)^2:

The MRS is given by the ratio of the marginal utilities:
MRS(x1,x2) = MU1(x1,x2) / MU2(x1,x2)

Substituting the values x1 = 2 and x2 = 4 into the expressions for MU1 and MU2 derived earlier, we get:
MRS(2,4) = [2(2 + 4(4))] / [8(2 + 4(4))]

Simplifying the expression, we have:
MRS(2,4) = 12 / 48 = 1/4

2. Utility function U2(x1,x2) = 5x1^3 * x2^4:

Similarly, the MRS is given by the ratio of the marginal utilities:
MRS(x1,x2) = MU1(x1,x2) / MU2(x1,x2)

Substituting the values x1 = 2 and x2 = 4 into the expressions for MU1 and MU2 derived earlier, we get:
MRS(2,4) = (15(2^2)(4^4)) / (20(2^3)(4^3))

Simplifying the expression, we have:
MRS(2,4) = 960 / 1280 = 3/4

3. Utility function U3(x1,x2) = x1 * (x2 + 2):

The MRS is given by the ratio of the marginal utilities:
MRS(x1,x2) = MU1(x1,x2) / MU2(x1,x2)

Substituting the values x1 = 2 and x2 = 4 into the expressions for MU1 and MU2 derived earlier, we get:
MRS(2,4) = (4 + 2) / 2 = 3/2

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Answer:

36

Step-by-step explanation:

Make a big square and a little one by cutting it. 6x5 is 30 and the small one is 3x2 which is 6....add then you get 36

Answer:

Step-by-step explanation:

Noah- 4 1/6 miles/hour

Emily- 8 1/10 miles/hour

Anna- 3 1/2 miles/ hour

Emily ran the quickest.

Answer:

Anna was the fastest.

Step-by-step explanation:

Following are the steps we take to determine each one's speed:

speed=distance/time

Noah went 4 1/6 miles an hour, Emily went 4 1/2 miles an hour, and Anna went 5 5/9 miles an hour. Therefore, Anna was the fastest.

The nurse researcher will be able to determine if there are significant differences in the mean amount of daily exercise between the groups and whether the intervention has had an impact on increasing exercise levels.

The statistical test that the nurse researcher should use in this scenario is Analysis of Variance (ANOVA). ANOVA is specifically designed to compare means and variances between multiple groups. It allows researchers to determine whether there are significant differences in the means of three or more groups based on the variability within and between the groups.

In this case, the nurse researcher wants to compare the mean group differences by examining the variability between groups and within groups. ANOVA assesses the between-group variability by comparing it to the within-group variability, providing insights into whether the intervention has a significant effect on increasing daily exercise in the three groups of adolescents.

By conducting ANOVA, the nurse researcher will be able to determine if there are significant differences in the mean amount of daily exercise between the groups and whether the intervention has had an impact on increasing exercise levels.

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Answer:

im just tryna get points  

Step-by-step explanation:

The equation of the plane through the points p(0, 1, 1), q(1, 0, 1), and

r(1, 1, 0) is x + y + z = 2  .

According to the question

Let the points

p(0, 1, 1) = (x1,y1,z1)

q(1, 0, 1)= (x2,y2,z2)

r(1, 1, 0)= (x3,y3,z3)

now,

The equation of the plane through the points

i.e

The formula of equation of a plane passing through three non collinear points

\(\left[\begin{array}{ccc}x-x1&y-y1&z-z1\\x2-x1&y2-y1&z2-z1\\x3-x1&y3-y1&z3-z1\end{array}\right] = 0\)

by substituting the values in the formula of equation of a plane

\(\left[\begin{array}{ccc}x-0&y-1&z-1\\1-0&0-1&1-1\\1-0&1-1&0-1\end{array}\right] = 0\)

\(\left[\begin{array}{ccc}x&y-1&z-1\\1&-1&0\\1&0&-1\end{array}\right] = 0\)  

x(1) - (y-1)(-1) + (z-1)(1) = 0

x + y - 1 + z - 1 = 0

x + y + z = 2

Hence, the equation of the plane through the points p(0, 1, 1), q(1, 0, 1), and r(1, 1, 0) is x + y + z = 2  .

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Answer:

Step-by-step explanation:

We can use the method of Lagrange multipliers to find the extreme values of the function f(x,y) subject to the constraint x^4 y^4 = 8.

Let L(x, y, λ) = x^2 y^2 + λ(x^4 y^4 - 8) be the Lagrangian function.

Taking partial derivatives of L with respect to x, y, and λ, we get:

∂L/∂x = 2xy^2 + 4λx^3 y^4 = 0

∂L/∂y = 2x^2 y + 4λx^4 y^3 = 0

∂L/∂λ = x^4 y^4 - 8 = 0

From the first equation, we get x(2y^2 + 4λx^2 y^4) = 0. Since x cannot be zero (otherwise, the constraint would not hold), we have 2y^2 + 4λx^2 y^4 = 0, or y^2 = -2λx^2 y^4. Similarly, from the second equation, we have x^2 = -2λx^4 y^2.

Substituting y^2 = -2λx^2 y^4 into x^4 y^4 = 8, we get x^4 (-2λx^2 y^4)^2 = 8, or λ = -1/(2x^2 y^2).

Substituting λ into x^2 = -2λx^4 y^2, we get x^2 = 1/(2y^2), or y^2 = 1/(2x^2).

Substituting these values of x^2 and y^2 into the constraint x^4 y^4 = 8, we get 8 = 8/(4x^4), or x^4 = 1. Similarly, y^4 = 1.

Therefore, x = ±1 and y = ±1, and the critical points of f(x, y) subject to the constraint x^4 y^4 = 8 are (1,1), (1,-1), (-1,1), and (-1,-1).

To find the maximum and minimum values of f(x, y) subject to the constraint, we evaluate f(x, y) at each of these points:

f(1,1) = 1

f(1,-1) = 1

f(-1,1) = 1

f(-1,-1) = 1

Therefore, the minimum and maximum values of f(x, y) subject to the constraint x^4 y^4 = 8 are both equal to 1.

To solve this problem, we will use the method of Lagrange multipliers.

First, we define the Lagrangian function as L(x,y,λ) = x^2y^2 + λ(x^4y^4 - 8).

Next, we take partial derivatives of L with respect to x, y, and λ and set them equal to 0:

∂L/∂x = 2xy^2 + 4λx^3y^4 = 0
∂L/∂y = 2x^2y + 4λx^4y^3 = 0
∂L/∂λ = x^4y^4 - 8 = 0

Solving for λ in the third equation gives λ = 1/(4x^3y^3).

Substituting this into the first two equations and setting them equal to each other, we get:

2xy^2 + 4(1/(4x^3y^3))x^3y^4 = 2x^2y + 4(1/(4x^3y^3))x^4y^3

Simplifying and rearranging, we get:

x^3 = y^3

Substituting this into the constraint x^4y^4 = 8, we get:

x^4(x^3)^4 = 8

Solving for x, we get:

x = (2/√(3))^(1/7)

Substituting this back into x^3 = y^3, we get:

y = (2√3/3)^(1/7)

Finally, substituting these values of x and y back into the original function f(x,y) = x^2y^2, we get:

f(x,y) = (2/√(3))^(2/7) * (2√3/3)^(2/7) = 4/3^(3/7)

Therefore, the minimum and maximum values of the function f(x,y) subject to the given constraint are both 4/3^(3/7).
To find the minimum and maximum values of the function f(x, y) = x^2y^2 subject to the constraint x^4y^4 = 8, we can use the method of Lagrange multipliers.

Let g(x, y) = x^4y^4 - 8. The Lagrange multiplier method requires finding points where the gradients of f(x, y) and g(x, y) are proportional:

∇f(x, y) = λ ∇g(x, y)

Calculating the gradients, we get:

∇f(x, y) = (2x*y^2, 2x^2*y)
∇g(x, y) = (4x^3*y^4, 4x^4*y^3)

Now, equating the components and dividing:

(2x*y^2) / (4x^3*y^4) = (2x^2*y) / (4x^4*y^3)

Simplifying:

1 / (2x^2*y^2) = 1 / (2x^2*y^2)

Since this equality holds, the gradients are proportional. Now we use the constraint x^4y^4 = 8:

x^4y^4 = 8

To find the minimum and maximum, we'll analyze the possible critical points. If x = 0 or y = 0, then f(x, y) = 0. However, this would not satisfy the constraint, so we must have x ≠ 0 and y ≠ 0.

Take the fourth root of both sides of the constraint:

x*y = ±2

Now we have two cases:

Case 1: x*y = 2
f(x, y) = x^2y^2 = (xy)^2 = 2^2 = 4

Case 2: x*y = -2
f(x, y) = x^2y^2 = (xy)^2 = (-2)^2 = 4

Thus, the minimum value of f(x, y) is not found, as the constraint x^4y^4 = 8 doesn't allow for a minimum. The maximum value of f(x, y) is 4.

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Answer: (3⁴)⁵ simplifies to 3^20

Please give Brainliest

To simplify an exponentiation expression, we need to use the following rule: (a^m)^n = a^(m*n). In this case, we have (3⁴)⁵, which can be rewritten as (3^4)^5. Applying the rule, we get:

(3^4)^5 = 3^(4*5)

(3^4)^5 = 3^20

Therefore, (3⁴)⁵ simplifies to 3^20.

Answer: \(3^{20}\)

Step-by-step explanation:

An exponential rule states that \((a^{b} )^{c}\) = \(a^{bc}\)

So \((3^{4} )^{5}\) = \(3^{(4)(5)}\) = \(3^{20}\)

The statement provides two quantities, A and B, expressed as ratios of positive integers c and d. The relationship between the quantities A and B cannot be determined from the information given.

The statement provides two quantities, A and B, expressed as ratios of positive integers c and d. However, no specific values or constraints are given for c and d. Without knowing the specific values or any relationship between c and d, it is impossible to determine the relationship between A and B.

The relative magnitudes of A and B will depend on the values of c and d. If the value of c is greater than d, then A would be greater than B. Conversely, if the value of d is greater than c, then B would be greater than A. However, without any information about the values of c and d or any relationship between them, we cannot determine the relationship between A and B.

Therefore, based on the given information, the relationship between quantities A and B cannot be determined.

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Let L be the line in R^3 that consists of all scalar multiples of the vector `[3, 4, 5]`. Find the reflection of the vector v = `[1, 2, 3]` in the line L. A reflection is a transformation that takes an object and reflects it over a line. This transformation is called an isometry because the distance between points on the object is preserved.

Let's call the point of intersection between the line and the plane `P`. To find the reflection of `v` in the line `L`, we need to find the point `R` on `L` that is equidistant from `v` and `P`. We can do this by finding the projection of `v` onto `L`, and then doubling the distance between `v` and the projection. The projection of `v` onto `L` is given by:


where `u` is a unit vector in the direction of `L`. Since `L` consists of all scalar multiples of `[3, 4, 5]`, we can take `u` to be:

\(u = (1/√(3² + 4² + 5²))[3, 4, 5] = (1/√50)[3, 4, 5]\)

Then, we have:

Now, we need to double the distance between `v` and `projL(v)` to find `R`. We have:

R = v + 2(projL(v) - v) = [1, 2, 3] + 2([(29/50)3, (29/50)4, (29/50)5] - [1, 2, 3]) = [(58/25) - 1, (58/25) - 2, (58/25) - 3] = [(33/25), (8/25), (-7/25)]

Therefore, the reflection of `v` in the line `L` is `[33/25, 8/25, -7/25]`.

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To find the y-coordinate of point P on the unit circle, given that its x-coordinate is 5/13, we can utilize the Pythagorean identity for points on the unit circle.

The Pythagorean identity states that for any point (x, y) on the unit circle, the following equation holds true:

x^2 + y^2 = 1

Since we are given the x-coordinate as 5/13, we can substitute this value into the equation and solve for y:

(5/13)^2 + y^2 = 1

25/169 + y^2 = 1

To isolate y^2, we subtract 25/169 from both sides:

y^2 = 1 - 25/169

y^2 = 169/169 - 25/169

y^2 = 144/169

Taking the square root of both sides, we find:

y = ±sqrt(144/169)

Since we are dealing with points on the unit circle, the y-coordinate represents the sine value. Therefore, the y-coordinate of point P is:

y = ±12/13

So, the y-coordinate of point P can be either 12/13 or -12/13.

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The trapezoidal rule is a numerical integration method that uses trapezoids to estimate the area under a curve. The trapezoidal rule can be used for both definite and indefinite integrals. The trapezoidal rule approximation, Tn, to the integral sin r dz is given by:

Tn = (b-a)/2n[f(a) + 2f(a+h) + 2f(a+2h) + ... + 2f(b-h) + f(b)]where h = (b-a)/n. To determine how large n should be so that Tn is accurate to within 0.00001, we can use the error bound given in Section 5.9 of the course text. According to the error bound, the error, E, in the trapezoidal rule approximation is given by:E ≤ ((b-a)³/12n²)max|f''(x)|where f''(x) is the second derivative of f(x). For the integral sin r dz, the second derivative is f''(r) = -sin r. Since the absolute value of sin r is less than or equal to 1, we have:max|f''(r)| = 1.

Substituting this value into the error bound equation gives:E ≤ ((b-a)³/12n²)So we want to choose n so that E ≤ 0.00001. Substituting E and the given values into the inequality gives:((b-a)³/12n²) ≤ 0.00001Simplifying this expression gives:n² ≥ ((b-a)³/(0.00001)(12))n² ≥ (b-a)³/0.00012n ≥ √(b-a)³/0.00012Now we just need to substitute the values of a and b into this expression. Since we don't know the upper limit of integration, we can use the fact that sin r is bounded by -1 and 1 to get an upper bound for the integral.

For example, we could use the interval [0, pi/2], which contains one full period of sin r. Then we have:a = 0b = pi/2Plugging in these values gives:n ≥ √(pi/2)³/0.00012n ≥ 5073.31Since n must be an integer, we round up to the nearest integer to get:n = 5074Therefore, we should choose n to be 5074 so that the trapezoidal rule approximation, Tn, to the integral sin r dz is accurate to within 0.00001.

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Answer:

12°

Step-by-step explanation:

it is a ratio let represent by x

6x+5x+4x=180

15x=180

x=12°