I need some help better understanding Area Volume/Differential Equations, as ive been stuck on this single string of questions in my workbook for some time now, any and all help would be appreciated.
"Let R be the region in quadrant 1 bounded by y=3sin(2x) and y=e^x "
1) Find the area of R
2) Let S be the solid generated by rotating R around the x-axis. Find the volume of S.
3) Let Q be the solid generated by rotating R around the horizontal line y=5. Find the volume of Q
4) Let P be the solid whose base is R and whose cross sections perpendicular to the x-axis are semicircles. Find the volume of P.

2/3. The probability of picking a card greater than 8 is 2/3, as there are two cards with values greater than 8 (9 and 10) out of three total cards (7, 8, and 9).

To calculate the probability of picking a card greater than 8, we need to know how many cards have values greater than 8 out of the total number of cards. In this case, there are three cards: 7, 8, and 9. Out of those three cards, two have values greater than 8 (9 and 10). Therefore, the probability of picking a card greater than 8 is 2/3. We can express this probability as a fraction (2/3) or as a decimal (0.67). Hence,The probability of picking a card greater than 8 is 2/3, as there are two cards with values greater than 8 (9 and 10) out of three total cards (7, 8, and 9).

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Each points can be determine as the ordered pair (x, y) with inequalities;

W  ⇒  x ≥ 5 and y < -1

X  ⇒   x ≥ 5 and y > 1

Y  ⇒   x < -5 and y ≥ 5

Z  ⇒   x < -1 and y < -4

A chart in x-y hub plot is a visual portrayal of numerical capabilities or data of interest on a Cartesian direction framework. The horizontal, or independent, variable is represented by the x-axis, while the vertical, or dependent, variable is represented by the y-axis. To demonstrate the connection between the two variables, a line or curve is drawn between the plotted points.

According to the graph each points can be determine with inequalities;

W = (5, -2) ⇒  x ≥ 5 and y < -1

X = (5, 2) ⇒    x ≥ 5 and y > 1

Y = (-6, 5) ⇒   x < -5 and y ≥ 5

Z = (-2, -5) ⇒  x < -1 and y < -4

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Answer:

D. The 7 in the thousands place is one hundredth the size of the 7 in the ten thousands place.

Step-by-step explanation:

The 7 in the thousands place is ten times greater than the 7 in the ten thousands place.

The relationship between the 7 in the thousands place and the 7 in the ten thousands place can be understood by their positions within the number. In a multi-digit number, each digit has a place value based on its position. The place value of a digit determines its worth. For example, the 7 in the thousands place is ten times greater than the 7 in the hundreds place, and the 7 in the ten thousands place is ten times greater than the 7 in the thousands place. Therefore, the 7 in the thousands place is ten times greater than the 7 in the ten thousands place.

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Answer:

It is C

Step-by-step explanation:

I took it. But, check to be sure.

Answer:

x = 21

General Formulas and Concepts:

Geometry

Step-by-step explanation:

Step 1: Identify

We see that the measures given are Corresponding Angles

Step 2: Solve for x

Answer: What number cards??

Step-by-step explanation:

Four triangles would be formed by drawing all the diagonals from a single vertex of a hexagon.

When all the diagonals are drawn from a single vertex of a polygon, the number of triangles formed depends on the number of sides of the polygon. To calculate the number of triangles, we need to use the formula:

number of triangles = (number of sides - 2)

For example, if we have a pentagon (a polygon with five sides), the number of triangles formed from a single vertex would be:

number of triangles = (5 - 2) = 3

So, three triangles would be formed by drawing all the diagonals from a single vertex of a pentagon.

Similarly, for a hexagon (a polygon with six sides), the number of triangles formed would be:

number of triangles = (6 - 2) = 4

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Answer:

The answer would be 9,210

There are 1300 Roman coins in the museum's collection in total.

How to determine the total number of Roman coins ?

To determine the total number of Roman coins in the museum's collection, we need to use the information given in the histogram. We know that there are 108 coins with a weight between 8 g and 17 g.

We can find the total frequency of all the coins by integrating the frequency density over the entire range of masses. To do this, we need to first find the width of each mass interval, which is given by the difference between the upper and lower mass values of each interval.

From the histogram, we can see that the width of each interval is 5 g.

So, the frequency of the coins between 8 g and 17 g can be calculated as:

Frequency = frequency density × interval width

Frequency = 10 × 5 = 50

This means that there are 50 coins in the museum's collection with a mass between 8 g and 17 g.

To find the total number of coins in the collection, we need to sum up the frequency of all the intervals.

To do this, we can calculate the area of each rectangle formed by the interval width and frequency density, and then sum up all these areas.

The total number of coins in the collection is given by:

Total number of coins = sum of frequencies over all intervals

Total number of coins = 50 + (15 × 15) + (20 × 20) + (25 × 25)

Total number of coins = 50 + 225 + 400 + 625

Total number of coins = 1300

Therefore, there are 1300 Roman coins in the museum's collection in total.

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The intercept might not make sense in these types of issues, but that is alright. The electrician is unaware of the significance of the x-value. intercept's

y=85x+90

The constant 90 is the hourly rate that does not fluctuate, and x is the amount of hours units are dollars. The rate at which the slope is increasing in this instance is 85 per hour. The independent variable is the number of hours that can be determined. The dependent variable is the price. depends on hours, which is typically on the y-axis, whereas the independent variable is typically on the x-axis.

cost $ 90, and the y-intercept (0,90)

Where y=0 is at -2.5 is where the x-intercept is located.

The intercept might not make sense in these types of issues, but that is alright. The electrician is unaware of the significance of the x-value. intercept's

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Answer:

 A. -114

Step-by-step explanation:

Got it right.

The statement "Construct a line from A perpendicular to the y-axis, determine the distance from A to the y-axis along this perpendicular line, find a new point on the other side of the y-axis that is equidistant from the y-axis" accurately describes how to reflect point A (3, -1) over the y-axis

To reflect a point over the y-axis, you need to find a new point that is the same distance from the y-axis as the original point, but on the other side of the y-axis.

This can be done by constructing a perpendicular line from the original point to the y-axis, determining the distance from the original point to the y-axis along this line, and then finding a new point on the other side of the y-axis that is the same distance from the y-axis as the original point.

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when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one.  Check the picture below.

The coordinates of the vertices of the image of the translation

J'(−2,−1) and K'(1,1) and L'(2,−1) and M’(1,−3) are:

(x, y)⇒ (x+3,y−2)

Add 3 to each x-coordinate and subtract 2 from each y-coordinate of the vertices of quadrilateral JKLM to find the vertices of the translated image.

J(-5,1): J' (-5 + 3, 1-2)

Or, J'(-2,-1)

K(−2,3): K’(−2+3,3−2)

Or, K’(1,1)

L(−1,1): L’(−1+3,1−2)

Or, L’(2,−1)

M(−2,−1): M’(−2+3,−1−2)

Or, M’(1,−3)

Now,

The vertices of the translated image are:

J’(−2,−1) and K’(1,1) and L’(2,−1) and M’(1,−3)

Again,

The algebraic rule to describe the translation is:

(x, y) ⇒ (x+3,y−2)

Therefore,

The vertices of the translated image:

J'(−2,−1) and K'(1,1) and L'(2,−1) and M’(1,−3) are:

(x, y)⇒ (x+3,y−2)

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Answer: C OR 4 a.m. on Wednesday

Step-by-step explanation:

The solution to the inequality is:

x ∈ (-√2, 3/4) ∪ (√2, 4).

What is inequality ?

An inequality is a mathematical statement that compares two values or expressions using symbols such as <, >, ≤, or ≥. It indicates that one value or expression is less than or greater than the other. Inequalities can be solved by using various algebraic techniques to find the range of values that satisfy the inequality. Inequalities are commonly used in many areas of mathematics, such as in algebra, geometry, and calculus, as well as in real-world applications such as economics, physics, and engineering.

According to the question:
To solve the inequality f(4x-3)/(2-x²)>0, we first need to find the critical values of x where the function is equal to zero or undefined.

For f(4x-3) to be zero, we have 4x-3 = 0, which gives us x = 3/4.

For 2-x² to be zero, we have 2-x² = 0, which gives us x = ±√2.

We also need to check where the function is undefined, which is where the denominator (2-x²) is equal to zero. This occurs at x = ±√2.

So, we have critical values at x = -√2, 3/4, and √2.

We can use a sign chart to determine the intervals where the function is positive.

x                     -√2    3/4 √2

f(x)

(4x-3)/(2-x²)        - + -

sign                  - + -

From the sign chart, we see that the function is positive on the intervals (-√2, 3/4) and (√2, 4). Therefore, the solution to the inequality is:

x ∈ (-√2, 3/4) ∪ (√2, 4).

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Answer:

A) x=12

Step-by-step explanation:

Total of markers in her bag is: 8+4+1+12=25.

The chanse that she can pull out green marker is  [tex]\frac{4}{25}[/tex].

[tex]\frac{4}{25} *75=4*3=12[/tex]

The ball is in the air for approximately 0.8 seconds before Ellie catches it.

The acceleration a body experiences as a result of gravity is known as the acceleration due to gravity. Its acceleration is around 9.81 metres per second squared close to the Earth's surface. In kinematics, many equations that describe how things move when affected by gravity include the acceleration caused by gravity as a constant.

Using kinematic equation to solve for the time (t):

Δy = vit + 0.5a*t²

Rearranging we have:

t = √((Δy - 0.5at²) / vi)

Substituting the values:

t = √((1 - 0.59.81t²) / 6)

t = 0.798 seconds

Hence, the ball is in the air for approximately 0.8 seconds before Ellie catches it.

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Answer:

Let's use algebra to solve the problem.

Let x be the number of 50 cent pieces in the moneybox.

Then the number of 20 cent pieces in the moneybox is 600 - x (since there are 600 coins in total).

The value of x 50 cent pieces is 50x cents.

The value of (600 - x) 20 cent pieces is 20(600 - x) = 12000 - 20x cents.

The total value of the coins is the sum of these two values:

50x + (12000 - 20x) = 3000 + 30x

So there are 3000 + 30x cents in the moneybox.

To find the total number of cents, we need to evaluate this expression for x:

3000 + 30x

We don't know the value of x, but we do know that there are 600 coins in the moneybox, so we can set up another equation:

x + (600 - x) = 600

Simplifying this equation, we get:

x + 600 - x = 600

Simplifying further, we get:

600 = 600

This equation is always true, which means we can solve for x in terms of 600:

x = 600 - (600 - x)

x = 600 - (600 - x)

x = 600 - (600 - x)

x = 600 - 600 + x

x = x

So x can be any value between 0 and 600.

To find the total number of cents in the moneybox, we need to evaluate the expression 3000 + 30x for any value of x between 0 and 600.

The minimum value of this expression occurs when x = 0:

3000 + 30(0) = 3000

The maximum value of this expression occurs when x = 600:

3000 + 30(600) = 21000

So there are between 3000 and 21000 cents in the moneybox, depending on how many 50 cent pieces there are.

Hope This Helps!

Answer:

1) Since 16 x 16 = 256, the square root of 256 is 16.

16÷2√8

2) Simplify 18 to 2√2.

16 ÷ 2 × 2√2

3) Simplify 16÷2 to 8.

8 × 2√2

4) Simplify.

16√2

Done

Decimal Form: 22.627417

Answer:

22.6 (approx)

Step-by-step explanation:

[tex] \sqrt{256} = 16[/tex]

[tex] \sqrt{8} = 2 \sqrt{2} [/tex]

[tex] \sqrt{2} = 1.41 \: approx[/tex]

16 ÷ 2×(2×1.41)

16 ÷ 2×2.82

8 × 2.82

Therefore, answer is 22.56

Answer:

y = 91

as the x value increases the y value also increases.

The x and y value will always be 9 numbers apart as it increases.

Step-by-step explanation:

y = x-9, x = 100

y = 100 - 9

y = 91

(100, 91)

Therefore , the solution of the given problem of triangle comes out to be  two triangles cannot be congruent because their side lengths and angle measurements vary.

If a polygon has at least one additional segment, it is a hexagon. Its form is a straightforward rectangle. Something like this can only be distinguished from a regular triangular by edges A and B. Euclidean geometry only creates a portion of the cube, despite the precise collinearity of the borders. A triangular has three sides and three angles.

Here,

The diagram's two rectangles are not parallel to one another. Here's how we can figure that out:

The two triangles' side lengths and angle measurements vary, as is evident. Triangle DEF's side lengths are

=> DE = 5, EF = 4, and DF = 7,

while Triangle ABC's side lengths are

=>  AB = 7, BC = 4, and AC = 8.

Triangle DEF has an acute angle at D, a right angle at E, and

an oblique angle at F,

whereas Triangle ABC has acute angles at A and B and a right angle

at C.

The two triangles cannot be congruent because their side lengths and angle measurements vary.

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Answer: between 4 and 9 is

4 *9=36=6

Step-by-step explanation:

Using triangle ratios:

x is to 20  as   21 is to 29

x/20 = 21/29       x = 20 *  21/29 = 14.5 units

OR

x is to 21 as 20 is to 29

x/21 = 20 / 29      x =  21 * 20/29  = 14.5 units

when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one.

Check the picture below.

Answer:

We can simplify the expression as follows:

- First, we can simplify inside the parenthesis: 12 - 3 + 6x = 9 + 6x.

- Next, we can substitute this simplified expression back into the original expression:

-1/3(9 + 6x) = -3 - 2x, distributing the -1/3 through.

Therefore, -1/3(12-3+6x) is equivalent to -3-2x.

The area of a semicircle with radius r is given by the formula A = (πr^2)/2.

Substituting r = 98cm, we get:

A = (π(98cm)^2)/2

A = 4,801.089 cm^2 (using π = 3.14159265)

Rounding to 1 decimal place we get 4,801.1 cm^2.

Therefore the area of semi-circle rounding to 1 decimal point is

4,801.1 cm^2.

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The four basic steps that should be followed to attain a structured analysis of transactions are identifying and analyzing transactions, recording transactions to a journal, posting journal entries to ledger accounts, and preparing a trial balance.

There are different variations of the steps involved in the accounting cycle or transaction analysis, but here are four basic steps that are commonly used:

Identify and analyze transactions: This involves identifying the financial transactions that have occurred and analyzing them to understand their nature, purpose, and effect on the business.

Record transactions to a journal: After analyzing the transactions, they need to be recorded in a journal. The journal entries should include the date, accounts involved, amounts, and a brief description of the transaction.

Post journal entries to ledger accounts: Once the transactions are recorded in the journal, they need to be posted to the corresponding ledger accounts, which are used to summarize and organize the transactions for each account.

Prepare a trial balance: After the transactions have been recorded and posted to the ledger accounts, a trial balance should be prepared to ensure that the debits and credits balance. This involves adding up all the debit balances and credit balances in the ledger accounts to see if they are equal.

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