Simplify 36ab divided by 40ab

Jasmine created a scale drawing of her room. She used a scale of 1 in:3 feet. The drawing is 8 inches long by 6 inches wide. Wha

sergiy2304 [10]

Answer:

The area of the room is 432 square feet

Step-by-step explanation:

Let us use the ratio method to solve the question

∵ The scale drawing of the room is 1 inch: 3 feet

→ That means each 1 inch in the drawing represents 3 feet in real

∵ The drawing is 8 inches long by 6 inches wide

∴ The drawing length of the room = 8 inches

∴ The drawing width of the room = 6 inches

→ By using the ratio method

→ inches : feet

→ 1 : 3

→ 8 : L

→ 6 : W

→ By using the cross multiplication

∵ 1 × L = 8 × 3

∴ L = 24

∴ The actual length of the room is 24 feet

∵ 1 × W = 6 × 3

∴ W = 18

∴ The actual width of the room is 18 feet

Use the formula of the area of the rectangle to find the area of the room

∵ Area of rectangle = length × width

∴ Area of the room = 24 × 18

∴ Area of the room = 432 feet²

∴ The area of the room is 432 square feet

8 0

3 years ago

Use undetermined coefficient to determine the solution of:y"-3y'+2y=2x+ex+2xex+4e3x

Kitty [74]

First check the characteristic solution: the characteristic equation for this DE is

r ² - 3r + 2 = (r - 2) (r - 1) = 0

with roots r = 2 and r = 1, so the characteristic solution is

y (char.) = C₁ exp(2x) + C₂ exp(x)

For the ansatz particular solution, we might first try

y (part.) = (ax + b) + (cx + d) exp(x) + e exp(3x)

where ax + b corresponds to the 2x term on the right side, (cx + d) exp(x) corresponds to (1 + 2x) exp(x), and e exp(3x) corresponds to 4 exp(3x).

However, exp(x) is already accounted for in the characteristic solution, we multiply the second group by x :

y (part.) = (ax + b) + (cx ² + dx) exp(x) + e exp(3x)

Now take the derivatives of y (part.), substitute them into the DE, and solve for the coefficients.

y' (part.) = a + (2cx + d) exp(x) + (cx ² + dx) exp(x) + 3e exp(3x)

… = a + (cx ² + (2c + d)x + d) exp(x) + 3e exp(3x)

y'' (part.) = (2cx + 2c + d) exp(x) + (cx ² + (2c + d)x + d) exp(x) + 9e exp(3x)

… = (cx ² + (4c + d)x + 2c + 2d) exp(x) + 9e exp(3x)

Substituting every relevant expression and simplifying reduces the equation to

(cx ² + (4c + d)x + 2c + 2d) exp(x) + 9e exp(3x)

… - 3 [a + (cx ² + (2c + d)x + d) exp(x) + 3e exp(3x)]

… +2 [(ax + b) + (cx ² + dx) exp(x) + e exp(3x)]

= 2x + (1 + 2x) exp(x) + 4 exp(3x)

… … …

2ax - 3a + 2b + (-2cx + 2c - d) exp(x) + 2e exp(3x)

= 2x + (1 + 2x) exp(x) + 4 exp(3x)

Then, equating coefficients of corresponding terms on both sides, we have the system of equations,

x : 2a = 2

1 : -3a + 2b = 0

exp(x) : 2c - d = 1

x exp(x) : -2c = 2

exp(3x) : 2e = 4

Solving the system gives

a = 1, b = 3/2, c = -1, d = -3, e = 2

Then the general solution to the DE is

y(x) = C₁ exp(2x) + C₂ exp(x) + x + 3/2 - (x ² + 3x) exp(x) + 2 exp(3x)

4 0

3 years ago

Prove Euler's identity using Euler's formula. e^ix = cos x + i sin x

Korolek [52]

First list all the terms out.

e^ix = 1 + ix/1! + (ix)^2/2! + (ix)^3/3! ...

Then, we can expand them.

e^ix = 1 + ix/1! + i^2x^2/2! + i^3x^3/3!...

Then, we can use the rules of raising i to a power.

e^ix = 1 + ix - x^2/2! - ix^3/3!...

Then, we can sort all the real and imaginary terms.

e^ix = (1 - x^2/2!...) + i(x - x^3/3!...)

We can simplify this.

e^ix = cos x + i sin x

This is Euler's Formula.

What happens if we put in pi?

x = pi

e^i*pi = cos(pi) + i sin(pi)

cos(pi) = -1

i sin(pi) = 0

e^i*pi = -1 OR e^i*pi + 1 = 0

That is Euler's identity.

3 0

3 years ago

Helppppp! what is 2+6????

yaroslaw [1]

Answer:

8...I want these points lol

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Each day in Bio 18, Derek leaves a stack of paper packets near the entry door for students to obtain. Eighty-one percent of stud

Rainbow [258]

Answer:

Step-by-step explanation:

This is a binomial probability distribution because there are only 2 possible outcomes. It is either a randomly selected student grabs a packet before being seated or the student sits first before grabbing a packet. The probability of success, p in this scenario would be that a randomly selected student sits first before grabbing a packet. Therefore,

p = 1 - 0.81 = 0.91

n = 9 students

x = number of success = 3

The probability that exactly two students sit first before grabbing a packet, P(x = 2) would be determined from the binomial probability distribution calculator. Therefore,

P(x = 2) = 0.297

5 0

3 years ago

Simplify 36ab divided by 40ab​

Simplify 36ab divided by 40ab