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4 years ago

Can someone explain the properties and help me with this work?

Mathematics

1 answer:

Sever21 [200]4 years ago

3 0

The first property is commutative ( the numbers 38 and 677 are swapped over)

Then we have the associative property ( where the paretheses are moved to get 38 and -38 together)

then the additive inverse ( 38 + (-38) = 0

and finally to get the 677 we use the additive identity property.

You might be interested in

Classify each differential equation as separable, exact, linear, homogeneous, or Bernoulli. Some equations may be more than one

sergey [27]

Answer:

a) dy/dx = (x − y)/x. This is exact, linear in y, and homogeneous.

b) (x + 1)dy/dx = −y + 20. This is separable, exact, and liner in x and y.

c) dy/dx = 1/(x(x − y2)). This is Bernoulli in x.

d) dy/dx =(y^2 + y)/(x^2 + x). This is Bernoulli in x and y, and Separable.

e) dy/dx = 5y + y^2. This is Bernoulli in y, and Separable.

f) y dx = (y − xy^2) dy. This is linear in x.

g) x dy/dx = ye^(xy) – x. This is homogeneous.

h) 2xyy' + y^2 = 2x^2. This is exact, homogeneous, and Bernoulli.

i) y dx + x dy = 0. This is exact, homogeneous, separable, and linear in x and y.

k) (x^2 + 2y/x) dx = (3 − ln x^2) dy. This is exact, and linear in y.

l) (y/x^2) dy/dx + e^(2x^3) + y^2 = 0. This is separable.

Step-by-step explanation:

The following categories of each of the differential equation are first explained as follows:

Separable differential equation: Any equation that can be expressed in the form y′=f(x)g is a separable differential equation (y).

Exact differential equation: This is a type of differential equation that can be solved directly without the use of any of the special techniques in the subject.

Linear differential equation: This is a form of differential equation that can be solved without resorting to any of the subject's unique techniques.

Homogeneous differential equation: A differential equation is said to be homogeneous if it is a homogeneous function of the unknown function and its derivatives.

Bernoulli differential equation: If an ordinary differential equation has the form y' + P(x)y = Q(x)y^n, where n is a real number, it is referred to as a Bernoulli differential equation.

Since the question indicates "Do not solve", we therefore only classify as follows:

a) dy/dx = (x − y)/x. This is exact, linear in y, and homogeneous.

b) (x + 1)dy/dx = −y + 20. This is separable, exact, and liner in x and y.

c) dy/dx = 1/(x(x − y2)). This is Bernoulli in x.

d) dy/dx =(y^2 + y)/(x^2 + x). This is Bernoulli in x and y, and Separable.

e) dy/dx = 5y + y^2. This is Bernoulli in y, and Separable.

f) y dx = (y − xy^2) dy. This is linear in x.

g) x dy/dx = ye^(xy) – x. This is homogeneous.

h) 2xyy' + y^2 = 2x^2. This is exact, homogeneous, and Bernoulli.

i) y dx + x dy = 0. This is exact, homogeneous, separable, and linear in x and y.

k) (x^2 + 2y/x) dx = (3 − ln x^2) dy. This is exact, and linear in y.

l) (y/x^2) dy/dx + e^(2x^3) + y^2 = 0. This is separable.

6 0

3 years ago

Jeremy uses 27 inches of board for each birdhouse he builds. How many yards of board does he need to make 6 birdhouses?

Blababa [14]

Answer:

$4.5\ yd$

Step-by-step explanation:

step 1

we know that

Jeremy uses 27 inches of board for each birdhouse

by proportion

Calculate how many inches of board does he need to make 6 birdhouses

$\frac{27}{1}\frac{in}{birdhouses}=\frac{x}{6}\frac{in}{birdhouses} \\ \\x=6*27\\ \\x=162\ in$

step 2

Convert inches to yards

$1\ yd =36\ in$

$162\ in=162/36=4.5\ yd$

7 0

4 years ago

What is the original number?

notsponge [240]

The number is 20. 20+10 (half of 20) + 4 (a fifth of 20) = 34

8 0

3 years ago

1. An observer 80 ft above the surface of the water measures an angle of depression of 0.7o to a distant ship. How many miles is

dybincka [34]

Answer:

1. The distance of the ship from the base of the lighthouse is approximately 1.24 miles

2. a)The horizontal distance the plane must start descending is approximately 190.81 km

b) The angle the plane's path will make with the horizontal is approximately 18.835°

3. The depth of the submarine is approximately 107.51 m

Step-by-step explanation:

The

1. From the question, we have;

The height of the observer above the water = 80 ft.

The angle of depression of the ship from the observer, θ = 0.7°

Let the position of the observer be 'O', let the location of the ship be 'S', let the point directly above the ship at the level of the observer be 'H', we have;

$tan(\theta) = \dfrac{Opposite \ leg \ length}{Adjacent \ leg \ length} = \dfrac{HS}{OH}$

$The \ horizontal \ distance \ of \ the \ ship, OH = \dfrac{HS}{tan(\theta) }$

HS = The height of the observer = 80 ft.

Therefore, we get;

$The \ horizontal \ distance \ of \ the \ ship, OH = \dfrac{80 \, ft.}{tan(0.7^{\circ}) } \approx 6,547.763 \ ft.$

The distance of the ship from the base of the lighthouse ≈ 6,547.763 ft. ≈ 1.24 miles

2. The elevation of the plane, h = 10 km

The angle of the planes path with the ground, θ = 3°

Similar to question (1) above, the horizontal distance the plane must start descending, d = t/(tan(θ))

∴ d = 10 km/(tan(3°)) ≈ 190.81 km

The horizontal distance the plane must start descending, d = 190.81 km

b) If the pilot start descending 300 km from the airport, the angle the plane's path will make with the horizontal, θ, will be given as follows;

From trigonometry, we have;

$tan(\theta) = \dfrac{Opposite \ leg \ length}{Adjacent \ leg \ length}$

Where the opposite leg length = The elevation of the plane = 10 km

The adjacent leg length = The horizontal distance from the airport = 300 km

$\therefore tan(\theta) = \dfrac{10 \, km}{300 \, km} = \dfrac{1}{3}$

$\theta = arctan\left(\dfrac{1}{3} \right ) \approx 18.835^{\circ}$

The angle the plane's path will make with the horizontal, θ ≈ 18.835°

3. The angle at which the submarine makes the deep dive, θ = 21°

The distance the submarine travels along the inclined downward path, R = 300 m

By trigonometric ratios, we have;

The depth, of the submarine, 'd' is given as follows;

$si(\theta)= \dfrac{Opposite \ leg \ length}{Hypotenuse \ length} = \dfrac{d}{R}$

∴ d = R × sin(θ)

d = 300 m × sin(21°) ≈ 107.51 m

The depth of the submarine ≈ 107.51 m

7 0

3 years ago

Which expression is equivalent to (2−√−4)+(1+√−49)? <br> 3−5i <br> 3+5i <br> 8+0i <br> −2+0i

sergij07 [2.7K]

Answer:

3 + 5i.

Step-by-step explanation:

(2−√−4)+(1+√−49)

√−4 = 2i and

√−49 = 7i.

So (2−√−4 + (1+√−49

= ( 2 - 2i) + (1 + 7i)

= 3 + -2i + 7i

= 3 + 5i.

3 0

4 years ago