The slope field for a differential equation is shown in the figure. Determine the general solution of this equation.

100 POINTS
slope field with positive slopes in quadrant 1 and 4, negative slopes in quadrants 2 and 3, horizontal slopes along the y axis

y=Cx2
x=Cy2
x2 – y2 = C2
x2 + y2 = C2

Remember that i = √(-1), so that

• i ² = -1,

• i ³ = i x i ² = i x (-1) = -i

• i ⁴ = i x i ³ = i x (-i) = -i ² = -(-1) = 1

Multiplying by i again gives i ⁵ = i and the cycle starts over.

The main observation to make here is that raising i to any multiple of 4 returns 1. So,

i ⁴⁸ = (i ⁴)¹² = 1¹² = 1

i ²²³ = i ²²⁰⁺³ = i ²²⁰ x i ³ = (i ⁴)⁵⁵ x i ³ = 1⁵⁵ x (-i) = -i

i ¹¹³ = i ¹¹²⁺¹ = i ¹¹² x i = (i ⁴)²⁸ x i = 1²⁸ x i = i

i ⁸² = i ⁸⁰⁺² = i ⁸⁰ x i ² = (i ⁴)²⁰ x i ² = 1²⁰ x (-1) = -1

i^48 = 1

i^223 = -i

i^113 = i

i^82 = -1

Answer:

2,870 and 30

Step-by-step explanation:

Answer:

Step-by-step explanation:

The triangles are similar because they have two sides and the angle between them (EFG) respectively equals, and it’s evident the factor between the two triangles is 2. So EG=2CB=2*8=16

Answer:

the value of EG is 20.

Step-by-step explanation:

3×4 = 12, AB and EF is similar but the value of AB is multiplied by 4 to become 12 for EF.

similarly, 4×4 = 16, BC and FG is similar but the value of BC is multiplied by 4 to become 16 for FG..

In this way, AC and EG are also similar so 5×4 = 20.

All the values are multiplied by 4 ...

Answer:

The guinea pig is 210 millimeters longer than the fish.

Step-by-step explanation:

Answer:

Jayla's expenses are: $245.00

Jayla's revenue from the sales are: $479.00

Total profit: $234.00

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Hope this helps! This should be correct !

Answer:

- $245

+ $479

+ $234

Step-by-step explanation:

expenses : (25 x 2) + (15 x 3) + (30 x 5) = 50 + 45 + 150 = 95 + 150 = $245

revenue : (38 x 2) + (26 x 3) + (65 x 5) =  76 + 78 + 325 = 154 + 325 = $479

total profit : 479 - 245 = $234

Answer:

x^5+2x^3+6x+1/5

Step-by-step explanation:

our given equation is already written in standard form.

Answer:

It is already in standard form

Step-by-step explanation:

The standard equation should be arranged from high order to low order

   So x^5+2x^3+6x+1/5 = x^5+2x^3+6x+1/5

It is already in standard form

Answer:  n = -2; i = 1

Step-by-step explanation:

i + 2n = -3

        i = -3 - 2n

Plug in i in 2i - 3n = 8, we get:

2i - 3n = 8

2(-3 - 2n) - 3n = 8

-6 - 4n - 3n = 8

-6 - 7n = 8

     -7n = 14

        n = -2

substitute n = -2 into i = -3 - 2n

i = -3 - 2n

i = -3 - 2(-2)

i = -3 + 4

i = 1

Solution:

Given ratio: [tex]0.45:1.35[/tex]

Multiply both sides by 100:

[tex]0.45:1.35[/tex]

[tex]\rightarrow 0.45 \times 100:1.35 \times 100[/tex]

[tex]\rightarrow 45:135[/tex]

Convert the ratio into a fraction:

[tex]\rightarrow 45:135 = \dfrac{45}{135}[/tex]

Simplify the fraction:

[tex]\rightarrow \dfrac{45}{135} = \dfrac{45 \div5}{135 \div 5} =\dfrac{9}{27} = \dfrac{9 \div 9}{27 \div 9} = \dfrac{1}{3}[/tex]

The simplified fraction representing the ratio 0.45 to 1.35 is 1/3.

To express the ratio 0.45 to 1.35 as a simplified fraction, we can divide both numbers by their greatest common divisor (GCD) to simplify the ratio. In this case, the GCD of 45 and 135 is 45.

So, divide both numbers by 45:

0.45 ÷ 45 = 0.01

1.35 ÷ 45 = 0.03

The simplified ratio is 0.01 to 0.03. To make it an integer ratio, we can multiply both parts by 100:

0.01 * 100 = 1

0.03 * 100 = 3

So, the simplified fraction representing the ratio 0.45 to 1.35 is 1/3.

To know more about fraction:

https://brainly.com/question/10354322

#SPJ3

The area of the triangle is the amount of space on it.

The area of the triangle is 85.5 square yard

The given parameters are:

a = 12 yd

b = 16 yd

c = 15 yd

Start by calculating the semi-perimeter (s)

s = 0.5 * (a + b + c)

This gives

s = 0.5 * (12 + 16 + 15)

s = 21.5

The area of the triangle is then calculated as:

[tex]A = \sqrt{s * (s - a) * (s - b) * (s - c)[/tex]

This gives

[tex]A = \sqrt{21.5 * (21.5 - 12) * (21.5 - 16) * (21.5 - 15)[/tex]

Evaluate the product

[tex]A = \sqrt{7301.9375[/tex]

Evaluate the square root

A = 85.5

Hence, the area of the triangle is 85.5 square yard

Read more about areas at:

https://brainly.com/question/24487155

Answer:

18x + 9

Step-by-step explanation:

[tex]\\ \rm\Rrightarrow tan^2135-cosec^260=-xcos45.sin45.cot60[/tex]

[tex]\\ \rm\Rrightarrow (-1)^2-(\dfrac{2}{\sqrt{3}})^2=-\dfrac{x}{\sqrt{2}}\times \dfrac{1}{\sqrt{2}}\times \dfrac{1}{\sqrt{3}}[/tex]

[tex]\\ \rm\Rrightarrow 1-\dfrac{4}{3}=\dfrac{-x}{2\sqrt{3}}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{3-4}{3}=\dfrac{-x}{2\sqrt{3}}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{-1}{3}=\dfrac{-x}{2\sqrt{3}}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{1}{\sqrt{3}}=\dfrac{x}{2}[/tex]

[tex]\\ \rm\Rrightarrow x=\dfrac{2}{\sqrt{3}}[/tex]

f(x) = 3x − 5 when x=−1, x=0, x=3

Answer:

-8, -2, 4

Step-by-step explanation:

1. Insert -1, 0, and 3 into x

2. Solve

Replace x with -1: f(-1) = 3(-1) − 5

Multiply 3(-1): f(-1) = -3 − 5

Subtract by 5: f(-1) = -8

The answer is -8

Now do this for the rest of the problems:

f(0) = 3(0) − 5 when x=−1, x=0, and x=3

-2 is the 2nd answer

f(3) = 3(3) − 5 when x=−1, x=0, and x=3

4 is the 3rd answer

This is my first answer, so I hope I explained it well!

Answer:

9m⁸

Step-by-step explanation:

3^2=9

(m⁴)² = m⁸

9*m⁸

Answer:

[tex]\displaystyle y = 4x + 12[/tex]

Step-by-step explanation:

−4x + y = 12

+ 4x + 4x

_________

[tex]\displaystyle \boxed{y = 4x + 12}[/tex]

I am joyous to assist you at any time.

I believe it is 35!

I hope this helps you, and don't forget to give this answer brainliest if it really helped!

Answer:

7.61 gallons.

Step-by-step explanation:

you take the 46, and you divide on both sides. 350÷46= approximately 7.61 gallons.

Answer:

i believe it's actually the fourth option: lines e and f are parallel bc their same side exterior angles are supplementary

Step-by-step explanation:

its part of a theorem you learn, don't remember exactly (haven't taken geo in like 2 years lol)

Answer:

i believe it shud be c

Step-by-step explanation: it really doesn't proof that for a and be the corresponding angles are congruent..

Hope this is correct!!

Answer:

  n² -10 = 6

Step-by-step explanation:

If n represents a positive number, then "the square of a positive number" is represented by n². When that value is decreased by 10, it becomes ...

  n² -10

and if that value is 6, the math expression is ...

  n² -10 = 6

__

Additional comment

Increasing the value by 10 gives ...

  n² = 16

and taking the positive square root gives us the value of the number:

  n = √16 = 4

in this question we have to multiply 4 with 4 then we have to minus 16 with 10 we get the answer 6

= 4 × 4 = 16

= 16 - 10

= 6

Answer:

x = 0

I hope this helps!

Answer:

B, 34 degrees

Step-by-step explanation:

Since all triangles equal to 180 degrees, you have to add together the angles you already know and subtract from 180.

123+23=146  180-146=34

Hopefully this helps, have a nice day/night!

Answer:

C)

Step-by-step explanation:

[tex]\sqrt{x}[/tex] : original function

[tex]\sqrt{-x}[/tex] : reflect across the y-axis

[tex]\sqrt{-\dfrac13x}[/tex] : horizontal stretch by a scale factor of 3

[tex]\sqrt{-\dfrac13(x-3)}[/tex]: translate right 3 units

f(x) : original function

f(-x) : reflection over y-axis

f(ax) : horizontal stretch of the graph by a scale factor of 1/a

f(x - a) : horizontal translation right a units

Answer:

1.) 75

2.) 75

3.) 2

Step-by-step explanation:

120n-150=45n

add 150 to both sides

120n=45n+150

subtract 45n from both sides

75n=150

divide by common number, since 75 is half of 150, use 75.

n=2

Answer:

The probability is [tex]P(X \le 0.60) = 0.000 [/tex]

Step-by-step explanation:

From the question we are told that

   The overall pass rate is  [tex]R  =  76\% =  0.76[/tex]

   The sample size is  n  =  400

   The percentage that passed is  [tex]k =  60\%  =  0.60[/tex]

Generally the standard error is mathematically represented as

     [tex]\sigma _{\= x } =  \sqrt{\frac{R (1 -R)}{n} }[/tex]    

  =>    [tex]\sigma _{\= x } =  \sqrt{\frac{0.76 (1 -0.76)}{400} }[/tex]

  =>    [tex]\sigma _{\= x } = 0.0214 [/tex]  

Generally the probability of a simple random sample of 400 having a pass rate of 60% or less is mathematically represented as

      [tex]P(X \le 0.60) = P(\frac{X - R}{ \sigma_{\= x}}  \le \frac{0.60 - 0.76}{0.0214} )[/tex]

=>   [tex]P(X \le 0.60) = P(Z \le -7.48 )[/tex]

Generally from the z-table  

      [tex]P(Z \le -7.48 ) =  0.000[/tex]

So

  [tex]P(X \le 0.60) = 0.000 [/tex]

Answer:

x=2

Hope this helps! :)

3x+5x=8x

23-7=16

16÷8

Answer:

x = 2

Step-by-step explanation:

3x + 7 = 23 - 5x

3x + 5x = 23 - 7

8x = 16

x = 2

Answer:

Step-by-step explanation:

Use slope formula:

1) Points (1, 2) and (5, 4)

2) Points (1, -5) and (3, 5)

3) Points (2, 3) and (-1, 6)

4) Points (4, 2) and (-2, 2)

Answer:

1/5, 1, decreasing, 0

Step-by-step explanation:

Answer:

Step-by-step explanation:

6/9 x 45 = 2/3 x 45 = 30

[tex] \frac{2}{3} \times 45 = 30[/tex]

one shirt is for $25 so multiple that by 3 and get $75

Answer:

36 degrees

Step-by-step explanation:

The whole shape is 90 degrees.

90 - 54 = 36

36 degrees

Answer:

36*

Step-by-step explanation:

a right angle is 90* and so you do

90-54=36

meaning your missing angle is 36*