2. Use MATLAB to draw direction fields for the differential equations listed in Prob- lem 1. In each of the following cases, show that the given function y(x) satisfies the associated differential equation. Then determine the value of c required by the initial condition. Finally, with reference to the general format in (8.7), identify f(x, z) for each differential equation. Table 8.7. Backward Euler Solution for (8.64); h = 0.5 Error: Error: Error: X = -1 2= -10 i = -50 2 2.08E-1 1.97E-2 3.60E - 3 -1.63E-1 -3.35E-2 -6.94E-3 6 -7.04E-2 8.19E-3 2.18E-3 8 2.22E-1 2.67E-2 5.13E-3 10 -1.14E-1 -3.04E-2 -6.45E-3 4 (b) Y'(x) = (Y(x) - Y(x))/x, Y(1) = 2; y(x) = x/(x + c), X>0 (d) Y'(x) = Y(x)[Y(x) - 1), Y(0) = {; Y(x) = 1/(1+ ce*) need Matlab thank you!

Answer:

-1, -7, -13, -19

Step-by-step explanation:

-2(-3)-7 =6-7= -1

-2(0)-7 =0-7= -7

-2(3)-7 =-6-7= -13

-2(6)-7 =-12-7= -19

Answer:

(-3,-1)(0,-7)(3,-13)(6,-19)

Step-by-step explanation:

Put the x number into the x in the equation to get your answer:

y=-2(-3)-7    y=-1

y=-2(0)-7     y=-7

y=-2(3)-7      y=-13

y=-2(6)-7     y=-19

(hope this helps :P)

The combination p AND (NOT q) is true when p is true and q is false, and false otherwise.

The statement "p AND (NOT q)" means that both p is true and q is false.

When p is true ("The pond is not frozen over") and q is true ("The fish are not jumping"), then (NOT q) is false, so the combination p AND (NOT q) is false.

When p is true and q is false ("The fish are jumping"), then (NOT q) is true, so the combination p AND (NOT q) is true.

When p is false ("The pond is frozen over"), then the combination p AND (NOT q) is false regardless of the truth value of q.

Therefore, the combination p AND (NOT q) is true when p is true and q is false, and false otherwise.

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0.578 can be expressed as a percent if we can multiply the decimal by 100%

Step 1: Multiply 0.578 by 100

To multiply by 100, we simply have to shift the decimal point by the number of zeros (twice)

0.578 x 100 = 57.8%

Answer = 57.8%

Answer:

x ≥ 18

Step-by-step explanation:

Given the inequality statement, 2/3x + 17 ≥ 29,

Subtract both sides by 17:

2/3x + 17 - 17 ≥ 29 - 17

2/3x  ≥ 12

Multiply both sides by 3/2 to isolate x:

\((\frac{3}{2}) \frac{2}{3}x \geq 12 (\frac{3}{2})\)

x ≥ 18

The probability that at least one of the selected marbles is green when 4 marbles are selected at random and without replacement is 88.46%.

To find the probability that at least one of the selected marbles is green, we can use the complementary probability approach.
In this case, we'll calculate the probability that all the selected marbles are red and then subtract it from 1 to find the desired probability.

Step 1: Calculate the probability of selecting all red marbles.
There are 10 red marbles out of a total of 16 marbles. So the probability of selecting the first red marble is 10/16.

Step 2: Since we're selecting without replacement, there are now 9 red marbles and a total of 15 marbles left. The probability of selecting the second red marble is 9/15.

Step 3: For the third red marble, there are now 8 red marbles and a total of 14 marbles. The probability of selecting the third red marble is 8/14.

Step 4: For the fourth red marble, there are now 7 red marbles and a total of 13 marbles. The probability of selecting the fourth red marble is 7/13.

Step 5: Multiply the probabilities from Steps 1-4 to find the probability of selecting all red marbles: (10/16) x (9/15) x (8/14) x (7/13) = 5040/43680 = 0.1153

Step 6: Subtract the probability of selecting all red marbles from 1 to find the probability that at least one marble is green: 1 - 0.1153 = 0.8846

So the probability that at least one of the selected marbles is green when selecting 4 marbles at random and without replacement from a bag containing 10 red and 6 green marbles is approximately 0.8846 or 88.46%.

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Answer:

B. False

Pont (2, -3) lies on the fourth quadrant.

Step-by-step explanation:

You're welcome.

Answer: Divide the amount that she wants to bake by the dimensions

Step-by-step explanation:

Area of 1 cone =4 times 4= 16cm squared

85/16=5.3125=5 rounded to a whole number

The measure of angle B crossing the river perpendicularly is 110°.

When the sum of the two angles is 180° they are said to be supplementary.

When the sum of the two angles is 90° they are said to be complementary.

Given, Bridge A crosses the river at an exterior angle of (2x),  Bridge B crosses at an angle of (4x-6) and these two angles are supplementary.

So, The sum of these two angles are 180°.

Therefore,

4x - 6 + 2x = 180°.

6x = 174°.

x = 174°/6.

x = 29°.

So, The measure of the angle B is (4(29) - 6)°.

= 116 - 6.

= 110°.

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The attenuated oral poliovirus vaccine (OPV) is no longer administered in the U.S.A. due to its potential to be spread to contacts and occasionally cause poliomyelitis.

The decision to discontinue the use of the attenuated oral poliovirus vaccine (OPV) in the U.S.A. was primarily based on concerns regarding its safety and efficacy. While the OPV was effective in providing immunity against poliovirus, it had some drawbacks that led to its discontinuation.

One of the major concerns with OPV was its ability to be spread to contacts. OPV contains live but weakened poliovirus strains, which can be shed in the stool of vaccinated individuals. In rare cases, these weakened strains can revert to a virulent form and cause poliomyelitis in contacts who come into contact with the virus through contaminated feces.

Additionally, the OPV has a small risk of causing poliomyelitis itself, although this risk is extremely rare. The weakened strains in the vaccine have a very low potential to cause disease, but in rare instances, they can regain their ability to cause paralysis.

To address these concerns, countries like the U.S.A. have shifted to using the inactivated poliovirus vaccine (IPV), which does not carry the risk of vaccine-derived poliovirus cases or transmission to contacts. IPV is a safer alternative that provides effective protection against poliovirus without the potential risks associated with OPV.

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Answer:

The correct option is;

It influenced the laws of other countries

Step-by-step explanation:

The Justinian Code was the rationalization of previous existing Roman laws so as to remove contradiction and eliminate conflicting statutes including the repeal of laws not included in the code.

For close to a millennia, the Justinian Code served as the bedrock of the Byzantine Judiciary and of civil law, fostering law and order for the people of Byzantines and civil law spread to Europe and Latin America.

The Justinian Code influenced the laws of other countries.  

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The expression (1 - cos²θ) / sin²θ simplifies to 1.

We have,

To solve the expression (1 - cos²θ) / sin²θ, we can simplify it using trigonometric identities.

First, we can rewrite cos²θ as (cosθ)² and sin²θ as (sinθ)².

(1 - (cosθ)²) / (sinθ)²

Next, we can use the Pythagorean identity, which states that

sin²θ + cos²θ = 1.

Rearranging this identity, we have 1 - (cosθ)² = (sinθ)².

Substituting this into the expression:

((sinθ)²) / (sinθ)²

Now, we can cancel out the common factor of (sinθ)² in the numerator and denominator, leaving us with 1

Therefore,

The expression (1 - cos²θ) / sin²θ simplifies to 1.

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Step-by-step explanation:

3x = 12 - 18

3x = (- 6)

X = (-6)/3

x = (-3)

Answer:

56

Step-by-step explanation:

48 ounces would feed 6 people and if 16 oz is for two people than 8 oz is for one person. So, 48 plus 8 is 56.

Answer:

3

Step-by-step explanation:

its 8 because if you round it by 1 then you get 3

The height of the building is 30 feet.

The height of the building can be calculated using the concept of similar triangles. The man, who is 6 feet tall, casts a shadow that is 4 feet long. At the same time, the building casts a shadow of 20 feet.

To solve this problem, we can set up a proportion between the height of the man and the length of his shadow, and the height of the building and the length of its shadow. Let's assume the height of the building is 'x' feet.

The proportion can be written as:

(Height of the man) / (Length of the man's shadow) = (Height of the building) / (Length of the building's shadow)

Substituting the given values, we have:

6 feet / 4 feet = x feet / 20 feet

To solve for 'x', we cross-multiply:

4x = 6 * 20

4x = 120

Dividing both sides of the equation by 4, we get:

x = 120 / 4

x = 30

Therefore, the height of the building is 30 feet.

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Answer:

Step-by-step explanation:

985 = 5 * 197 = 1 * 5 * 197

The product of the divisors is 985

The sum is 203

9514 1404 393

Answer:

  x = 3

Step-by-step explanation:

The points have the same x-coordinate, so lie on a vertical line. The equation of a vertical line is x=constant. The constant must match the x-coordinate of the points:

  x = 3 . . . . equation of the line

Answers:

\(\csc(\theta) = \frac{7\sqrt{33}}{33}\\\\\sin(\theta) = \frac{\sqrt{33}}{7}\\\\\cot(\theta) = \frac{4\sqrt{33}}{33}\\\\\)

=============================================

Explanation:

Before we can find the trig ratios, we need to determine the length of the missing side. Apply the pythagorean theorem

\(a^2+b^2 = c^2\\\\4^2+b^2 = 7^2\\\\16+b^2 = 49\\\\b^2 = 49-16\\\\b^2 = 33\\\\b = \sqrt{33}\)

The vertical side is \(\sqrt{33}\) units long.

------------------------------------

The side we just found is the opposite side to angle \(\theta\) (greek letter theta)

The hypotenuse is 7 units long. The hypotenuse is always opposite the right angle.

Divide the hypotenuse over opposite to get the cosecant.

\(\csc(\theta) = \frac{\text{hypotenuse}}{\text{opposite}}\\\\\csc(\theta) = \frac{7}{\sqrt{33}}\\\\\csc(\theta) = \frac{7\sqrt{33}}{\sqrt{33}*\sqrt{33}}\\\\\csc(\theta) = \frac{7\sqrt{33}}{\sqrt{33*33}}\\\\\csc(\theta) = \frac{7\sqrt{33}}{\sqrt{33^2}}\\\\\csc(\theta) = \frac{7\sqrt{33}}{33}\\\\\)

Note: In the third step, I multiplied top and bottom by sqrt(33) to rationalize the denominator.

------------------------------------

Recall that sine is the reciprocal of cosecant, and vice versa.

So we'll use the same idea as before, but flip the original fraction.

\(\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}\\\\\sin(\theta) = \frac{\sqrt{33}}{7}\\\\\)

The denominator is already a rational number, so there's not much else to do here.

--------------------------------------

Cotangent is the ratio of adjacent over opposite

\(\cot(\theta) = \frac{\text{adjacent}}{\text{opposite}}\\\\\cot(\theta) = \frac{4}{\sqrt{33}}\\\\\cot(\theta) = \frac{4\sqrt{33}}{\sqrt{33}*\sqrt{33}}\\\\\cot(\theta) = \frac{4\sqrt{33}}{\sqrt{33*33}}\\\\\cot(\theta) = \frac{4\sqrt{33}}{\sqrt{33^2}}\\\\\cot(\theta) = \frac{4\sqrt{33}}{33}\\\\\)

The steps are pretty much nearly identical as the section involving csc, except we're using the adjacent in place of the hypotenuse (so that means we use 4 in place of 7).

Answer:

Percent error is approx. 22%

Step-by-step explanation:

So to do this you need to know the formula for percent error, which is

percent error = l measured - theoretical / theoretical l * 100%

With this just plug in 18 (real) and 14 (measured).

percent error = l 14 - 18 / 18 l * 100%

percent error = l -4 / 18 l *100%

percent error = l -2/9 l *100%

You then do absolute value because the percent error must be positive not negative! So -2/9 becomes 2/9. You then divide 2/9 to get approx. 0.22... and you muliply by 100% to get 22%.

The simplified form of the expression \((x^4 - 4x^3 - 8x^2 + 9x + 2) / (x + 2)\) is \(x^3 - 6x^2 + 4x - 5 - 62/(x+2).\) This is achieved by polynomial division.

The solution using polynomial division can be shown as:

\(x+2 | x^4 - 4x^3 - 8x^2 + 9x + 2\)

\(- (x^4 + 2x^3)\)

----------------

\(-6x^3 - 8x^2\)

\(+ (6x^3 + 12x^2)\)

-------------------

\(-20x^2 + 9x\)

\(+ (20x^2 + 40x)\)

Therefore, the result of the division is \(x^3 - 6x^2 + 4x - 5\) with a remainder of 62.

So, the simplified form of the given expression is \(x^3 - 6x^2 + 4x - 5 - 62/(x+2).\)

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What is the simplified form of the expression (x^4 - 4x^3 - 8x^2 + 9x + 2) / (x + 2)

Answer:

hence the required minimum production level is 12units

Step-by-step explanation:

Given the cost function expressed as c(x) = x^3 - 24x^2 + 30,000x

The average cost function will be c(x)/x

Dividing the cost function through by x

Average cost function = c(x)/x = x³/x - 24x²/x + 30,000x/x

Average cost function = x²-24x + 30,000

A(x) = x²-24x + 30,000

If the average cost is minimized, hence dA/dx = 0

dA/dx = 2x - 24

0 = 2x - 24

-2x = -24

Divide both sides by -2

-2x/-2 = -24/-2

x = 12

For the second deriviative

d²A/dx² = 2 which is greater than zero

Hence a production level that will minimize the average cost per item of making x items is 12

The production level that will minimize the average cost per item of making x items is  x = 12

To find the minimum of a continuous and twice differentiable function f(x), we can firstly differentiate it with respect to x and equating it to 0 will give us critical points.

Putting those values of x in the second rate of function, if results in negative output, then at that point, there is maxima. If the output is positive then its minima and if its 0, then we will have to find the third derivative (if it exists) and so on.

For this case, the function in consideration is: \(c(x) = x^3 - 24x^2 + 30000x\)

This is cost function for x items' manufacturing.

The average cost per item would be c(x) / x

This gives us a function a(x) as:

\(a(x) = c(x)/x = x^2 -24x + 30000\)

For finding  the minimum of a(x), getting its first two derivatives as:

\(a'(x) = 2x - 24\\a''(x) = 2 > 0\)

Equating first rate to 0,

\(a'(x) = 2x - 24 = 0\) critical point.

Since second rate is positive, the point x = 12 is point of minima, and since only one critical point is there, it is the point on which a(x) is minimum.

Thus, the production level that will minimize the average cost per item of making x items is  x = 12

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The value of c that the quadratic equation -x² + 4x + c = 0

The equation is given as

-x² + 4x + c = 0

Calculate the discriminant using

d = b² - 4ac

Where

a = -1, b = 4, and c = c

So, we have

d = 4² - 4 * -1 * c

Evaluate

d = 16 + 4c

No real roots

This means that d < 0

So, we have

16 + 4c < 0

So, we have

4c < -16

Divide by 4

c < -4

This means that c is less than -4

A possible value of c is -5

Two real roots of the same sign

This means that d > 0

So, we have

16 + 4c > 0

So, we have

4c > -16

Divide by 4

c > -4

Also, the value of c must be less than 0

A possible value of c is -3

Have one negative root and one root equal to 0

This value does not exist

Have two roots with opposite signs

This means that d > 0

So, we have

16 + 4c > 0

So, we have

4c > -16

Divide by 4

c > -4

Also, the value of c must be greater than 0

A possible value of c is 3

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Based on the given information, we cannot prove that △EFG and △KLM are similar using the SSS or SAS similarity theorems. The correct answer is option D) No, they cannot be proven similar by SSS or SAS.

To determine if the triangles △EFG and △KLM can be proven similar using the SSS (Side-Side-Side) or SAS (Side-Angle-Side) similarity theorems, we need to compare their corresponding sides and angles.

SSS Similarity Theorem states that if the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar.

SAS Similarity Theorem states that if two corresponding sides of two triangles are proportional, and the included angles are congruent, then the triangles are similar.

Let's examine the given information:

Side lengths of △EFG: EF = 18, EG = 24, FG = 15.

Side lengths of △KLM: KL = 6, KM = 8, LM = 5.

By comparing the side lengths, we can see that they are not proportional. For example, the ratio of EF/KL is 18/6 = 3, while the ratio of EG/KM is 24/8 = 3. Therefore, the corresponding sides of △EFG and △KLM are not proportional, which means we cannot establish similarity using the SSS theorem.

Now, let's consider the SAS theorem. For this, we also need to compare the included angles.

Angles of △EFG: ∠EFG, ∠EFG, ∠EGF.

Angles of △KLM: ∠KLM, ∠KML, ∠KLM.

The given information states that ∠EFG and ∠KLM are congruent. However, we don't have any information about the other angles. Without knowing the congruency of the remaining angles, we cannot establish similarity using the SAS theorem

Option D.

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Answer: Its C

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

If you consider an open circle, it would exclude the value with which we have circled when writing the inequality. Hence the only possible signs with in such an example can be a greater than sign ( > ) or less than sign ( < );

Let us take a look at an example to help. We are given a graph with an open circle on the number say 3. An arrow extends to the right of this number 3;

\(Inequality Sign - <,\\Inequality - x > 3,\\\)

Hope this helps!

Answer:5.7ft

Step-by-step explanation:

sin = opposite/adjacent

sin 35 = x/10

10 * sin 35 = x

x=5.7

The range between a drug's effective dose and its toxic dose is called the theurapeutic index.

The therapeutic index, often known as the therapeutic ratio, is a numerical evaluation of a drug's relative safety. The amount of a therapeutic agent that has a therapeutic impact is compared to the amount that has a harmful effect.

A range of doses calibrated between efficacy and toxicity, achieving the maximum therapeutic benefit without producing intolerable side-effects or toxicity, is referred to as the therapeutic window or safety window.

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8.9 yards far you should be from the enormous pumpkin.

Given that,

You ride a hayride to capture pictures of famous places. Two landmarks and your route are shown on the map. The coordinate plane's units are equivalent to 10 yards.

We have to Calculate how far you should be from the enormous pumpkin.

Suppose that we have a linear function defined according to the following rule, in standard notation:

Ax + By + C = 0.

And a point with coordinates given by:

P(x*,y*)

The following formula gives the shortest distance between the line and the point:

d=|Ax*+By*+C|/√A²+B²

The line of the path in this problem has:

Intercept of 0,

0.5 slope means that when x rises by 4, y rises by 2.

We get,

y = 0.5x.

-0.5x + y = 0

-x + 2y = 0.

The coefficients are:

A = -1, B = 2.

The giant pumpkin has coordinates given by:

(x*, y*) = (-4, -3).

Now, the distance in units is

d = |(-1)(-4) + 2(-3)|/√(-1)²+2²

d = |(-1)(-4) + 2(-3)|/√5

d = 2/√5

d = 0.89 units.

Since each unit is equal to 10 yards, the following is the shortest distance in yards:

10.x.0.89 = 8.9 yards

Therefore, 8.9 yards far you should be from the enormous pumpkin.

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Answer:

The minimum number of different rooms for accommodating 390 classes if there are 10 different time periods is 39

Step-by-step explanation:

Number of time periods = 10

Number of Classes = 390

Now, if we have a single room, then we can accommodate 10 classes

if we have 2 rooms, we can accommodate (10)(2) = 20 classes

and so on

so we have the relation,

(number of rooms)(number of time periods) = (number of classes that can be accommodated)

We need to find the number of rooms for 390 classes, given that number of time periods is 10, so we get,

(number of rooms)(10) = 390

number of rooms = 390/10

number of rooms =39

The area of the parallelogram with a base of 22 and one-half feet and a height of 19 and one-fourth feet is,

⇒ four hundred thirty-three and one-eighth ft²

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

A parallelogram with a base of 22 and one-half feet and a height of 19 and one-fourth feet.

Now, We know that;

Area of a parallelogram = Base × Height

Substitute the given values, we get;

⇒ Area of a parallelogram = Base × Height

⇒ Area of a parallelogram = 22 1/2 × 19 1/4

⇒ Area of a parallelogram = 45/2 × 77/4

⇒ Area of a parallelogram = 3465/8

⇒ Area of a parallelogram = 433 1/8 ft²

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Answer:

13.9

Step-by-step explanation:

13.85 feet far up the side of the house will the ladder reach now.

Given that, a 26 feet ladder is set against the side of a house so that it reaches up 24 feet.

In mathematics, you can calculate the height of an object using the distance and angles. Here distance is the horizontal distance between the object and the angle is the angle above the horizontal of the top of the object, which gives the height of the object.

Let the distance between base of house to foot of the ladder be x.

Using Pythagoras theorem 26²=24²+x²

⇒ 676 = 576 + x²

⇒ x² = 100

⇒ x =10 feet

Mila grabs the ladder at its base and pulls it 12 feet farther from the house.

Now, the distance between base of house to foot of the ladder = x+12

= 10+12 = 22 feet.

So, up the side of the house the ladder reach = 24-h

Then, 26² = (24-h)²+22²

⇒ 676 = (24-h)²+484

⇒ (24-h)² = 192

⇒ (24-h) = √192

⇒ (24-h) = 13.85

⇒ h = 24-13.85

⇒ h = 10.15 feet

Therefore, 13.85 feet far up the side of the house will the ladder reach now.

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