(x² +x-y)dy+ x dy=0
Differential equations

Answer:

See Below.

Step-by-step explanation:

We want to show that the normal line to the parabola:

[tex]y^2=8x[/tex]

At the point (2, 4) meets the parabola again at (18, -12).

First, find the tangent line to the parabola at the point (2, 4). We can take the derivative of both sides with respect to x:

[tex]\displaystyle \frac{d}{dx}\left[ y^2\right]=\frac{d}{dx}\left[8x\right][/tex]

Implicit differentiation:

[tex]\displaystyle 2y\frac{dy}{dx}=8[/tex]

Therefore:

[tex]\displaystyle \frac{dy}{dx}=\frac{8}{2y}=\frac{4}{y}[/tex]

Then the slope of the tangent line to the point (2, 4) is:

[tex]\displaystyle \frac{dy}{dx}\Big|_{y=4}=\frac{4}{(4)}=1[/tex]

Thus, the slope of the normal line is -1.

And since it passes through the point (2, 4), by the point-slope form:

[tex]y-(4)=-1(x-2)[/tex]

Simplify:

[tex]y=-(x-2)+4[/tex]

By letting x = 18:

[tex]y=-(18-2)+4=-16+4=-12[/tex]

So, the normal line indeed passes through (18, -12).

Answer:

answer is in the picture.

9514 1404 393

Answer:

  15

Step-by-step explanation:

(2 loaves)(5/2 cups/loaf)/(1/3 cup/scoop) = (2)(5/2)(3/1) scoops = 15 scoops

The baker will need 15 scoops of flour.

Answer:

72

72

96

120

Step-by-step explanation:

The arcs are in the ratio:

3 : 3 : 4 : 5

Add all numbers in the ratio:

3 + 3 + 4 + 5 = 15

In the ratio, the sum of all numbers is 15.

In the real circle, the sum of the measures of all the arcs is 360.

360/15 = 24

Multiply all numbers in the ratio by 24.

72 : 72 : 96 : 120

Answer:

72

72

96

120

Answer:

Step-by-step explanation:

Answer:

spongebob at the bottom of the sea

Step-by-step explanation:

In a plain, robust, conversational style, the author known as “Elena Ferrante” has captivated readers worldwide with her chronicle of a complicated friendship between two women.

The step would be, "Suppose not. That is, suppose there exist irrational numbers a and b such that b ≠ 0, r is a rational number, and a + br is rational." Option A is correct.

Given that,
a and b are rational numbers, b ≠ 0, and r is an irrational number, then a + br is irrational. the first step of the proof with contradiction is to be determined.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
For the statement,

a and b are rational numbers, b ≠ 0, and r is an irrational number, then a + br is irrational.

Contradiction will be "suppose there exist irrational numbers a and b such that b ≠ 0, r is a rational number, and a + br is rational."

Thus, the step would suppose not. That is, suppose there exist irrational numbers a and b such that b ≠ 0, r is a rational number, and a + br is rational.

Learn more about simplification here:

https://brainly.com/question/12501526

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Answer:

The equation of the new function is [tex]g(x) = \frac{x}{3}[/tex]

Step-by-step explanation:

Horizontally stretching a function:

Horizontally stretching a function f(x), by a factor of a, means that:

[tex]g(x) = f(\frac{x}{a})[/tex]

In this question:

[tex]f(x) = x[/tex], horizontally stretched by a factor of 3, so [tex]a = 3[/tex], and:

[tex]g(x) = f(\frac{x}{3}) = \frac{x}{3}[/tex]

The equation of the new function is [tex]g(x) = \frac{x}{3}[/tex]

Part 1: Do not reject H0. There has not been a significant change in the viewing audience proportions.(The above conclusion holds as the p-value is greater than the significance level of 0.05)

Part 2:

H0:  

Ha:  

Part 3: The test statistic is given as 3.0081.

Part 4: The p-value is given as  0.39037

Step-by-step explanation:

As per the data

Part 2

H0:  

Ha:  

Part 3

As per the sample is of 300 homes, the expected values are given as

ABC=p(ABC)*300=0.30*300=90

CBS=p(CBS)*300=0.27*300=81

NBC=p(NBC)*300=0.26*300=78

IND=p(IND)*300=0.17*300=51

Now the values actually are given as

ABC=94

CBS=71

NBC=88

IND=47

So the test static is given as

So the test statistic is given as 3.0081.

Part 4

Now the degree of freedoms are given as 4-1=3

and chi square  is given as 3.0081 so for α = 0.05 , the p-value is given as  0.39037

Part 1.

As the value of p in part 4 is greater than the value of α = 0.05, thus Do not reject H0. There has not been a significant change in the viewing audience proportions.(The above conclusion holds as the p-value is greater than the significance level of 0.05)

Answer:

x=109/56

dn did djs. hd hd hd hd hd hd

1:6

Hope this helps! :)

______________

Answer:

n value is 6

2:12=1:6

n is 6

Answer:

10

Step-by-step explanation:

Sum of 8 and 7 = 8 + 7 = 15

5 subtracted from sum of  8 and 7 = 15 - 5 = 10

The answer to this question = 10

The sum is the result of the addition of two or more numbers.

The difference between the two numbers is called subtraction.

First, we find the sum of 8 and 7

8 + 7 = 15

Now, we subtract 5 from 15

15 - 5 = 10

∴ The result to the given question = 10

Learn more about the Addition/Subtraction at

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Answer:

it could only accomplish it's goal on Friday

Step-by-step explanation:

all you had to do was multiply 8 with the number of people and 2 with the number of tickets on each day and add them together to see if it was more than 1650. it was only more on Friday

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

Explanation:

Let's say that point A is at (0,0) and B is somewhere else on the parabola.

I'll make point B go to the right of point A.

For now, let's say B is at (4,16).

If we compute the slope of line AB, then we find the average rate of change (AROC). The AROC in this case is (y2-y1)/(x2-x1) = (16-0)/(4-0) = 16/4 = 4. Because point A is at (0,0), we're really just computing y/x where the x,y values come directly from point B.

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

Now let's move B to (3,9). If we used the slope formula again, we would get the slope of 3. Note how y/x = 9/3 = 3.

Then let's move B to (2,4). The AROC is now y/x = 4/2 = 2

As B gets closer to A, the AROC is decreasing. The AROC is slowly approaching the IROC (instantaneous rate of change).

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

Point B is generally located at (x,x^2) for any real number x. Keeping A always fixed at the origin, the slope of line AB is y/x = (x^2)/x = x.

What does this all mean? It means that if x = 0, then the IROC is 0. You might be quick to notice that we cannot divide by zero. So instead of letting x be zero itself, we'll just get closer and closer to it. This is where the concept of limits come into use. This is what calculus is based on (both integral and differential calculus).

Anyway, when calculating the IROC, we're really calculating the slope of the tangent line to the f(x) curve. Refer to the diagram below.

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

In short, the slope of the tangent line at x = 0 is m = 0. We have a flat horizontal line that touches the parabola at (0,0).

Answer:

3 units

Step-by-step explanation:

Answer:

H0 : p = 0.5

H1 : p ≠ 0.5

Two tailed test

Step-by-step explanation:

The test if the true proportion of heads is different from 50%; this means the initial truth, that is the true proportion is 50% ; which is the null ;

H0 : p = 0.5

The researcher intends to test if the true proportion is not 50% ; that is the researcher is n spwcudfic about if the proportion is lower or higher, he just wants to test that the proportion is different, hence the test could go either way ;

Alternative hypothesis ;

H1 : p ≠ 0.5

Since the sign in the alternative hypothesis could be in either direction, then we have a two tailed test

Answer:

1+1=11 2+2=22 ok na yan kuya or ate

Answer:

Step-by-step explanation:

y=3√x

domain : all real values≥0

Answer:

75

Step-by-step explanation:

∠K and ∠ R are congruent (equal)

Triangle Sum Theory - angles of all triangles add to 180

180 - 79 - 26 = 75

Answer:

A and E

Step-by-step explanation:

x²+3x-28=0

x²+7x-4x-28=0

x(x+7)-4(x+7)=0

(x-4)(x+7)=0

x=4, x= -7

Please give brainliest if it helps

Answer:

[tex]\huge\boxed{\boxed{\underline{\textsf{\textbf{Answer}}}}}[/tex]

[tex] \frac{x}{7} - 4 = 6 \\ \frac{x}{7} = 6 + 4 \\ \frac{x}{7} = 10 \\ x = 10 \times 7 \\ x = 70[/tex]

____________________

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

➳ RainbowSalt2²2² ❦

Step-by-step explanation:

V≈3323.42cm³

r Radius

11.2

cm

h Height

25.3

cm

Solution

V=πr2h

3=π·11.22·25.3

3≈3323.41966cm³

hope it is helpful

Answer: Choice B

Game A is not fair, and game B is fair.

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

We'll start with game A.

The sides of the dice are {1,2,3,4,5,6}

There are 6*6 = 36 ways to roll two dice.

If we roll two odd numbers, say 3 and 5, the product is odd because 3*5 = 15.

If any of the numbers are even, then the product is even. Eg: 4*5 = 20 or 2*6 = 12.

To be an even number, 2 must be a factor.

So you can probably see that it's more likely to get an even number product considering that in order to get an odd product, both values must be odd (which narrows the selection pool). We can say that game A is not fair. It favors player 1 more. If you're sure about this, then I recommend looking at a multiplication table but only focus on the first 6 rows and 6 columns. Ignore the row and column that has 0s in it.

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

Now onto game B

The rules are nearly the same, except now instead of multiplying the dice values, we add them up.

We still have 6*6 = 36 outcomes.

Here are some handy rules we'll take into account

If the first dice rolls to '1', then there are 3 ways to get an even number (rolling either 1,3,or 5 on the second dice) and there are 3 ways to get an odd number (rolling either 2,4,or 6 on the second dice). We can see that there are the same number of ways to get an even sum or an odd sum. Apply this in general to any result that the first dice shows, and this basically leads to the conclusion that half of the 36 sums are even, and the other half are odd. We have a fair game now. Refer to a sum of dice chart if you need more convincing.

Answer:

Game A is not fair, and game B is fair.

Step-by-step explanation:

test on iready

Step-by-step explanation:

base = 11

height = 8

so are is 11 x 8 /2

= 44

Answer:

The Area of the Enclosed Region Is 64/3.

Step-by-step explanation:

As Given in Question

We have, Curve 4x+[tex]Y^{2}[/tex]=12

& X=Y

Solution.

4Y+[tex]Y^{2}[/tex]=12   (X=Y)

[tex]Y^{2}[/tex]+4Y-12=0

[tex]Y^{2}[/tex]+6Y-2Y-12=0

Y(Y+6)-2(Y+6)=0

(Y-2)*(Y+6)=0

Y=2 & -6  (X=Y)

Now at (2,2) & (-6,-6) both curves intersect each other.

The Area Of Enclosed Region is    [tex]\int\limits^2_{-6} [(3-Y^{2}/4 )-Y] \, dy[/tex]

by Solving This Equation we get Area of Region = 64/3 .    

this equation Solution & Curve Diagram please see In Attachment .  

Answer:

One leg: 3

So, the hypo: 2*3 = 6

And the third is according to the formula for right angle triangles: a^2 + b^ = c^2

So: √9+36= c

6.7 to get an exact number round it: 7

Answer:

sides are √3 ft,2√3 ft,3 ft

Step-by-step explanation:

let one leg=x

length of hypotenuse=2x

third side=3 ft

(2x)²=x²+3²

4x²-x²=9

3x²=9

x²=9/3=3

x=√3 ft

hypotenuse=2√3 ft

Answer:

67 mph

Step-by-step explanation:

201/3 = 67

Answer:

8.5 miles an hour.

Step-by-step explanation:

There are many ways to do this, but I am going to do it the way I think is the most simple.

First, divide 748 yards by 3 minutes to get the amount of yards per minute. 748 / 3 = 249.33333

Second, divide the previously gotten number (249.33333, [3's go on forever]) by the amount of yards in a mile (which is 1760 yards per mile). This turns into 249.33333 / 1760 = 0.1416666 (6's go on forever). This is miles per minute so you must make it per hour.

You then multiply that infinite number by the amount of minutes in an hour (60 minutes per hour). 0.14166666 * 60 = 8.5 miles per hour.

Answer:

f(x) - g(x) = x^3 - 3x^2 - 4x - 4

Step-by-step explanation:

f(x) - g(x)

x^3 - 2x^2 - 3x - 5 - ( x^2 + x - 1 )

x^3 - 2x^2 - 3x - 5 - x^2 - x + 1

x^3 - 3x^2 - 4x - 4