Can someone help me please

Applying the Solution to a 3X3 System


At a family reunion, there only blood relatives, consisting of children, parents, and grandparents, in attendance. There were 400 people total. There were twice as many parents as grandparents, and 50 more children than parents. How many children, parents, and Grandparents were in attendance?

Show up all steps please

The given differential equation is not exact, if we convert it to an exact one, we get:

\(2ydx + 2*(x - sin(y)^{1/2})*dy = 0\)

A differential equation:

\(Ndx + Mdy = C\)

Is exact only if:

\(\frac{dM}{dy} = \frac{dN}{dx}\)

In this case, we have:

\(2ydx + (x - sin(y)^{1/2})*dy = 0\\\\then:\\\\N = 2y\\M = x - sin(y)^{1/2}\)

If we differentiate, we will get:

\(\frac{dN}{dy} = 2\\\\\frac{dM}{dx} = 1\)

So, to convert this to an exact differential equation, we need to add a factor 2 to N, this will give:

\(2ydx + 2*(x - sin(y)^{1/2})*dy = 0\)

This is, in fact, an exact differential equation.

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Answer:

what is your question

Step-by-step explanation: am not trying to steal ur points

a. The  slope of the curve at the point (4,16)   is approximately 1.165, and at the point (16,4)  is approximately -0.496.

b. The   curve has a horizontal tangent line at the points(0,0) and (3,27).

c. The   curve has a vertical tangent lineat the points (0,0) and (65/2, (65/2)³).

a. To find the   slope of the curve given by the equation x³ + y³ - 65xy = 0 at the points (4,16) and (16,4),we can differentiate the equation implicitly with respect to x and solve for dy/dx.

Differentiating the equation with respect to x, we have  -

3x² + 3y²(dy/dx) - 65y - 65x(dy/dx) = 0

To find the slope at a specific point, substitute the x and y coordinates into the equation and solve for dy/dx.

For the point (4,16)  -

3(4)² + 3(16)²(dy/dx) - 65(16) - 65(4)(dy/dx) = 0

48 + 768(dy/dx) - 1040 - 260(dy/dx) = 0

508(dy/dx) = 592

(dy/dx) = 592/508

(dy/dx) ≈ 1.165

For the point (16,4)  -

3(16)² + 3(4)²(dy/dx) - 65(4) - 65(16)(dy/dx) = 0

768 + 48(dy/dx) - 260 - 1040(dy/dx) = 0

(-992)(dy/dx) = 492

(dy/dx) = 492/(-992)

(dy/dx) ≈ -0.496

Thus, the slope of the   curve at the point (4,16) isapproximately 1.165, and at the point (16,4) is approximately -0.496.

b. To find the point where the curve has   a horizontal tangent line, we need to find the x-coordinate(s)where dy/dx equals zero.

This means   the slope is zero and the tangent line is horizontal.

From the derivative we obtained earlier  -

3x² + 3y²(dy/dx) - 65y - 65x(dy/dx) = 0

Setting dy/dx equal to zero  -

3x² - 65y = 0

Substituting y = x³/65 into the equation  -

3x² - 65(x³/65) = 0

3x² - x³ = 0

Factoring out an x²  -

x²(3 - x) = 0

This equation has two solutions  -  x = 0 and x = 3.

hence, the curve has a horizontal   tangent line at the points(0,0) and (3,27).

c. To find the point where the curve has a vertical tangent line, we need to find the x-coordinate(s)   where the derivative is undefinedor approaches infinity.

From the derivative  -

3x² + 3y²(dy/dx) - 65y - 65x(dy/dx) = 0

To find the vertical tangent line, dy/dx should be undefined or infinite. This occurs when the denominator of dy/dx is zero.

Setting the denominator equal to zero:  -

65x = 65y

x = y

Substituting this condition back into the original equation  -

x³ + x³ - 65x² = 0

2x³ - 65x² = 0

x²(2x - 65) = 0

This equation has two solutions  - x = 0 and x = 65/2.

Therefore, the curve has a vertical tangent line   at the points (0,0)

and(65/2, (65/2)³).

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Answer:

96.25%

Step-by-step explanation:

The empirical rule regarding mean and standard deviation is that

Therefore between mean and +2 standard deviation or between mean and -2 standard deviation you will find  approximately 95/2 = 47.5% of the values

Between mean and ± 3 standard deviations you will find approximately 97.5/2 = 48.75% of the values

Therefore between 2 standard deviations above and 3 standard deviations below you will find approximately 47.5 + 48.75 = 96.25% of values

1. Figure STUV is congruent to Figure KLMN because rigid motions can be used to map Figure STUV onto Figure KLMN.

2. Figure STUV is also similar to Figure KLMN because rigid motions and/or dilations can be used to map Figure STUV onto Figure KLMN. The scale factor is 2.

When it is said that two figures are congruent, like the ones shown on the graph, This means that they have the same shape and size.

Similar figures have the same shape, but they may have different sizes and be located in different positions.

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The amount of ingredients necessary to serve 5 people is 3.75 cups spaghetti sauce, 2.5 cups ricotta cheese, and 2.5 cups mozzarella cheese.

It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

We have:

A recipe for 8 servings lists: 6 cups spaghetti sauce 4 cups ricotta cheese and 4 cups mozzarella cheese.

First we take the ratio of ingredients for 8 servings:

spaghetti sauce : ricotta cheese : mozzarella cheese = 6:4:4

The ratio of ingredients for 1 servings:

spaghetti sauce : ricotta cheese : mozzarella cheese = 6/8 : 4/8 : 4/8

The ratio of ingredients for 5 servings:

spaghetti sauce : ricotta cheese : mozzarella cheese

= 5×0.75 : 5×0.5 : 5×0.5

= 3.75 : 2.5 : 2.5

The amount of ingredients necessary to serve 5 people:

Thus, the amount of ingredients necessary to serve 5 people is 3.75 cups spaghetti sauce, 2.5 cups ricotta cheese, and 2.5 cups mozzarella cheese.

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Answer:

No problem

Step-by-step explanation:

Answer:

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

We are given that:

Find the value of y by substituting the given values into formula:

Answer:

1unit scale on map is equal to 100.16 km in real life

Step-by-step explanation:

since in map 12.cm =1262km in real life

1cm=(1262/12.6) km

therefore it gives us 100.158km which is approximately 100.16 km .

Answer: 375

Step-by-step explanation:

Ruling out each number:

6: In the first two rows, the 6's placement did not change but the clue did, meaning that it is talking about a different number. Otherwise, it would say it's in the right place twice or in the wrong place twice.

3 & 5: Since we know 6 is already ruled out, both 5 & 3 would have to be correct.

2 & 4 & 8: Is proven wrong in the 4th clue.

7: 7 would have to be in the middle since the second clue says it's in the wrong place. If it was 1, it would say it's in the right space.

1: Is proven wrong after 7 is proven true.

Figuring out placement:

5: For the first clue, it says that it's in the correct place meaning that 5 is the last digit.

3: For both of the times 3 appears, it is in the wrong spot, revealing that it's the first digit.

7: In the second clue, it could either be 1 or 7. However, since 3 took the first spot and 5 took the last spot, 7 would have to be in the middle since the clue says it's in the wrong place. If it was 1, it would say it's in the right space.

Answer:

cross multiple

17×f=34×7

17f/17=578/17

f=34

Answer:

1 hour and 40 minutes

Step-by-step explanation:

→ Convert 3 hr and 25 minutes to minutes

( 3 × 60 ) + 25 = 205 minutes

→ Convert 1 hr and 45 minutes to minutes

( 1 × 60 ) + 45 = 105 minutes

→ Minus the answers from each other

205 - 105 = 100 minutes

→ Convert 100 minutes to hours and minutes

1 hour and 40 minutes

Answer:

choice 2) 21x^3 - 12x^2y^4

Step-by-step explanation:

3x^2(7x - 4y^4) = 21x^3 - 12x^2y^4

The actual length and actual width in meters of the community pool are respectively; 28 meters and 10.5 meters

In the scale drawing of Joe as attached, we see that the community pool has a length to width ratio of;

(length : width) = 8 : 3

Let the actual length of the pool be 8x meters and the actual width be 3x meters.

We are told that the actual pool has a perimeter of 77 meters.

Thus;

2(8x + 3x) = 77

22x = 77

x = 3.5

Therefore, the length of the pool is 8x = 8(3.5) = 28 meters.

The width of the pool is 3x = 3(3.5) = 10.5 meters

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Complete Question is;

Joe made a scale drawing of the community pool in his town. the pool has a perimeter of 77 meters, what is the length and width in meters?

Answer:

∠x and ∠y are congruent or equal

Step-by-step explanation:

∠x and ∠y are congruent or equal because their vertical angles are alternate interior angles.

OR vertical angle of ∠x is congruent with ∠y because they are both corresponding angles

OR vertical angle of ∠y is congruent with ∠x because they are both corresponding angles

The teacher's question, the student can provide a List of words including "sixty," "zesty," "skit," "site," "size," "exit," "yeti," "kits," "kite," and "ties."

Let unscramble the jumbled word "gzeysktqix" and find the possible words that can be formed.

Upon unscrambling, we can find several possible words:

1. Sixty

2. Zesty

3. Skit

4. Site

5. Size

6. Exit

7. Yeti

8. Kits

9. Kite

10. Ties

These are some of the words that can be formed from the jumbled letters "gzeysktqix." There may be additional words that can be created, depending on the specific rules or restrictions given by the teacher.

Unscrambling words can be a fun and challenging exercise that helps improve vocabulary, word recognition, and problem-solving skills. It allows students to enhance their language abilities and discover new words they might not have known before.

Remember, the key is to rearrange the given letters systematically and try different combinations until meaningful words are formed.

So, in response to the teacher's question, the student can provide a list of words including "sixty," "zesty," "skit," "site," "size," "exit," "yeti," "kits," "kite," and "ties."

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The next term in the sequence is 98. None of the given options (60, 81, 90, 101) match the expected next term. None of the option is correct.

To find the pattern in the sequence 1, 1, 3, 8, 19, 41, we can examine the differences between consecutive terms:

1 1 3 8 19 41

0 2 5 11 22

Looking at the differences, we can observe that each subsequent difference is obtained by adding consecutive odd numbers: 2, 3, 4, 5, etc. This suggests that the original sequence may be related to square numbers.

Let's check if the differences between consecutive terms are square numbers:

2 = 1²

5 = 2² + 1²

11 = 3² + 2²

22 = 4² + 3²

Based on this pattern, we can make a reasonable assumption that the next difference should be 5² + 4² = 41 + 16 = 57. Adding this difference to the last term of the sequence (41), we get the next term:

41 + 57 = 98

Therefore, the next term in the sequence is 98. None of the given options (60, 81, 90, 101) match the expected next term.

Hence, none of the given options accurately continue the pattern of the sequence. It's important to note that patterns in sequences can sometimes have multiple possible interpretations, and it's always essential to consider alternative patterns or extend the sequence further to confirm the pattern.

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Answer:  1) \(\pm \sqrt{x+4}\)

               2) see graph

               3) Choose one color from the graph

               4) D: x ≥ -4

                   R: y ≥ 0 for \(\sqrt{x+4}\)     or      y ≤ 0   for \(-\sqrt{x+4}\)

Step-by-step explanation:

1) To find the inverse, swap the x's and y's and solve for y:

Given: y = x² - 4

Swap: x = y² - 4

    x + 4 = y²

  \(\pm \sqrt{x+4}=y\)

2) see attachment. Red and Blue combined creates the graph of the inverse.

3) Choose either the positive (red graph) or the negative (blue graph).

red graph: \(y= \sqrt{x+4}\)

blue graph: \(y= -\sqrt{x+4}\)

4) Domain reflects the x-values of the function.  The x-values for the red graph is the same as the blue graph so the answer will be the same regardless of which equation you choose.

Domain: x ≥ 0

Range reflects the y-values of the function.  The y-values differ between the positive and negative inverse functions. Positive is above the x-axis. Negative is below the x-axis.

Range (red graph): y ≥ 0 for  \(y= \sqrt{x+4}\)

Range (blue graph):  y ≤ 0 for \(y= -\sqrt{x+4}\)

SOLUTION

The graph is shown below

Answer:

c Christopher

Step-by-step explanation:

hope this helps

Answer: 51/100

Step-by-step explanation:

I'm assuming that the numerator is supposed to be a whole number, because there is an infinite number of answers if it is not a whole number. 5/10 can be rewritten as 50/100 by multiplying the numerator and denominator by 10. The only fraction with a whole number numerator between 50/100 and 52/100 is 51/100.  Hope this helped!

Answer: The answer is 11x+4y+13

ANSWER: y = (1/2)x - 1.

To find the equation of the tangent line to the curve y = √(x - 3) at the point (4, 1), we need to determine the slope of the tangent line and its y-intercept.

First, let's find the derivative of the function y = √(x - 3) using the power rule:

dy/dx = 1/(2√(x - 3))

Now, we can substitute x = 4 into the derivative to find the slope of the tangent line at that point:

m = dy/dx = 1/(2√(4 - 3)) = 1/2

So, the slope of the tangent line is 1/2.

Next, we can use the point-slope form of a line to find the equation of the tangent line. Given the point (4, 1) and the slope m = 1/2, the equation becomes:

y - y1 = m(x - x1)

Substituting the values (x1, y1) = (4, 1):

y - 1 = (1/2)(x - 4)

Simplifying the equation:

y - 1 = (1/2)x - 2

y = (1/2)x - 1

Therefore, the equation of the tangent line to the curve y = √(x - 3) at the point (4, 1) is y = (1/2)x - 1.

Answer:

y = (1/2)x - 1/2

Step-by-step explanation:

Step 1: Find the derivative of the function

The derivative of a function gives the slope of the tangent line to the curve at any point. To find the derivative of the given function y = sqrt(x - 3), we can use the power rule of differentiation which states that:

d/dx (x^n) = nx^(n-1)

Applying this rule to our function, we get:

dy/dx = d/dx sqrt(x - 3)

To differentiate the square root function, we can use the chain rule of differentiation which states that:

d/dx f(g(x)) = f'(g(x)) * g'(x)

Applying this rule to our function, we have:

g(x) = x - 3

f(g) = sqrt(g)

So,

dy/dx = d/dx sqrt(x - 3) = f'(g(x)) * g'(x) = 1/(2*sqrt(g(x))) * 1

Substituting g(x) = x - 3, we get:

dy/dx = 1/(2*sqrt(x - 3))

So, the derivative of y with respect to x is 1/(2*sqrt(x - 3)).

Step 2: Evaluate the derivative at the given point

To find the slope of the tangent line at the point (4, 1), we need to substitute x = 4 into the derivative expression:

dy/dx = 1/(2*sqrt(4 - 3)) = 1/2

So, the slope of the tangent line at the point (4, 1) is 1/2.

Step 3: Use point-slope form to write the equation of the tangent line

Now that we know the slope of the tangent line at the point (4, 1), we can use point-slope form to write the equation of the tangent line. The point-slope form of a line is given by:

y - y1 = m(x - x1)

where (x1, y1) is the point on the line and m is the slope of the line.

Substituting the values x1 = 4, y1 = 1, and m = 1/2, we get:

y - 1 = (1/2)*(x - 4)

Simplifying this equation, we get:

y = (1/2)x - 1/2

So, the equation of the tangent line to the curve y = sqrt(x - 3) at the point (4, 1) is y = (1/2)x - 1/2.

Hope this helps!

Answer:

There is no solution

Step-by-step explanation:

Answer:

Yes your answer is rather false

Step-by-step explanation:

\( {2}^{x} \)

this is equivalent to 2^x

Now when x = -2 ,

2^-2 = (1/2)^2 = 1/4

And when x = 3,

2^3 = 2×2×2 = 8

Thus f(-2) = 1/4

and f(3) = 8

Answer:

\(\displaystyle y = -\frac{2}{3}\, x - 3\).

Step-by-step explanation:

Rewrite the equation \(3\, x - 2\, y + 6 = 0\) in the slope-intercept form \(y = m_{1} \, x + b\) to find the slope of this given line:

\(\displaystyle y = \frac{3}{2}\, x + 3\).

Thus, the slope of this given line is \(m_{1} = (3/2)\).

Let \(m_{1}\) and \(m_{2}\) denote the slope of the given line and the slope of line \(L\), respectively. Two lines in a plane are perpendicular to one another if and only if the product of their slopes is \((-1)\). Therefore, for these two lines to be perpendicular to one another, \(m_{1} \, m_{2} = (-1)\).

Since \(m_{1} = (3/2)\) according to the equation of the given line, the slope of line \(L\) would be:

\(\begin{aligned} m_{2} &= \frac{(-1)}{m_{1}} \\ &= \frac{(-1)}{(3/2)} \\ &= \frac{(-2)}{3}\end{aligned}\).

If a line in a plane has slope \(m\) and goes through the point \((x_{0},\, y_{0})\), the slope-point equation of that line would be \((y - y_{0}) = m\, (x - x_{0})\).

Since the line \(L\) goes through \((3,\, -5)\), the equation of this line in slope-point form would be:

\(\displaystyle y - (-5) = \frac{(-2)}{3}\, (x - 3)\).

Rearrange to find the equation of line \(L\) in slope-intercept form:

\(\displaystyle y = -\frac{2}{3}\, x - 3\).

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

\(3x-2y+6=0\implies 3x-2y=-6\implies -2y=-3x-6 \implies y=\cfrac{-3x-6}{-2} \\\\\\ y=\cfrac{-3x}{-2}-\cfrac{6}{-2}\implies y=\stackrel{\stackrel{\stackrel{m}{\downarrow }}{}}{\cfrac{3}{2}} x+3\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\)

therefore then

\(\stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{\cfrac{3}{2}} ~\hfill \stackrel{reciprocal}{\cfrac{2}{3}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{2}{3}}}\)

so we're really looking for the equation of a line whose slope is -2/3 and passes through (3 , -5)

\((\stackrel{x_1}{3}~,~\stackrel{y_1}{-5})\qquad \qquad \stackrel{slope}{m}\implies -\cfrac{2}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-5)}=\stackrel{m}{-\cfrac{2}{3}}(x-\stackrel{x_1}{3}) \\\\\\ y+5=-\cfrac{2}{3}x+2\implies y=-\cfrac{2}{3}x-3\)

dy/dt is \(-\frac{(21x^2+2y)\frac{dx}{dt}}{2x+9y^2}\)

What is differentiation?

Differentiation is a method of finding the derivative of a function. Differentiation is a process, in mathematics, where we find the instantaneous rate of change in function based on one of its variables. The most common example is the rate change of displacement with respect to time, called velocity.

We can find the dy/dx as shown below:

7x^3+2xy+3y^3=3

differentiating with respect to t.

\(7\frac{d(x^3)}{dt} +2\frac{d(xy)}{dt}+3\frac{y^3}{dt}=0\)

\(7\frac{3x^2dx}{dt}+2y\frac{dx}{dt}+2x\frac{dy}{dt}+3\frac{3y^2dy}{dt}=0\)

\(21\frac{x^2dx}{dt}+2y\frac{dx}{dt}+2x\frac{dy}{dt}+9\frac{y^2dy}{dt}=0\)

\((21x^2+2y)\frac{dx}{dt}+(2x+9y^2)\frac{dy}{dt}=0\)

\((21x^2+2y)\frac{dx}{dt}=-(2x+9y^2)\frac{dy}{dt}\)

\(-\frac{(21x^2+2y)\frac{dx}{dt}}{2x+9y^2}=\frac{dy}{dt}\)

\(\frac{dy}{dt}=-\frac{(21x^2+2y)\frac{dx}{dt}}{2x+9y^2}\)

Hence, dy/dt is \(-\frac{(21x^2+2y)\frac{dx}{dt}}{2x+9y^2}\)

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The answer is 1/5

= 1+1/10

= 2/10

= 2÷2/10÷2

= 1/5

Answer:

2/5

Step-by-step explanation: