Type an expression using x and y as the variables.
∂z/∂x = ____
∂x/∂t = ____
∂z/∂y = ____
dy/dt = ____
dz/dt = ____
∂z/∂x = ____
dx/dt = ____
∂z/∂y = ____
dy/dt = ____
dz/dt = ____
Use the Chain Rule to find dw/dt where w = cos 12x sin 4y, x=t/4, and y=t^4.
∂w/∂x = ____
(Type an expression using x and y as the variables.)

The numerical values of the circumference and area are equal.

Answer:

To simplify it a

Step-by-step explanation:

Here is ur perfect answer

Answer:

x = 207

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

(\(\sqrt{x}\) )² + 7² = 16²

x + 49 = 256 ( subtract 49 from both sides )

x = 207

Answer: B

Step-by-step explanation:

The system stable with P(1)=1.7 and P(-1)=2.7. The correct answer is b.

To test the stability of a discrete control system with an open loop transfer function, we need to examine the roots of the characteristic equation, which is obtained by setting the denominator of the transfer function equal to zero.

The characteristic equation for the given transfer function G(z) is:

z^2 - 1.2z + 0.2 = 0

We can find the roots of this equation by factoring or using the quadratic formula. In this case, the roots are complex conjugates:

z = 0.6 + 0.4i

z = 0.6 - 0.4i

For a discrete control system, stability is determined by the location of the roots in the complex plane. If the magnitude of all the roots is less than 1, the system is stable. If any root has a magnitude greater than or equal to 1, the system is unstable.

In this case, the magnitude of the roots is less than 1, since:

|0.6 + 0.4i| = sqrt(0.6^2 + 0.4^2) ≈ 0.75

|0.6 - 0.4i| = sqrt(0.6^2 + 0.4^2) ≈ 0.75

Therefore, the system is stable.

The correct answer is:

b. Stable with P(1)=1.7 and P(-1)=2.7

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By 6.2 miles per hour, Sheri commutes more quickly.

We are given that,

John travels to work = 20km/hr

Sheri travels to work = 500m/min converting this into km/hr we get ,

1.61km/hr or 1 mile

John travels to work at the following rate:

\(\frac{20 km}{1 hr} * \frac{1 mile}{1.61km} = 12.42 miles/hr\)

Sheri travels work at the following rate:

\(\frac{500m}{1min} *\frac{1km}{1000 m}*\frac{1mile}{1.61km}*\frac{60min}{1hr}=18.63 miles/hr\)

Computing the difference between the two,

18.63 miles/hr - 12.42 miles/hr = 6.21 miles/ hr ≈ 6.2 miles/ hr

thus, by 6.2 miles per hour, Sheri commutes more quickly.

What are conversions in maths?

An amount that is multiplied or divided between one set of units and another is known as a conversion factor. In the event that a conversion is necessary, it must be carried out with the proper conversion factor to produce an equivalent value. For instance, when translating between inches and feet, 12 inches equals one foot.

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The given fractions have equal value, so Liam is correct.

Equivalent fractions are defined as fractions that have different numerators and denominators but the same value. For example, 2/4 and 3/6 are equivalent fractions because they are both equal to 1/2. A fraction is part of a whole. Equivalent fractions represent the same part of a whole.  

Liam is claiming that the fraction -(5/12) is equivalent to 5/-12.

Thus, we can say that:

The fraction  -(5/12) can be described as the opposite of a positive number divided by a positive number. A positive number divided by a positive number always results in a positive quotient and its' opposite is always negative.

The fraction 5/-12 can be described as a positive number divided by a negative number which always results in a negative quotient

The fractions have equal value, so Liam is correct

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Answer:

5.7 = \(\frac{57}{10}\) as an improper fraction

Step-by-step explanation:

When dividing a number by 10 the decimal moves one place to the left. When we take 57 and divide it by 10, we get 5.7

Answer:

6

Step-by-step explanation:

If you divide 78 by all of the numbers, only one, 6, is a whole number, making it the only factor. You can check this by multiplying 6 by 13, (you get 13 from the division) and you get 78.

I hope this helps!

Answer:

4x3=12

12x4=48

48/12=4

48/4=12

Step-by-step explanation:

The value of x is 24. The perimeter of his square is 96 inches.

To solve the equation 4(x2) = 96, we first need to isolate the variable x by dividing both sides of the equation by 4. This gives us x2 = 24. Taking the square root of both sides of the equation gives us x = ±√24. However, since x represents the length of a side of a square, it must be positive, so we take the positive square root of 24, which is approximately 4.899, but rounded off to the nearest whole number, x =  24.

Therefore, the value of x in this case would be 24 inches.

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The cost of constructing the box will be = $81.77

Since the question gives us information about the rectangle,

so the area of the rectangle is shown by,

Area = 2 x (length + width)

So we have the area as,

Area = 2(lh + wh) +lw

(since the area per square meter is also given so we added l x w)

Since the cost of the base is = $5 per square meter and the cost of the sides is = $3 per square meter, so area in terms of the cost function,

⇒ C = 3 x 2(lh + wh) + 5 x l x w

⇒ C = 6(lh + wh) +5lw ---------equation 1

According to the question, the length of the rectangular container is twice that of the width of the container,

⇒ l = 2w

Substituting the new value of l in equation 1,

⇒ C = 6(2wh + wh) + 10 \(w^{2}\)

⇒ C = 18wh + 10 \(w^{2}\) ---------- equation 2

To calculate the volume of the rectangle,

V = length x width x height ( lwh )

substituting v = 10 and 2w = l,

2\(w^{2}\)h = 10

h = \(\frac{5}{w^{2} }\)

Substitute the value of h in equation 2,

⇒ C = 18w x \(\frac{5}{w^{2} }\) + 10\(w^{2}\)

⇒ C = \(\frac{90}{w}\) + 10\(w^{2}\) --------- equation 3

Differentiating the above equation we get,

⇒ C* = - \(\frac{90}{w^{2} }\) + 20w

⇒ 20w = \(\frac{90}{w^{2} }\)

Multiply both sides by \(w^{3}\)

⇒ \(20w^{3}\) = 90

⇒ \(w^{3}\) = 4.5

w = 1.65

Put the value of w in equation 3,

⇒ C = \(\frac{90}{1.65}\) + 10 x \(1.65^{2}\)

⇒ C = 81.77

Therefore, The cost of constructing the box will be = $81.77

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The coordinates of point D in the rectangle are (-4, 0)

We can find the coordinate of point D by using the fact that opposite sides of a rectangle are parallel and have equal length. We can start by finding the length of AB and BC:

AB = √(0 - (-2))²+ (3 - 4)²)

= √4 + 1 = √5 units

BC = √(-2 - 0)² + (-1 - 3)² =√4 + 16) = √20=2√5 units

CD= √(-2 - x)² + (-1 -y)²

AB =CD

√5  = √(-2 - x)² + (-1 -y)²

√5  =√(-2 +4)² + (-1-0)²

√5  =√5 units

Hence, the coordinates of point D in the rectangle are (-4, 0)

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\( \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star\)

\(\textsf{ \underline{\underline{Steps to solve the problem} }:}\)

Both the figures are similar to each other, so ratio of their corresponding sides will be equal to one another.

\( \qquad❖ \: \sf \: \dfrac{2.6}{5.4} = \dfrac{x}{6.21} \)

( taking missing width be x )

\( \qquad❖ \: \sf \: x = \dfrac{1.3}{2.7} \sdot6.21\)

\( \qquad❖ \: \sf \: x = {(1.3)}{} \sdot(2.3)\)

\( \qquad❖ \: \sf \:x = 2.99 \: \: in\)

\( \qquad \large \sf {Conclusion} : \)

Missing side measures : 2.99 inches

You missed a small portion of the question in the end. If I am not mistaken, I am able to find the complete question which you should have added. Anyways, this would help you clear your concept as I would explain the context.

Here is the complete question:

Tanya is printing a report. There are 92 sheets of paper in the printer, and the number of sheets of paper p left after t minutes of printing is given by the function p(t) = -8t + 92.

How many minutes would it take the printer to use all 92 sheets of paper?

Answer:

It would take 11.5 minutes for the printer to use all 92 sheets of paper

Step-by-step explanation:

Given:

To determine:

How many minutes would it take the printer to use all 92 sheets of paper?

Given the function

\(p(t) = -8t + 92\)

We know that when all the 92 sheets of paper will be printed, there will be no more sheets left to be printed.

Therefore, we need to substitute p(t) = 0 in the given function to determine the value of time in minutes

\(0 = -8t + 92\)

\(8t = 92\)

Divide both sides by 8

\(\frac{8t}{8}=\frac{92}{8}\)

\(t=\frac{23}{2}\)

\(t = 11.5\) minutes

Answer:

Let's actually find the line of best fit...

m=(nΣyx-ΣyΣx)/(nΣx^2-ΣxΣx)

m=(11*836-130*55)/(11*385-3025)

m=2046/1210  

m=93/55

b=(Σy-93Σx/55)/n

b=(55Σy-93Σx)/(55n)

b=(7150-5115)/(55*11)

b=185/55, so the line of best fit is:

y=(93x+185)/55

A)  The approximate y-intercept (the value of y when x=0) is 185/55≈3.36.

Which means that those who do not practice at all will win about 3.36 times

B) y(13)=(93x+185)/55

y(13)≈25.34

So after 13 months of practice one would expect to win about 25.34 times.

Unit 2 Summary Notes: Statistics - One Variable Activity 4: Measures of Central Tendency.

In this activity, we learned about measures of central tendency in statistics. Measures of central tendency are statistical measures that provide information about the center or average of a dataset. The three main measures of central tendency are the mean, median, and mode.

The mean is the arithmetic average of a dataset and is calculated by summing all the values in the dataset and dividing by the number of values. It is often used when the data is approximately normally distributed.

The median is the middle value of a dataset when the values are arranged in ascending or descending order. If there is an even number of values, the median is calculated by taking the average of the two middle values. The median is useful when dealing with skewed distributions or datasets with outliers.

The mode is the value that appears most frequently in a dataset. It can be used for both numerical and categorical data.

These measures of central tendency provide different insights into the characteristics of a dataset. The choice of which measure to use depends on the nature of the data and the specific question or problem being addressed.

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Answer:1. Let  a = 1  and  b = 1 .

2. Now this means that  a = b .

3. If we multiply both sides by  a  we get  a^{2} = ab .

4. If we then subtract  b^{2}  from both sides we would have  a^{2} - b^{2} = ab - b^{2} .

5. We can then factorise both sides to get  (a + b)(a - b) = b(a - b) .

6. Dividing both sides by  (a - b)  would give us  a + b = b .

7. Substituting back the values of  a = 1  and  b = 1  would give us that  1 + 1 = 1 .

8. So this "proves" that  1 + 1 = 1  not  2 .

Except that in step 6, when we are dividing by  a - b , we are in fact dividing by zero. This is a violation of the rules of mathematics :/ soo... Um lol...

Step-by-step explanation: this is what happens when you dont do math correct

The average rate of change of the function f(x) = |x| + 2 over the interval

[-2, 0], and [0, 3] is constant with a value of -1 and hence a straight line

For the internal [-2, 3] the rate of change is 1/5. hence we can say the function consist of two straight lines like every absolute value functions

Average rate of change is solved by the ratio of output functions to the ratio of input functions.

f(x) = |x| + 2 for [-2, 0]

f(x) = |-2| + 2 = 4

f(x) = |0| + 2 = 2

average rate of change = (4 - 2) / (-2 - 0) = 2 / -2 = -1

f(x) = |x| + 2 for  [0, 3]

f(x) = |3| + 2 = 5

f(x) = |0| + 2 = 2

average rate of change = (5 - 2) / (0 - 3) = 3 / -3 = -1

f(x) = |x| + 2 for  [-2, 3]

f(x) = |3| + 2 = 5

f(x) = |-2| + 2 = 4

average rate of change = (4 - 5) / (-2 - 3) = -1 / -5 = 1/5

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If we live on the moon, a day on the Moon is about a lunar month long

The correct answer is an option (c)

We know that a day is the length of time between two noons or sunsets. A day is of 24 hours on Earth and 708.7 hours (which is 29.53 Earth days) on the moon.

We know that a lunar month is nothing but the time the Moon takes to go around the Earth.

A lunar month is of approximately 29.53 days.

This means, a day on the Moon is about a lunar month.

Therefore, a day on the Moon is of 708.7 hours i.e., about a lunar month.

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Answer:

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

Since absolute value is never negative, this inequality is correct for any value of m.

Correct answer choice is B.

Answer:

All real numbers.

Step-by-step explanation:

The bars either side of an expression or a value are the absolute value symbol. "Absolute value" means how far a value is from zero. Therefore, the absolute value of a number is its positive numerical value.

Given inequality:

\(|9m|+40 > 4\)

Subtract 40 from both sides to isolate the absolute value on one side of the equation:

\(\implies |9m|+40-40 > 4-40\)

\(\implies |9m| > -36\)

As the absolute value of a number or expression is its positive numerical value:

\(\implies |9m| \geq 0\)

Therefore, as 9m is always greater than or equal to zero, it will always be greater than -36, regardless of the value of m.

Therefore, the solution of the given inequality is all real numbers.

Answer:

Its A- 25 coin tosses

Step-by-step explanation:

I took the test

Answer:

x=8

Step-by-step explanation:

Visualize the points X Y and Z.  X and Z form a line, and Y is between them (on the same line).

Several distances are given, some as numbers, one as an expressions containing "x".

By the segment addition postulate, the two small line segments add up to the larger line segment:

\(\text{XY}+\text{YZ}=\text{XZ}\)

Substituting:

\((12)+(2x)=(28)\)

Then, use algebra to solve for x.  Note that "x" only appears once, so to solve for "x", we only need to isolate it (undo the things connected to it).

There are two things done to "x".  Multiplying by 2, and Adding 12.  Since multiplication normally happens before addition, to undo these things, we must undo the addition first, then undo the multiplication:

\((12+2x)-12=(28)-12\)

\(2x=16\)

\(\dfrac{2x}{2}=\dfrac{16}{2}\)

\(x=8\)

In the function P(x) = -x^2 + 40x - 376 that represents Ahmad's profit, the range of bays that Ahmad needs to build to make a profit is

To solve the problem, we have to be aware that the curve opens downwards. values at negative side of the y coordinates  will mean loss hence for profit we take values that will be at y = 0

The points at y = 0 is called the root and it is solved by solving the quadratic equation

P(x) = -x^2 + 40x - 376

applying {-b ± √(b² - 4ac)}/2a

{-40 ± √(40² - 4 * -1 * -376)}/2 * -1

{-40 ± √(1600 - 1504)}/-2

{-40 ± √(96)}/-2

= 24.9 OR 15.1

since the number of bays cannot be in decimal 15.1 to 24.9. Hence Ahmad should build 16 bays (the number of bay above 15.1) to 24 bays (the number of bays next to 24.9) to make profit

16 ≤ x ≤ 24

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The simplified form of the expression log(10⁸) - log(10⁴) ÷ log(10⁴) - log(10²) is 5.

Given the expression in the question;

log(10⁸) - log(10⁴) ÷ log(10⁴) - log(10²)

To simplify, first we find the common denominator.​

log(10⁸) - log(10⁴) ÷ log(10⁴) - log(10²)

(log(10⁸)log(10⁴))/log(10⁴) - log(10⁴) ÷ log(10⁴)  + ( - log(10²)log(10⁴))/log(10⁴)

Now, combine the numerators over the common denominator.

( (log(10⁸)log(10⁴) - log(10⁴) - log(10²)log(10⁴) ) / log(10⁴)

Simplify each terms

( 32 - 4 - 8 ) / log(10⁴)

( 20 ) / log(10⁴)

( 20 ) / 4log(10)

5 / log(10)

5/1

5

Therefore, 5 is the simplified form of the expression.

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The data plotted on the scatter plot reveals there is a positive linear association between the number of hours worked and tips earned. (Option C).

Recall:

The scatter plot given shows a trend line of the data. It also shows that as time worked increases, tips earned also increases. This shows a positive linear association between tips earned and time worked. (Option C).

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Answer:

2−12x+36

Step-by-step explanation:

Answer:

(x-6)² = (x-6)(x-6) = x² - 12x + 36

Step-by-step explanation:

Money market accounts allow for the creation of savings for current or upcoming requirements.

Savings for immediate or future needs can be made in money market accounts. To maintain your emergency savings in a convenient and secure location, for instance, you can think about opening a money market account. You desire to earn an APY similar to CDs without locking up your money for months.

You can get instant access to your money using money market accounts almost whenever you need it. A common feature of MMAs is the availability of check writing and debit card cash access. Also, be aware that you can often withdraw funds without being charged a fee, just like you could with a certificate of deposit (CD).

Therefore, the correct answer is option A. want to make numerous transactions and earn interest.

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Answer:

\(x=7\)

Step-by-step explanation:

First, add like terms. In this case, you would add \(8\) to both side to get rid of it from the left side, and with its like term, \(20\).

\(4x-8=20→4x=28\)

Then, divide both side by 4 to isolate \(x\).

\(4x=28→x=7\)

The answer is \(x=7\).

Horizontal translation: 2 units right.

Vertical translation: 5 units up

Stretch/compression: stretched by a factor of 3.

Reflection: not reflected.

Answer:

0.21 square meter

Step-by-step explanation:

Area of the section of wall = 1 square meter

Dimension of part of mural completed = \(\frac{1}{4}\) meter by \(\frac{5}{6}\) meter

Part of the mural completed = Area of the rectangular part of mural completed

But,

Area of a rectangle = length x width

So that,

Part of the mural completed = length x width

                                             = \(\frac{1}{4}\) x \(\frac{5}{6}\)

                                            = \(\frac{5}{24}\)

                                            = 0.2083

Part of the mural completed = 0.21 square meter

The part of the mural that has been completed by Beverly is 0.21 square meter.

Answer: 5/24

Explanation:

A=l*w

A=1/4*5/6

A=5/24.