What is the slope of the line tangent to the curve 3y^2-2x^2=6-2xy at the point (3 2)?

At 9:00 p.m, the temperature would be equal to -0.4°C

We have got an equation that can relate these three units of measurement of temperature, as given below:

[tex]\dfrac{C}{5} = \dfrac{F - 32}{9} = \dfrac{K - 273}{5}[/tex]

where C represents the measurement of a fixed temperature in celsius, F represents the measurement of that same intensity temperature in fahrenheit, and K represents the measurement of equally intense temperature in kelvin.

We are given that

On a winter day in Alaska, the temperature at noon = -0.6°C.

Then From noon to 3:00, the temperature increased by 1.2°C. From 3:00 to 6:00, it dropped 0.4°C, and from 6:00 to 9:00, it decreased by 0.6°C.

-0.4

Therefore, the expression could be;

-0.6+1.2-0.4-0.6

=-0.4

The expression that shows the temperature in °C at 9:00 p.m is -0.6+1.2-0.4-0.6

Learn more about temperature scale here:

https://brainly.com/question/2919967

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To find the median, sort the numbers in ascending order and average the two middle values. The median of the given numbers is 29.5.

To find the median of the numbers 26, 30, 24, 32, 32, 31, 27, and 29, follow these steps:

Thus, the median of the given set of numbers is 29.5.

To convert gallons to cups, multiple conversion factors can be used. Assuming a typo in '4 4/1 gallons' and correcting it to '4 gallons,' the conversion shows that there are 16 cups in a gallon. Thus, 4 gallons of water is equivalent to 64 cups.

To convert gallons to cups, you can use conversion factors that relate these two units of volume. First, we need to correct the expression given for the volume of water in the pail. It seems there is a typo because '4 4/1 gallons' isn't a proper number. Assuming it's intended to be '4 gallons,' we can proceed with the conversion.

Since 1 gallon is equivalent to 4 quarts and 1 quart is equivalent to 2 pints, and 1 pint is equivalent to 2 cups, we can create a chain of multiplications to convert from gallons to cups.

Multiplying these together gives us:

1 gallon = 4 x 2 x 2 = 16 cups

Therefore, to find out how many cups are in 4 gallons:

4 gal x 16 cups/gal = 64 cups

So, 4 gallons of water is equivalent to 64 cups.

Final answer:

To convert 4 gallons to cups using the provided conversion factors, multiply the gallons by 4 to get quarts, then multiply by 2 to get pints, and again multiply by 2 to get cups, resulting in a total of 64 cups.

Explanation:

The student's question involves converting a quantity of gallons into cups, which is a Mathematics problem specifically dealing with units of volume conversion. The amount given, 4 4/1 gallons, seems to be a typo, but assuming the intention was to convert 4 gallons into cups, we can use the given conversion factors:

To find out how many cups are in 4 gallons, we follow these steps:

Therefore, 4 gallons is equivalent to 64 cups.

The answer is 16 mins

Answer:

7%(plzzzz brainlist thiss!!!)

Step-by-step explanation:

Answer:

7.6 inches

Step-by-step explanation:

The ratio of the height to the width of a packaging label is 5 to 19, that is,

h/w = 5/19 [1]

If the height of the label is 2 inches, and its width is unknown (x), that is,

h/w = 2 in/x [2]

We can set up a proportion with [1] and [2],

5/19 = 2 in/x

We use the cross product property of proportions.

5 × x = 19 × 2 in

x = 19 × 2 in/ 5 = 7.6 in

The width is 7.6 inches.

The 95% confidence interval for the mean number of hours Americans spend relaxing or engaging in enjoyable activities post-work is between 1.38 and 1.92 hours per day, which signifies the statistical range where the true mean likely falls. This statistic is crucial for understanding leisure's role in health and well-being.

The 95% confidence interval given in the General Social Survey of (1.38, 1.92) hours for the mean number of hours spent relaxing or pursuing activities after an average workday suggests that we can be 95% confident that the actual mean number of hours all Americans have for such activities falls within this range. This is an important statistic considering that leisure and recovery are essential for well-being, mental health, and stress prevention, as pointed out by researchers like Sonnentag & Zijlstra and Juliet Schor. Juliet Schor also highlighted that Americans have significantly declined in leisure time. The comparison of leisure time across different countries, such as Americans working more hours compared to Europeans, adds context to the importance of this interval in reflecting Americans' potential lack of leisure that could impact health.

Answer: 3*2^-3a^2b^3c^5x^-4y^-3z^-1 (graded correct)

Step-by-step explanation:

meaganblatcher (original poster)

you take away 8 and multiply  and get 3a^2b^3c^5 * x^4y^3z or something

This becomes 3a^2b^3c^5x^-4y^-3z^1/8

Then you move the 8 up using multiplication and get -24a^2b^3c^5x^4y^3z^1

This can be simplifed as 3*2^-3a^2b^3c^5x^-4y^-3z^-1

regardless that's the real answer.

The solution of given system of equations is [tex]\boxed{(10,-1)}[/tex].

Further explanation

The system of equations is given  as follows:

[tex]\begin{aligned}x+3y&=7\\2x-4y&=24\end{aligned}[/tex]

The equations are the form of linear equation in two variables.

The general form of linear equation in two variables is [tex]ax+by+c=0[/tex] where [tex]a,b,c[/tex]are real numbers.

Here, the system of equations is as follows:

[tex]x+3y=7[/tex]      .....(1)

[tex]2x-4y=24[/tex]  ......(2)

Now, we can rewrite the equation (1) as follows:

[tex]x=7-3y[/tex]  

Substitute the value of [tex]x=7-3y[/tex] in equation (2) as follows:

[tex]2(7-3y)-4y=24[/tex]  

Solve the above expression to find the value of [tex]y[/tex].

[tex]\begin{aligned}14-6y-4y&=24\\14-10y&=24\\-10y&=24-14\\-10y&=10\\y&=-1\end{aligned}[/tex]  

Therefore, the value of [tex]y[/tex] is [tex]-1[/tex].

Now, Substitute the value of [tex]y=-1[/tex] in equation (1) to get the value of [tex]x[/tex].

[tex]\begin{aligned}x+(3\times(-1))&=7\\x-3&=7\\x&=7+3\\x&=10\end{aligned}[/tex]  

Therefore, the value of [tex]x[/tex] is [tex]10[/tex].

The solution of given system of equations is [tex](10,-1)[/tex].

Option (a)

In option (a) it is given that the solution is [tex](2,-6)[/tex].

But as per the calculation solution of the given system of equations is [tex](10,-1)[/tex].

Therefore, option (a) is incorrect.

Option (b)

In option (b) it is given that the solution is [tex](10,-1)[/tex].

As per the calculation solution of the given system of equations is [tex](10,-1)[/tex].

Therefore, option (b) is correct.

Option (c)

In option (c) it is given that the solution is [tex](-2,8)[/tex].

But as per the calculation solution of the given system of equations is [tex](10,-1)[/tex].

Therefore, option (c) is incorrect.

Option (d)

In option (d) it is given that there are infinte solution.

But as per the calculation solution of the given system of equations is [tex](10,-1)[/tex] which is a unique solution.

Therefore, option (d) is incorrect.

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Answer details:

Grade: Middle school

Subject: Mathematics

Chapter: Linear equations in two variables

Keywords: Linear equations in one variable, linear equations in two variables, function, sets, real numbers, ordinates, abscissa, interval, open interval, closed intervals, semi-closed intervals, semi-open interval.

Answer:

TRUE.

Step-by-step explanation:

It's in an assignment I'm doing.

Also, THERE ARE WAYS TO FIND THE AREA UNDER A NORMAL CURVE is also TRUE

the answer is log3x=2!

hope this helps :D. just took a test online and this was one of the questions. got it right btw.

Answer:

Kramer is wrong trust me

The answers are:

1. A

2. B

3. B

4. C

100% just took it :)

Lesson 6 - Compound inequalities

Step-by-step explanation:

Final answer:

Dots sold 192 T-shirts and 64 shorts in April. We found this by setting up a system of equations with the given information and solving for the number of T-shirts (T) and shorts (S) sold.

Explanation:

To solve the problem of how many T-shirts and shorts Dots sold, we use a system of equations. Let's denote the number of T-shirts as T and the number of shorts as S. Given that T-shirts cost $2 each and shorts cost $3 each, and the total sales were $576, we can write our equations as follows:

2T + 3S = $576

We are also told that the store sold 3 times as many T-shirts as shorts, which gives us the second equation:

T = 3S

Substituting the second equation into the first, we get:

2(3S) + 3S = $576

6S + 3S = $576

9S = $576

Now, dividing both sides by 9 to isolate S, we get:

S = $576 / 9

S = 64

Since T is three times S:

T = 3 × 64

T = 192

Therefore, Dots sold 192 T-shirts and 64 shorts in April.

The ratio of the linear acceleration of a point on the rim of disk A to the linear acceleration of a point on the rim of disk B is [tex]\( \frac{r_A}{r_B} \), where \( r_A \) and \( r_B \)[/tex] are the radii of disks A and B, respectively.

Linear acceleration ( a ) of a point on the rim of a rotating disk is given by [tex]\( a = r \alpha \)[/tex], where ( r ) is the radius of the disk and [tex]\( \alpha \)[/tex] is the angular acceleration.

Since both disks are rotating with constant angular acceleration, the linear acceleration of a point on the rim of each disk is directly proportional to the radius of the disk.

Therefore, to find the ratio of the linear accelerations, we only need to compare the radii of the two disks.

Let [tex]\( r_A \) and \( r_B \)[/tex] be the radii of disks A and B, respectively.

The ratio of linear accelerations is given by [tex]\( \frac{a_A}{a_B} = \frac{r_A \alpha}{r_B \alpha} \)[/tex].

Notice that the angular accelerations cancel out since both disks have the same angular acceleration.

Thus, the ratio simplifies to [tex]\( \frac{r_A}{r_B} \)[/tex].

This ratio represents how many times larger the radius of disk A is compared to the radius of disk B.

For example, if [tex]\( r_A = 2r_B \)[/tex], then the linear acceleration of a point on the rim of disk A is twice that of disk B.

Therefore, the ratio of the linear acceleration of a point on the rim of disk A to the linear acceleration of a point on the rim of disk B is [tex]\( \frac{r_A}{r_B} \)[/tex].

Complete Question:

For the two disks in problem 3, what is the ratio of the linear acceleration of a point on the rim of disk A to the linear acceleration of a point on the rim of disk B? Please show detailed calculation.

Final answer:

To find the height of the Statue of Liberty, we set up an equation considering the total height of the pedestal and the height difference between the statue and the pedestal. Solving the system of linear equations, we determine that the height of the Statue of Liberty itself is 46.05 meters.

Explanation:

To find how tall the Statue of Liberty is, excluding its pedestal, we can set up an equation based on the information given. Let's denote the height of the Statue of Liberty as S, and the height of the pedestal as P.

We know that the total height of the Statue of Liberty and its pedestal is 92.99 meters, and we can express that as:

S + P = 92.99

Additionally, it is given that the pedestal is 0.89 meters taller than the Statue of Liberty, so we have:

P = S + 0.89

Using substitution, we can replace P in the first equation with S + 0.89:

S + (S + 0.89) = 92.99

This simplifies to:

2S + 0.89 = 92.99

To find the height of the Statue of Liberty (S), we subtract 0.89 from both sides of the equation:

2S = 92.99 - 0.89

2S = 92.10

And then we divide both sides by 2 to solve for S:

S = ​92.10 / 2

S = 46.05

So, the height of the Statue of Liberty itself is 46.05 meters.

The derivative of y = (x³ + 2)²(x⁴ + 4)⁴ using logarithmic differentiation is;

y' =  {[6x²In(x³ + 2)]/(x³ + 2)} + {[16x³In(x⁴ + 4)⁴]/(x⁴ + 4)} × [(x³ + 2)²(x⁴ + 4)⁴]

We are given the function;

y = (x³ + 2)²(x⁴ + 4)⁴

We want to find the derivative using logarithmic differentiation;

Step 1; Take the natural log of both sides;

In y = In[(x³ + 2)²(x⁴ + 4)⁴]

Step 2;

Using log of a product property on this, we have;

In y = In(x³ + 2)² + In(x⁴ + 4)⁴

Step 3; We will now differentiate both sides with chain rule to get;.

y'/y = [6x²In(x³ + 2)]/(x³ + 2) + [16x³In(x⁴ + 4)⁴]/(x⁴ + 4)

Step 4; Using multiplication property of equality, multiply both sides by y to get;

y' =  {[6x²In(x³ + 2)]/(x³ + 2) + [16x³In(x⁴ + 4)⁴]/(x⁴ + 4)} × y

Step 5; Plug in the value of y = (x³ + 2)²(x⁴ + 4)⁴ to get;

y' =  {[6x²In(x³ + 2)]/(x³ + 2)} + {[16x³In(x⁴ + 4)⁴]/(x⁴ + 4)} × [(x³ + 2)²(x⁴ + 4)⁴]

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Answer:

The answer is [tex]4x^3-29x^2+10x-21[/tex]

Step-by-step explanation:

In order to determine the answer, we have to know what it means (t*s)(x).

When we need to multiply two functions, where y(x) and z(x) are the functions, we can describe the process with the notation (y*z) (x). This notation means that the function y(x) is being multiplying by the function z(x).

So, in this case, we have two functions:

[tex]s(x)=x-7\\t(x)=4x^2-x+3[/tex]

Multiplying both functions (t*s) (x):

[tex](t*s)(x)=t(x)*s(x)\\(4x^2-x+3)(x-7)\\4x^3-28x^2-x^2+7x+3x-21\\4x^3-29x^2+10x-21[/tex]

Finally, the expression is:

[tex]4x^3-29x^2+10x-21[/tex]