MATHEMATICS MIDDLE SCHOOL

Determine the slope of the graph of x^4=ln(xy) at the point (1,e)

Answers

Answer 1

Answer:

Answer:

Answer is 3e.

Step-by-step explanation:

The slope is given by the derivative at the given point.

Differentiating:-

4x^3 = 1/xy *(x * dy/dx + y)

4x^3 = 1/y * dy/dx + 1/x

dy/dx = (4x^3 - 1/x) * y

At the point (1, e) x = 1 and y = e so substituting

slope at (1,e) = dy/dx = (4(1)^3 - 1/1) * e

= 3e (answer)

Answer 2

Answer: It is 3e. Differentiating x^4=ln(xy), we have to implicitly differentiate this.

$4x^(3)= (1)/(xy) \cdot (d)/(dx)(xy)$

The derivative of xy you have to use the chain rule.

$(d)/(dx)(xy)=x \cdot (dy)/(dx)+y$

So now it's

$4x^(3)=(y+(dy)/(dx) \cdot x)/(xy)$

Now we want the slope when x=1 and y=e

$4(1)^(3)=(e+(dy)/(dx))/(e)$

$4=(e+(dy)/(dx))/(e)$

$4=1+(dy)/(dx) \cdot (1)/(e)$

$(dy)/(dx)=3e$

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What is the image of (-5,5) after a dilation by a scale factor of 4 centered at the
origin?

Answers

The image of (-5,5) is (-20, 20).

What is image point?

Its image refers to the new position of a point, line, line segment, or figure following a transformation.

for instance, the image of the triangle A'B'C following translation is the triangle A'B'C. The images of points A, B, and C are represented by the letters A, B, and C. The images of the original line segments AB, BC, and AC are represented by the line segments A'B', B'C', and A'C', respectively.

Given coordinates (-5,5) dilation by a scale factor of 4 centered at the

origin, If a point's preimage is P(x, y), then its image after a dilation with a scale factor of k and centered at the origin (0, 0) is P′(kx, ky).

Using this rule we can find the image of (-5 , 5)

Here P(x , y) = (-5 , 5) and k = 4

So P'(x , y) = 4(-5 , 5) = (-20, 20)

Hence the new coordinates are (-20, 20).

Learn more about image point;

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Answer:

x=-5 and y=5

It's too short. Write at least 20 characters to explain it well.

Use cramers rule to solve each system of equations : 6x = 2 - y
3x + 1 = 2y , please explain thank you :)

Answers

Answer:

just follow the rules

Step-by-step explanation:

Cramer's rule applies to the case where the coefficient determinant is nonzero. ... A simple example where all determinants vanish (equal zero) but the system is still incompatible is the 3×3 system x+y+z=1, x+y+z=2, x+y+z=3.

Write the system as a matrix equation. ...

Create the inverse of the coefficient matrix out of the matrix equation. ...

Multiply the inverse of the coefficient matrix in the front on both sides of the equation. ...

Cancel the matrix on the left and multiply the matrices on the right.

Of the 50 U.S. states, 4 have names that start with the letter W.What percentage of U.S. states start with the letter W?

Answers

4/50
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8/100
Then your percentage would be 8%

There are 50 states and 4 have names starting with W. (Washington, West Virginia, Wisconson, and Wyoming)
You need to find 4 is what % of 50.
It will be 8%

A high-speed computer printer prints a page in 1/6 second. Using this printer, how long would it take to print 30 pages?

Answers

$30*(1)/(6)=(30)/(6)=5$

5 minutes. Because 30/6=5

PLEASE ANSWER ALL ASAP PLZ1) Aaron rides his bike at a constant rate of 10 miles per hour. Which table represents y, the number of miles Aaron rides his bike in x hours?

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A) x = y + 2.99

B) y = 2.99 + x

C) y = 2.99x

D) x = 2.99y

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A) 1 1/3 cups

B) 4/7 cups

C) 2 1/3 cups

D) 3/7 cups
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Question 4 options:

A) $20.70

B) $1.79

C) $1.38

D) $2.38

5) Another name for slope is the constant rate of change or speed.

A) True
B) False