Question 1 [5 points]

If the point A (6,9) is translated 4 units left, then find the new coordinates of the point A.

Alex_Xolod [135]

Answer:

(2, 9 )

Step-by-step explanation:

A translation of 4 units left is equivalent to subtracting 4 from the value of the x- coordinate, that is

(6, 9 ) → (6 - 4, 9 ) → (2, 9 )

6 0

3 years ago

Differentiating a Logarithmic Function in Exercise, find the derivative of the function. See Examples 1, 2, 3, and 4.

wlad13 [49]

Answer:

$\frac{dy}{dx}=\frac{x(1-2lnx)}{x^{4}}$

Step-by-step explanation:

To solve the question we refresh our knowledge of the quotient rule.

For a function f(x) express as a ratio of another functions u(x) and v(x) i.e

$f(x)=\frac{u(x)}{v(x)}\\$ , the derivative is express as

$\frac{df(x)}{dx}=\frac{v(x)\frac{du(x)}{dx}-u(x)\frac{dv(x)}{dx}}{v(x)^{2} }$

from $y=lnx/x^{2}$

we assign u(x)=lnx and v(x)=x^2

and the derivatives

$\frac{du(x)}{dx}=\frac{1}{x}\\\frac{dv(x)}{dx}=2x\\$ .

Note the expression used in determining the derivative of the logarithm function.it was obtain from the general expression of logarithm derivative i.e $y=lnx\\\frac{dy}{dx}=\frac{1}{x}$

If we substitute values into the quotient expression we arrive at

$\frac{dy}{dx}=\frac{(x^{2}*\frac{1}{x})-(2x*lnx)}{x^{4}}\\\frac{dy}{dx}=\frac{x-2xlnx}{x^{4}}\\\frac{dy}{dx}=\frac{x(1-2lnx)}{x^{4}}$

8 0

3 years ago

When solving a compound inequality. Micah wrote the solution as x> or equal to 50 OR x>or equal to 75. What is a simpler w

REY [17]

Answer:

The best way of writing this answer in an inequality pattern is 50 ≤ x ≥ 70

Step-by-step explanation:

The variable "x" is said to be greater than or equal to 50, that means that x could be 50, 51, 52, 53, 54......to infinity, all these values are true for x.

The second solution said x is greater or equal to 70. This also means that x could be 70, 71, 72, 73, ......... to infinity.

The inference that can be drawn from here is that x actually started from 50, so anything lesser than 50 is lesser than x, so 50 ≤ x. We can join the two answers together to get a range in a form like: 50 ≤ x ≥ 70

4 0

3 years ago

The competitive advantage of small American factories such as Tolerance Contract Manufacturing lies in their ability to produce

Tom [10]

Answer:

Following are the solution to the given question:

Step-by-step explanation:

Please find the complete question in the attached file.

$H_0: \sigma^{2} \leq 0.0008\\\\H_a: \sigma^{2} > 0.0008$

The testing states value is:

$\to x^2=\frac{(n-1)s^2}{\sigma^2}=32.6250$

therefor the $\rho - \ value = 0.2931$

Through out the above equation its values Doesn't rejects the H_0 value, and its sample value doesn't support the claim that although the configuration of its dependent variable has been infringed.

5 0

2 years ago

A house was valued at $100,000 in the year 1987. The value appreciated to $165,000 by the year 2002.

iris [78.8K]

Answer:

A) The annual multiplier was 1.0339; the annual increase was 0.0339 of the value.

B) 3.39% per year

C) $182,000

Step-by-step explanation:

A) Let's let t represent years since 1987. Then we can fill in the numbers and solve for r.

165000 = 100000(1 +r)^15

1.65^(1/15) = 1 +r . . . . . divide by 100,000; take the 15th root

1.03394855265 -1 = r ≈ 0.0339

The value was multiplied by about 1.0339 each year.

__

B) The value increased by about 3.39% per year.

__

C) S = $100,000(1.03394855265)^18 ≈ $182,000

8 0

3 years ago