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4 years ago

Please Help!

1 answer:

6 0

The equation that Carissa should use to determine the volume of the box, where x is the side length of the original piece of cardboard is:

V = 5x^2 - 100x + 500

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What is the length of side m in AMNP shown below, given M - 350, P-65°, and p = 207

Nimfa-mama [501]

Answer:

m = 12.657

Step-by-step explanation:

5 0

3 years ago

Factor the expression 48g^2 -22gh -15h^2

sasho [114]

Answer:

factor the expression 48g^2 -22gh -15h^2

5 0

3 years ago

Pls help this is pretty urgent

laiz [17]

Answer:

(a) See below.

(b) x = 0 or x = 1

Step-by-step explanation:

Given rational function:

$f(x)=\dfrac{\ln |x-1|}{x}$

Part (a)

Substitute x = 2 into the given rational function:

$\begin{aligned}\implies f(2) & =\dfrac{\ln |2-1|}{2}\\\\ & =\dfrac{\ln 1}{2}\\\\ & =\dfrac{0}{2}\\\\ & =0\end{aligned}$

Therefore, as the function is defined at x = 2, the function is continuous at x = 2.

Part (b)

Given interval: [-2, 2]

Logs of negative numbers or zero are undefined. As the numerator is the natural log of an absolute value, the numerator is undefined when:

|x - 1| = 0 ⇒ x = 1.

A rational function is undefined when the denominator is equal to zero, so the function f(x) is undefined when x = 0.

So the function is discontinuous at x = 0 or x = 1 on the interval [-2, 2].

Part (c)

x = 1 is a vertical asymptote. As the function exists on both sides of this vertical asymptote, it is an infinite discontinuity. Since the function doesn't approach a particular finite value, the limit does not exist. Therefore, x = 1 is a non-removable discontinuity.

A hole exists on the graph of a rational function at any input value that causes both the numerator and denominator of the function to be equal.

$\implies f(0)=\dfrac{\ln |0-1|}{0}=\dfrac{\ln 1}{0}=\dfrac{0}{0}$

Therefore, there is a hole at x = 0.

The removable discontinuity of a function occurs at a point where the graph of a function has a hole in it. Therefore, x = 0 is a removable discontinuity.

3 0

2 years ago

Read 2 more answers

A rectangular prism is 7 cm long, 4 cm wide and 4 cm tall. How many 2 times 2 times 2 cm cubes can the prism be cut into? What i

Fantom [35]

Answer: The number of 2 times 2 times 2 cm cubes is 14. The total surface area of all the 2 times 2 times 2 times cm cubes is 336 cm square. The total volume of all the 2 times 2 times 2 times cm cubes is 112 cm cube.

Explanation:

It is given that the A rectangular prism is 7 cm long, 4 cm wide and 4 cm tall.

The volume of rectangular prism is,

$V_1=l\times b\times h$