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Rama09 [41]
2 years ago
6

A function f(x) is said to have a removable discontinuity at x=a if: 1. f is either not defined or not continuous at x=a . 2. f(

a) could either be defined or redefined so that the new function IS continuous at x=a. Let f(x) = {((6)/(x)+(-5 x+18)/(x(x-3)), "if", x doesnt = 0 "and" x doesnt =3),( 3, "if", x=0) :} Show that f(x) has a removable discontinuity at x=0 and determine what value for f(0) would make f(x) continuous at x=0 . Must redefine f(0)= ?
Mathematics
1 answer:
Alexeev081 [22]2 years ago
8 0

Answer:

it would be 5

Step-by-step explanation:

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Jasmine mixes 37 ounces of grape juice and 13 ounces of apple juice to make a fruit punch. She will pour the punch into 6-ounce
Anastaziya [24]
First we have to figure out how much fruit punch Jasmine has.
To do this, we just have to add the number of ounces of grape juice she mixes with the number of ounces of apple juice.

37 + 13 = 50.

Jasmine is pouring the punch into 6 ounce cups.  To find out how many cups of punch she can make, you have to divide the number of ounces of punch she has (50) by the number of ounces she can put in a cup (6).

50/6 ≈ 8.33

Therefore, Jasmine can 

A. make 8 full cups of punch with the apple juice and grape juice.

and 

B.  Yes, there will be juice left over, because the amount of cups Jasmine could fill had a decimal, or a remainder.

8 0
2 years ago
(cot^2x - 1)/(csc^2x) = cos2x​
Alex787 [66]

Answer:

Step-by-step explanation:

The idea here is to get the left side simplified down so it is the same as the right side. Consequently, there are 3 identities for cos(2x):

cos(2x)=cos^2x-sin^2x,

cos(2x)=1-2sin^2x, and

cos(2x)=2cos^2x-1

We begin by rewriting the left side in terms of sin and cos, since all the identities deal with sines and cosines and no cotangents or cosecants.  Rewriting gives you:

\frac{\frac{cos^2x}{sin^2x} -\frac{sin^2x}{sin^2x} }{\frac{1}{sin^2x} }

Notice I also wrote the 1 in terms of sin^2(x).

Now we will put the numerator of the bigger fraction over the common denominator:

\frac{\frac{cos^2x-sin^2x}{sin^2x} }{\frac{1}{sin^2x} }

The rule is bring up the lower fraction and flip it to multiply, so that will give us:

\frac{cos^2x-sin^2x}{sin^2x} *\frac{sin^2x}{1}

And canceling out the sin^2 x leaves us with just

cos^2x-sin^2x which is one of our identities.

5 0
3 years ago
Help on this math question? If you don't know how please don't answer :/
just olya [345]
4/x = 6/(x+3)
6x = 4(x+3)
6x = 4x + 12
2x = 12
  x = 6

P = (4 + 6) +(6+3) + 6
P = 10 + 9 + 6
P = 25
8 0
3 years ago
Mark bought 4 pounds of apples for 7.56 what was the cost per pound
marusya05 [52]

Answer:

1.89

Step-by-step explanation:

7.56 ÷ 4 = 1.89

3 0
3 years ago
Read 2 more answers
Deon plots points to show the time it takes him to swim laps on two days. Is there a proportional relationship between the numbe
Sever21 [200]

Answer:

There's no proportional relationship between number of laps and minutes.

Step-by-step explanation:

The graph given above is a straight line graph, however, it does not cut across the point of origin (0, 0). As a result of this, it would be difficult to get a constant of proportionality, as you'd likely get different constant of proportionality between different points on the line. Thus, the ratio of y and x for each set of points may vary.

So therefore, the relationship between the x and y cannot be proportional.

We can conclude that the graph does not represent a proportional relationship between number of laps and minutes.

6 0
3 years ago
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