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notsponge [240]
2 years ago
8

Evaluate lim x approaches to 2 : (sqrt(6-x)-2)/(sqrt(3-x)-1)

Mathematics
1 answer:
solong [7]2 years ago
5 0

Answer:

The answer is "0.5".

Step-by-step explanation:

Given:

\to \lim_{x\to 2}  \frac{(\sqrt{(6-x)}-2)}{(\sqrt{(3-x)}-1)}\\\\ \to \lim_{x\to 2}  \frac{\frac{d(\sqrt{(6-x)}-2)}{dx}}{\frac{(\sqrt{(3-x)}-1)}{dx}}\\\\

\to \lim_{x\to 2} \frac{\frac{-1}{2\sqrt{(6-x)} }}{\frac{-1}{2\sqrt{(3-x)}}}\\\\

\to \lim_{x\to 2} \frac{\sqrt{3-x}}{\sqrt{6-x}}\\\\ \to \frac{\sqrt{3-2}}{\sqrt{6-2}}\\\\ \to \frac{\sqrt{1}} {\sqrt{4}}\\\\ \to \frac{1}{2}\\\\ \to 0.5

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2203
ale4655 [162]

Answer:

sorry im just answering this cuz need points

Step-by-step explanation:

5 0
3 years ago
Apply the distributive property to factor out the greatest common factor: 27+16
notsponge [240]

The greatest common factor (GCF or GCD or HCF) of a set of whole numbers is the largest positive integer that divides evenly into all numbers with zero remainder.

Answer:

GCF = 1

for the values 16, 27

The factors of 16 are: 1, 2, 4, 8, 16

The factors of 27 are: 1, 3, 9, 27

4 0
1 year ago
Jack travels to work on the Eastern Freeway. He notices that the difference in time between if he drives 5 mph below the speed l
Misha Larkins [42]
Let's denote s as the speed limit. To find the total time it takes for Jack to drive given the speed, we just divide the total number of miles he covered (10 miles) by the speed he's traveling at.

Accounting for the given of the problem, we'll have the following equation:
\frac{10}{s-15} - \frac{10}{s-5}= \frac{1}{30} (from the fact that the difference between the time it takes to drive five miles below the speed limit versus 15 miles below is 2 mins or \frac{1}{30} hours.)

Since we only have one unknown variable, we can freely solve for s:
\frac{10}{s-15} - \frac{10}{s-5}= \frac{1}{30} 
\frac{10(s-5)-10(s-15)}{(s-15)(s-5)}= \frac{1}{30} 
\frac{10s-50-10s+150}{s^{2}-5s-15s+75}= \frac{1}{30} 
\frac{100}{s^{2}-20s+75}= \frac{1}{30}  
3000=s^{2}-20s+75
0=s^{2}-20s-2925
s_{1}=65
s_{2}=-45 (we ignore the negative value since there is no negative <u>speed</u>.)

ANSWER: The speed limit of the freeway is 65 mph.
3 0
3 years ago
Read 2 more answers
Helpppp plzzzzz :/ :(
Alex73 [517]

Answer:

Step-by-step explanation:

For this you will start at negative 3 then go up 5 spaces and to the right 4 times. Once you run out of space in one direction go in the opposite doing the opposite steps. Going down 5 times and to the left 4 times. If you need any more help with these, I'll be glad to help as I am learning these in class right now. The way to determine which way your going is on the slope. The slope in those equations is the number before x. The coefficient. When the numerator(y axis) is positive, that means you go up on the graph by the number shown. If its a negative go down. If the denominator (x-axis) is a positive that means you go to the right by the number shown. If it's a negative you go to the right. The number all the way on the right, in this case the -3, that is the y intercept.

4 0
3 years ago
Please answer asap!!!!!!
Greeley [361]

Answer:

that should be 32

Step-by-step explanation:

3 0
2 years ago
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