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Artyom0805 [142]
3 years ago
14

3.

Mathematics
1 answer:
krek1111 [17]3 years ago
6 0

Answer:

2

Step-by-step explanation:

Let L be a real number.

\lim_{x \rightarrow 2}f(x) equals L if:

\lim_{x \rightarrow 2^-}f(x)=L

\lim_{x \rightarrow 2^+}f(x)=L

----------------------------

\lim_{x \rightarrow 2^-}f(x) means what does y get close to as we move x closer to 2 from the left. Please look at the orange to see what that looks like visually.

We see that y tends to 2.

This means:

\lim_{x \rightarrow 2^-}f(x)=2

-----------------------------

\lim_{x \rightarrow 2^+}f(x) means what does y get close to as we move x closer to 2 from the right. Please look at the blue to see what that looks like visually.

We see that y tends to 2.

This means:

\lim_{x \rightarrow 2^+}f(x)=2

----------------------------

Therefore,

\lim_{x \rightarrow 2}f(x)=2.

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A country's population in 1992 was 72 million. In 1998 it was 76 million. Estimate the population in 2012 using the exponential
stepan [7]
We assume the annual percentage increase is the same. We will work out the constant k using the formula

We have
P = 76
A = 72
t = 6 years (from 1992 to 1998)

Substitute into the formula
76=72e^{6k}
\frac{76}{72}=e^{8k}
Take log both sides give
ln( \frac{76}{72})=ln(e^{6k})
0.05406722127=6k
k=0.009

We can now work out the number of population by the end of 2012 using the formula

We have
A = 72 million
k = 0.009
t = 10 years (1992 to 2012)

P=72e^{0.009*10}P=78.78≈79 million


7 0
3 years ago
There are 72 students in the gym. 45 students are girls. The rest are boys. What is the ratio of boys to girls?
PIT_PIT [208]

Answer:

3 to 5

Step-by-step explanation:

To find the number of boys, take the total students and subtract the girls

72 -45 =27

We want the ratio of boys:girls

boys:girls

27:45

Divide each number by 9

27/9:45/9

3    : 5

3 0
2 years ago
At a bake sale, as student spent $11.00 buying 3 brownies and 5 cookies. His friend spent $3.95 buying 1 brownie and 2 cookies.
riadik2000 [5.3K]

Answer:

$$2.25

Step-by-step explanation:

Let b = the cost of one brownie, c = cost of one cookie

3b + 5c = 11

b+2c = 3.95

Times 3 on both sides on the second equation above to get the following:

3b + 6c = 11.85

3b+6c - (3b+5c) = 11.85-11

3b+6c-3b-5c = 0.85

c = 0.85

To find the value of b, use substitution:

b+2c = 3.95

b = 3.95-2c

= 3.95 - 2\times0.85

= 2.25

\therefore the cost of a brownie is $$2.25

Hope this helps :)

4 0
3 years ago
-3.25 (5 continues forever) ○ -3.2 (2 continues forever) Greater than or less than​
vazorg [7]

Answer:

Less than.    <

Step-by-step explanation:

8 0
2 years ago
A dilation with a scale factor of 3. 5 and centered at the origin is applied to PQ¯¯¯¯¯ with endpoints P(2, 5) and Q(2, 1)
velikii [3]

Answer: The answer is P'(7, 17.5) and Q'(7, 3.5).

Step-by-step explanation:  Given that a line segment PQ is dilated with a scale factor of 3.5 where origin is the centre of dilation.

The end points of segment PQ are P(2, 5) and Q(2, 1).

Therefore, after dilation, the coordinates of the end points become

Thus, the coordinates of P' are (7, 17.5) and the co-ordinates of Q' are (7, 3.5).

7 0
2 years ago
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