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Yakvenalex [24]
3 years ago
14

Please help !!

Mathematics
1 answer:
shutvik [7]3 years ago
4 0

Given:

The limit problem is:

\lim_{x\to 3}(x^2+8x-2)

To find:

The limit of the function by using direct substitution.

Solution:

We have,

\lim_{x\to 3}(x^2+8x-2)

Applying limit, we get

\lim_{x\to 3}(x^2+8x-2)=(3)^2+8(3)-2

\lim_{x\to 3}(x^2+8x-2)=9+24-2

\lim_{x\to 3}(x^2+8x-2)=33-2

\lim_{x\to 3}(x^2+8x-2)=31

Therefore, the correct option is D.

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Solve the simultaneous equation x+y/4=1/2 and x-3y/3=2
Feliz [49]

Answer:

x+y/4 = 1/2

x-3y/3 = 2

move variables to one side:

multiply the first equation by 4 to get: x+y =2

and the second equation by 3 to get: x-3y =6

then subtract the equations to cancel out x:

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3 0
3 years ago
Read 2 more answers
How many quarts of pure antifreeze must be added to 8 quarts of a 40% antifreeze solution to obtain a 60% antifreeze solution
anyanavicka [17]

Let <em>q</em> be the number of quarts of pure antifreeze that needs to be added to get the desired solution.

8 quarts of 40% solution contains 0.40 × 8 = 3.2 quarts of antifreeze.

The new solution would have a total volume of 8 + <em>q</em> quarts, and it would contain a total amount of 3.2 + <em>q</em> quarts of antifreeze. You want to end up with a concentration of 60% antifreeze, which means

(3.2 + <em>q</em>) / (8 + <em>q</em>) = 0.60

Solve for <em>q</em> :

3.2 + <em>q</em> = 0.60 (8 + <em>q</em>)

3.2 + <em>q</em> = 4.8 + 0.6<em>q</em>

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4 0
2 years ago
charles deposited $12,000 in the bank. He withdrew $5,000 from his account after one year. If he recives a total amount of $9,34
Schach [20]

Answer:

The rate of simple interest is 9%

Step-by-step explanation:

* Lets talk about the simple interest

- The simple Interest Equation (Principal + Interest)  is:

  A = P(1 + rt)  , Where

# A = Total amount (principal + interest)

# P = Principal amount

# I = Interest amount

# r = Rate of Interest per year in decimal r = R/100

# R = Rate of Interest per year as a percent R = r * 100

# t = Time period involved in months or years

- The rule of the simple interest is I = Prt

* lets solve the problem

- Charles deposited $12,000

∴ P = $12,000

- He withdrew $5,000 from his account after one year

- He receives a total amount of $9,340 after 3 years

∴ A = $9340 and t = 3

- Lets find the inetrest after 1 year

∵ I = Prt

∵ P = 12000

∵ t = 1

∴ I = 12000(r)(1) = 12000r

- Lets subtract the money that he withdrew

∵ He withdrew $5000

∵ He deposit at first 12000

∴ He has after the withdrew 12000 - 5000 = 7000

- The new P for the next 2 years is 7000

- This amount will take the same rate r for another two years

- The total money is $9340

∵ I = A - P

∵ A = 9340

∵ P = 7000

∴ The amount of interest = 9340 - 7000 = 2340

- The amount of interest after 3 years is 2340

- Lets find the amount of interest in the two years

∴ I = 7000(r × 2) = 14000r

- The amount of interest after the 3 years is the sum of the interest in

  the 1st year and the other 2 years

∴ 2340 = 14000r + 12000r

∴ 2340 = 26000r ⇒ divide both sides bu 2340

∴ r = 2340 ÷ 26000 = 0.09

∵ The rate R in percentage = r × 100

∴ R = 0.09 × 100 = 9%

∴ The rate of simple interest is 9%

8 0
3 years ago
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