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erastova [34]
3 years ago
10

1/7f- 5 1/2= 9/14. what is f?

Mathematics
1 answer:
Alex777 [14]3 years ago
8 0
To solve this equation, we have to isolate the variable f, or get it alone on one side of the equation.

1/7f - 5 1/2 = 9/14

To do this, we need to add 5 1/2 to both sides of the equation to 1) cancel out the - 5 1/2 on the left side of the equation, and 2) maintain equality both sides of the equation.

1/7f - 5 1/2 + 5 1/2 = 9/14 + 5 1/2

1/7f = 6 2/14

Next, we have to divide both sides by 1/7, to get rid of the coefficient of f on the left side of the equation.

1/7f ÷ 1/7 = 6 2/14 ÷ 1/7

f = 43

Therefore, the the value of f is 43.
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find the value of "a" and "b" for which the limit exists both as x approaches 1 and as x approaches 2:
lbvjy [14]

Answer:

a = 4

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Step-by-step explanation:

If the given function is continuous at x = 1

\lim_{x \to 1^{-}} f(x)=(x+1)

                     =2

\lim_{x \to 1^{+}} f(x)=ax+b

                     =a+b

\lim_{x \to 1} f(x)=ax+b

                   =a+b

And for the continuity of the function at x = 1,

\lim_{x \to 1^{-}} f(x)=\lim_{x \to 1^{+}} f(x)=\lim_{x \to 1} f(x)

Therefore, (a + b) = 2 -------(1)

If the function 'f' is continuous at x = 2,

\lim_{x \to 2^{-}} f(x)=ax+b

                     =2a+b

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

                     =6

\lim_{x \to 2} f(x)=3x

                   =6

Therefore, \lim_{x \to 2^{-}} f(x)=\lim_{x \to 2^{+}} f(x)=\lim_{x \to 2} f(x)

2a + b = 6 -----(2)

Subtract equation (1) from (2),

(2a + b) - (a + b) = 6 - 2

a = 4

From equation (1),

4 + b = 2

b = -2

3 0
3 years ago
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