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3 years ago

If a = 0.6(the 6 repeating) and b= 0.75, then a·b= (blank) and a/b=(blank)

Mathematics

1 answer:

Phoenix [80]3 years ago

5 0

0.6666 (repeating) x 0.75 = 0.5

0.6666 (repeating) / 0.75 = 0.8888888 (repeating)

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There are 1639 students in attendance at Auburn High School. What percentage does one student count towards the total number of

ruslelena [56]

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3 years ago

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There are 20 students in a drama class. The mean age of 12 students is 18 years. The mean age of the remaining 8 students of the

Marta_Voda [28]

Answer:

Step-by-step explanation:

Total sum of age of 12 students = 12*18 = 216;

Total sum of age of 8 students = 8*23 = 184;

Total sum of age of 20 students = 216+184 = 400;

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= 400/20 = 20 year

Step-by-step explanation:

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2 years ago

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3 years ago

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Identify each expression that represents the slope of a tangent to the curve y=1/x+1 at any point (x,y) .

tankabanditka [31]

Answer:

Slope of a tangent to the curve = $f'(x) = \frac{-1 }{(x+1)^{2} }$

Step-by-step explanation:

Given - y = 1/x+1

To find - Identify each expression that represents the slope of a tangent to the curve y=1/x+1 at any point (x,y) .

Proof -

We know that,

Slope of tangent line = f'(x) = $\lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$

We have,

f(x) = y = $\frac{1}{x+1}$

So,

f(x+h) = $\frac{1}{x+h+1}$

Now,

Slope = f'(x)

And

$f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h} \\= \lim_{h \to 0} \frac{\frac{1}{x+h+1} - \frac{1}{x+1} }{h}\\= \lim_{h \to 0} \frac{x+1 - (x+h+1) }{h(x+1)(x+h+1)}\\= \lim_{h \to 0} \frac{x +1 - x-h-1 }{h(x+1)(x+h+1)}\\= \lim_{h \to 0} \frac{-h }{h(x+1)(x+h+1)}\\= \lim_{h \to 0} \frac{-1 }{(x+1)(x+h+1)}\\= \frac{-1 }{(x+1)(x+0+1)}\\= \frac{-1 }{(x+1)(x+1)}\\= \frac{-1 }{(x+1)^{2} }$

∴ we get

Slope of a tangent to the curve = $f'(x) = \frac{-1 }{(x+1)^{2} }$

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