How do I solve what is 2/3 of 90

Mathematics

2 answers:

masya89 [10]4 years ago

6 0

Answer:

Thus, $\frac{2}{3}\times 90=60$

Step-by-step explanation:

Given: $\frac{2}{3}$ of 90

We have to write the simplified form of $\frac{2}{3}$ of 90

Consider the given expression

$\frac{2}{3}$ of 90

of means multiplication

thus, $\frac{2}{3}$ of 90 means $\frac{2}{3}\times 90$

Simplify, we have,

$2\times 30=60$

Thus, $\frac{2}{3}\times 90=60$

Sergeu [11.5K]4 years ago

3 0

<span>The answer is 60.

Explanation<span>:
In mathematics, the word "of" indicates multiply. This means we would multiply 2/3 * 90.

We can write 90 as a fraction by putting it over 1, which gives us 2/3(90/1).

To multiply fractions, we multiply straight across: (2*90)/(3*1) = 180/3 = 60.</span></span>

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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

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