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Romashka-Z-Leto [24]
3 years ago
14

7. Jena has a triangular garden with a perimeter that can be represented by 25r ^ 2 - 9r + 14 . The sum of two sides of the gard

en is represented by 10r ^ 2 + 12r + 9 . Which expression represents the length of the third side ?
Mathematics
1 answer:
galben [10]3 years ago
5 0

Answer: 15r^2-21r+5

Step-by-step explanation:

Given: Perimeter of triangular garden = 25r^2 - 9r + 14

The sum of two sides of the garden = 10r^2 + 12r + 9

Perimeter is the sum of all sides of a triangle.

Third side = Perimeter of triangular garden - sum of two sides of the garden

=25r ^ 2 - 9r + 14-(10r ^ 2 + 12r + 9)\\\\=25r ^ 2 - 9r + 14-10r ^ 2 - 12r - 9\\\\=15r^2-21r+5

The expression represent the third side = 15r^2-21r+5.

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Answer:

Option a.

\lim_{x \to \frac{\pi}{2}}(3e)^{xcosx}=1

Step-by-step explanation:

You have the following limit:

\lim_{x \to \frac{\pi}{2}{(3e)^{xcosx}

The method of direct substitution consists of substituting the value of \frac{\pi}{2} in the function and simplifying the expression obtained.

We then use this method to solve the limit by doing x=\frac{\pi}{2}

Therefore:

\lim_{x \to \frac{\pi}{2}}{(3e)^{xcosx} = \lim_{x\to \frac{\pi}{2}}{(3e)^{\frac{\pi}{2}cos(\frac{\pi}{2})}

cos(\frac{\pi}{2})=0\\

By definition, any number raised to exponent 0 is equal to 1

So

\lim_{x\to \frac{\pi}{2}}{(3e)^{\frac{\pi}{2}cos(\frac{\pi}{2})} = \lim_{x\to \frac{\pi}{2}}{(3e)^{\frac{\pi}{2}(0)}\\\\

\lim_{x\to \frac{\pi}{2}}{(3e)^{0}} = 1

Finally

\lim_{x \to \frac{\pi}{2}}(3e)^{xcosx}=1

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Five-hundred sixty two divided by seven
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