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3 years ago

Find the exact length of the third side.

Mathematics

2 answers:

KATRIN_1 [288]3 years ago

7 0

Answer:

The third side is sqrt(5)

Step-by-step explanation:

This is a right triangle so we can use the Pythagorean theorem

a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse

We know the legs are 1 and 2 and we are looking for the hypotenuse.

1^2+2^2 = c^2

1+4 = c^2

5 =c^2

Take the square root of each side

sqrt(5) = sqrt(c^2)

sqrt(5) =c

The third side is sqrt(5)

adell [148]3 years ago

6 0

Answer:

$\sqrt{5}$ or 2.236

Step-by-step explanation:

The pythagorem theorm states that side 1^2 + side^2 = hypotenuse^2

2^2 + 1^2 = h^2

4+1 = h^2

5 = h^2

$\sqrt{5} = \sqrt{h^{2} }$

$\sqrt{5} =h$

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Luda [366]

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To get the answer we need to add, subtract, and divide. So, for the first month we pay $115 cause $65 + $50 = $115. So, $850 - $115 = $735. Now, $735/$65 = 11.3076923077 but, you can't have .3076923077 of a class so, she will only have enough for 11 classes.

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3 years ago

Find the derivative of <img src="https://tex.z-dn.net/?f=tan%5E%7B-1%7D%20x" id="TexFormula1" title="tan^{-1} x" alt="tan^{-1} x

sladkih [1.3K]

$\huge{\color{magenta}{\fbox{\textsf{\textbf{Answer}}}}}$

$\frak {\huge{ \frac{1}{1 + {x}^{2} } }}$

Step-by-step explanation:

$\sf let \: f(x) = { \tan }^{ - 1} x \\ \\ \sf f(x + h) = { \tan}^{ - 1} (x + h)$

$\sf f'(x) = \frac{f(x+h) - f(x) }{h}$

$\sf \implies \lim_{ h \to 0 } \frac{ { \tan }^{ - 1}(x + h) - { \tan}^{ - 1}x }{h} \\ \\ \\ \sf \implies \lim_ {h \to 0} \frac{ { \tan}^{ - 1} \frac{x + h - x}{1 + (x + h)x} }{h}$

By using

$\sf { \tan}^{ - 1} x - { \tan}^{ - 1} y = \\ \sf { \tan}^{ - 1} \frac{x - y}{1 + xy} formula$

$\sf \implies \large \lim_{h \to0 } \frac{ { \tan}^{ - 1} \frac{h}{1 + hx + {x}^{2} } }{h} \\ \\ \\ \sf \implies \large{\lim_{h \to0} } \frac{ { \tan}^{ - 1} \frac{h}{1 + hx + {x}^{2} } }{ \frac{h}{1 + hx + {x}^{2} } \times (1 + hx + {x}^{2} )} \\ \\ \\ \sf \implies \large \lim_{h \to0} \frac{ { \tan}^{ - 1} \frac{h}{1 + hx + {x}^{2} } }{ \frac{h}{1 + hx + {x}^{2} } } + \lim_{h \to0} \frac{1}{1 + hx + {x}^{2} }$

Now putting the value of h = 0

$\sf \large \implies 0 + \frac{1}{1 + 0 + {x}^{2} } \\ \\ \\ \purple{ \boxed { \implies \frac{1}{1 + {x}^{2} } }}$

6 0

2 years ago

If your car gets 28 miles per gallon and you travel 30 miles round-trip to work five days a week, how much do you pay each 4-wee

disa [49]

Answer:

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Step-by-step explanation:

First you have to gather all the miles.

30 miles x 5 = 150

So that is 150 miles/per week

Then you have to devide the miles by how many gallons per gas you travle.

150/28 miles per gallon = 5.3571....

That how many gallons you'll need a week.

Now, you times the gallons by the price of the gas

5.3571... x $3.05 = $16.3392...

Finally you times the amoutn of money for a week time 4 weeks.

$16.3392... x 4 = $65.35 (to the two decimal mark)

Hope this helped you! : )

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3 years ago

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Murljashka [212]

Answer:

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Step-by-step explanation:

If you need a step by step explanation, I will edit this later.

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4 years ago

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Answer:
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Step-by-step :
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3 years ago