What does 5.401 * 10^-1 equal?

Mathematics

1 answer:

vlabodo [156]3 years ago

7 0

5.401 * 10^-1 equals
0.5401 or 5401/10000

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There are 43 pine trees currently in the park. Park workers will plant more pine trees

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Answer:

20 pine trees

Step-by-step explanation:

No of pine trees today = 63

No of pine trees there = 43

So no of pine trees planted today= 63-43= 20

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3 years ago

Every weekend Jill bikes 7.5 miles from home to the tennis court. His cousin Jun does the same thing. He bikes 80% as far as Jil

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80% of 7.5 is 6.
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Which two numbers add up to ___ and multiply to ___?

Assoli18 [71]

1. multiply to -18 add to -17 = Multiplying -18 and 1 will give -18 as the result and then on adding -18 and + 1 the result comes to -17
2. multiply to 36 add to -13 = Multiplying -9 and -4 will give -36 as the result and then on adding -9 and -4 the result comes to -13
3. multiply to -24 add to -5= Multiplying -8 and +3 will give -24 as the result and then on adding -8 and +3 the result comes to -5
4. multiply to -18 add to 7= Multiplying +9 and -2 will give -18 as the result and then on adding +9 and -2 the result comes to 7
5. multiply to -36 add to 9= Multiplying +12 and -3 will give -36 as the result and then on adding +12 and -3 the result comes to 9
 6. multiply to 24 add to 10= Multiplying +6 and +4 will give 24 as the result and then on adding +6 and +4 the result comes to 10
 7. multiply to 18 add to -9= Multiplying -6 and -3 will give -18 as the result and then on adding -6 and -3 the result comes to -9
 8. multiply to -36 add to -16= Multiplying -18 and +2 will give -36 as the result and then on adding -18 and +2 the result comes to -16

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3 years ago

1. (5pts) Find the derivatives of the function using the definition of derivative.

andreyandreev [35.5K]

2.8.1

$f(x) = \dfrac4{\sqrt{3-x}}$

By definition of the derivative,

$f'(x) = \displaystyle \lim_{h\to0} \frac{f(x+h)-f(x)}{h}$

We have

$f(x+h) = \dfrac4{\sqrt{3-(x+h)}}$

and

$f(x+h)-f(x) = \dfrac4{\sqrt{3-(x+h)}} - \dfrac4{\sqrt{3-x}}$

Combine these fractions into one with a common denominator:

$f(x+h)-f(x) = \dfrac{4\sqrt{3-x} - 4\sqrt{3-(x+h)}}{\sqrt{3-x}\sqrt{3-(x+h)}}$

Rationalize the numerator by multiplying uniformly by the conjugate of the numerator, and simplify the result:

$f(x+h) - f(x) = \dfrac{\left(4\sqrt{3-x} - 4\sqrt{3-(x+h)}\right)\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)}{\sqrt{3-x}\sqrt{3-(x+h)}\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)} \\\\ f(x+h) - f(x) = \dfrac{\left(4\sqrt{3-x}\right)^2 - \left(4\sqrt{3-(x+h)}\right)^2}{\sqrt{3-x}\sqrt{3-(x+h)}\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)} \\\\ f(x+h) - f(x) = \dfrac{16(3-x) - 16(3-(x+h))}{\sqrt{3-x}\sqrt{3-(x+h)}\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)} \\\\ f(x+h) - f(x) = \dfrac{16h}{\sqrt{3-x}\sqrt{3-(x+h)}\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)}$

Now divide this by h and take the limit as h approaches 0 :

$\dfrac{f(x+h)-f(x)}h = \dfrac{16}{\sqrt{3-x}\sqrt{3-(x+h)}\left(4\sqrt{3-x} + 4\sqrt{3-(x+h)}\right)} \\\\ \displaystyle \lim_{h\to0}\frac{f(x+h)-f(x)}h = \dfrac{16}{\sqrt{3-x}\sqrt{3-x}\left(4\sqrt{3-x} + 4\sqrt{3-x}\right)} \\\\ \implies f'(x) = \dfrac{16}{4\left(\sqrt{3-x}\right)^3} = \boxed{\dfrac4{(3-x)^{3/2}}}$