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skad [1K]
3 years ago
5

Write the value of the expression 2^3/2^3

Mathematics
1 answer:
kiruha [24]3 years ago
6 0

Answer:

1

Step-by-step explanation:

\frac{2^3}{2^3}\\\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=x^{a-b}\\=2^{3-3}\\2^{3-3}=1\\2^{3-3}\\\mathrm{Subtract\:the\:numbers:}\:3-3=0\\=2^0\\\mathrm{Apply\:rule}\:a^0=1,\:a\ne \:0\\=1

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Alina spent no more than $45 on gas for a road trip. The first gas station she used charged $3.50 per gallon and the second gas
Paraphin [41]

Answer:  3.50x + 4.00y ≤ 45

                0 < y < 11.25

<u>Step-by-step explanation:</u>

3.50x + 4.00y \leq 45\\\\\\\text{Subtract 3.50x from both sides:}\\4.00y\leq -3.50x+45\\\\\\\text{Divide everything by 4.00 (to isolate y):}\\\dfrac{4.00y}{4.00}\leq \dfrac{-3.50x}{4.00}+\dfrac{45}{4.00}\\\\\\y\leq-0.875x+11.25\\\\\\\text{Both x and y must be greater than zero, so:}\\0

8 0
2 years ago
Read 2 more answers
18)Write 4 expressions that are equivalent to 6(c<br> 5) - 6?
Vikki [24]

Answer:

the answer is 6C+24 or if you divide 6 on both sides c+4

examples/expressions:

1. 4(1.5c+6)

2. 3(2c+8)

3. 2(3c+12)

4. 12(0.5c+2)

4 0
2 years ago
5. Daniel arrives at his campsite out of breath from his swim and jog. His sister tells him that he should have swam to the boat
frosja888 [35]

Answer:

hello your question is incomplete attached below is the complete question

answer :

<em>Daniels sister is not correct because the time that will be taken by Daniel will be greater than the initial total time taken by Daniel.</em>

Step-by-step explanation:

<u>First determine the time it will take Daniel to reach the Boat and the jogging time</u>

time = distance / rate

where distance can be calculated using this equation: sin 53° = 400 / x

hence x ( distance ) = 500 ft

rate = 150

therefore Time ( t )  to reach boat = 500 / 150 = 3.33 minutes

Time for jogging ( as calculated ) = 3.69 minutes

therefore total time taken by Daniel = 3.33 + 3.69 = 7.02 minutes

<u>Finally determine if Daniel's sister is correct that he should have swam to the boat ramp and then jogged </u>

lets assume Distance to swim  =  x  ( according his sister )

determine the value of x = \sqrt{400^2 + 1400^2 }   therefore X = 1456.02 feet

∴

Total time to be taken if Daniel follows his sister's instruction  = 1456.02 / 150 = 9.71 minutes

<em>Daniels sister is not correct because the time that will be taken by Daniel will be greater than the initial total time taken by Daniel.</em>

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6 0
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 <em>h</em> and take the limit as <em>h</em> 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}}}

3.1.1.

f(x) = 4x^5 - \dfrac1{4x^2} + \sqrt[3]{x} - \pi^2 + 10e^3

Differentiate one term at a time:

• power rule

\left(4x^5\right)' = 4\left(x^5\right)' = 4\cdot5x^4 = 20x^4

\left(\dfrac1{4x^2}\right)' = \dfrac14\left(x^{-2}\right)' = \dfrac14\cdot-2x^{-3} = -\dfrac1{2x^3}

\left(\sqrt[3]{x}\right)' = \left(x^{1/3}\right)' = \dfrac13 x^{-2/3} = \dfrac1{3x^{2/3}}

The last two terms are constant, so their derivatives are both zero.

So you end up with

f'(x) = \boxed{20x^4 + \dfrac1{2x^3} + \dfrac1{3x^{2/3}}}

8 0
2 years ago
Will give brainliest!
Fed [463]
I think the answer might be B. $4,754.60 but I'm not sure. Sorry
7 0
3 years ago
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