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3 years ago

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Find the domain of f(x)={-4x if x ≤ 0 { 4x+2 if > 0

1 answer:

guapka [62]3 years ago

7 0

Answer:

The domain of f(x) ={-4x if x <u><</u> 0} and {4x +2 if > 0}

The correct answer are -8 <u><</u> 0 and 18 > 0

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You want to get from a point A on the straight shore of the beach to a buoy which is 54 meters out in the water from a point B o

anyanavicka [17]

Answer:

$x =\dfrac{45 \sqrt{6}}{ 2}$

Step-by-step explanation:

From the given information:

The diagrammatic interpretation of what the question is all about can be seen in the diagram attached below.

Now, let V(x) be the time needed for the runner to reach the buoy;

∴ We can say that,

$\mathtt{V(x) = \dfrac{70-x}{7}+\dfrac{\sqrt{54^2+x^2}}{5}}$

In order to estimate the point along the shore, x meters from B, the runner should stop running and start swimming if he want to reach the buoy in the least time possible, then we need to differentiate the function of V(x) and relate it to zero.

i.e

The differential of V(x) = V'(x) =0

= $\dfrac{d}{dx}\begin {bmatrix} \dfrac{70-x}{7} + \dfrac{\sqrt{54^2+x^2}}{5} \end {bmatrix}= 0$

$-\dfrac{1}{7}+ \dfrac{1}{5}\times \dfrac{x}{\sqrt{54^2+x^2}}=0$

$\dfrac{1}{5}\times \dfrac{x}{\sqrt{54^2+x^2}}= \dfrac{1}{7}$

$\dfrac{5x}{\sqrt{54^2+x^2}}= \dfrac{1}{7}$

$\dfrac{x}{\sqrt{54^2+x^2}}= \dfrac{1}{\dfrac{7}{5}}$

$\dfrac{x}{\sqrt{54^2+x^2}}= \dfrac{5}{7}$

squaring both sides; we get

$\dfrac{x^2}{54^2+x^2}= \dfrac{5^2}{7^2}$

$\dfrac{x^2}{54^2+x^2}= \dfrac{25}{49}$

By cross multiplying; we get

$49x^2 = 25(54^2+x^2)$

$49x^2 = 25 \times 54^2+ 25x^2$

$49x^2-25x^2 = 25 \times 54^2$

$24x^2 = 25 \times 54^2$

$x^2 = \dfrac{25 \times 54^2}{24}$

$x =\sqrt{ \dfrac{25 \times 54^2}{24}}$

$x =\dfrac{5 \times 54}{\sqrt{24}}$

$x =\dfrac{270}{\sqrt{4 \times 6}}$

$x =\dfrac{45 \times 6}{ 2 \sqrt{ 6}}$

$x =\dfrac{45 \sqrt{6}}{ 2}$

8 0

3 years ago

Miguel bought 2 1/4 pounds of hamburgers,1 1/5 pounds of sliced turkey ,and 2 pounds of cheese.what was the total weight of all

irinina [24]

the answer you are looking for is 5 9/20 pounds

sorry but it as to be twenty character

7 0

3 years ago

What is the volume of the composite figure? Express the

Papessa [141]

Answer:

$V=312\pi\ mm^{3}$

Step-by-step explanation:

we know that

The volume of the composite figure is equal to the volume of a semi-sphere plus the volume of the cone

so

$V=\frac{4}{6}\pi r^{3} +\frac{1}{3} \pi r^{2} h$

we have

$r=6\ mm$

$h=14\ mm$

substitute

$V=\frac{4}{6}\pi (6)^{3} +\frac{1}{3} \pi (6)^{2} (14)$

$V=144\pi +168\pi$

$V=312\pi\ mm^{3}$

3 0

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What is the value of m? 12+(7+m)=30<br><br> 11<br> 19<br> 25<br> 35<br> 49

Marat540 [252]

The answer is 11
hope that helps

4 0

3 years ago

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A die is rolled 3 times. What is the probability of getting 1’s on each roll?

meriva

Answer: The answer is around 16.66%

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3 years ago

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