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2 years ago

6

How many hours is 10:30 am to 2:30 pm?

1 answer:

KonstantinChe [14]2 years ago

7 0

4 hours. 10:30 am to 11:30 am is 1 hour. 11:30 am to 12:30 pm is 1 hour. 12:30 pm to 1:30 pm is 1 hour, and 1:30 pm to 2:30 pm is 1 hour, totaling 4 hours. :)

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If the two legs of the right triangle are 5

yanalaym [24]

Answer:

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2 years ago

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

2 years ago

If $12.000 is invested in an account in which the interest earned is continuously

kykrilka [37]

Answer:

If 12,000 are put at an account with 2.5% compound interest in 15 years your total would be $17,379.58

7 0

2 years ago

!NEED HELP URGENTLY!<br> p − 10p + -5p + 14p − -9p − 2 = -20

bekas [8.4K]

Answer:

p = -2

Step-by-step explanation:

p − 10p + -5p + 14p − -9p − 2 = -20

-9p + 9p + 9p = -20 + 2

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2 years ago

The equation of a line is given below . 6x+2y =-18 find the x intercept and the y intercept

vova2212 [387]

Answer: x intercept is -3

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divide both sides by 6, and get -3 as an x intercept

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2 years ago