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Murljashka [212]

3 years ago

10

Which expression is equivalent to 1/4x+3−1/3x+(−2)?

1 answer:

mote1985 [20]3 years ago

5 0

Answer:

7/12x+5

Step-by-step explanation:

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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

Computer models are systems of mathematical equations that describe the behavior of the atmosphere. Select one: True False

Assoli18 [71]

Answnser: True

Step-by-step explanation:

4 0

3 years ago

The radius of circle C is 6 units and the measure of central angle ACB is I radians. What is the approximate area of the entire

VARVARA [1.3K]

Answer:

Step-by-step explanation:

see attachment

3 0

3 years ago

Read 2 more answers

Let f(x) = x2 − 3x − 7. Find f(−3).

MrRa [10]

Answer is:
f(-3) = 11

5 0

3 years ago

Read 2 more answers

6)<br> Solve.<br> x + 5 = 10<br> A)<br> x = 2<br> B)<br> x = 3<br> 09<br> x = 4<br> D)<br> X = 5

LenaWriter [7]

D is the correct answer
x+5=10: subtract 5 from both sides the 5 will cancel out leaving x=5
x+5=10
-5 -5
x=5

4 0

3 years ago