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3 years ago

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The number of visitors to a park is expected to follow the function v(x) = 7(x − 1), where x is the number of days since opening

. On the first day, there will be a ceremony with 39 people in attendance. What is the function that shows total visitors, including the ceremony?
c(x) = 7(x − 1) − 39
c(x) = 39x − 7
c(x) = 39 − 7(x − 1)
c(x) = 39 + 7(x − 1)

2 answers:

Vedmedyk [2.9K]3 years ago

6 0

C(x) = 39 + 7(x - 1)

Genrish500 [490]3 years ago

6 0

The answer is D. c(x) = 39 + 7(x - 1)

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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

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

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

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

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

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

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

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

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

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

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

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3 years ago

Show the number on a number line:<br> -12 ÷ 4 =

Gwar [14]

Answer:

well if we take -12 and divide it by four we will get -3.

Step-by-step explanation:

If we have a total of negative 12, just divide it by 4 and the difference between each division is the sum.

Your answer will be -3 on the number line.

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2 years ago

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What are the square roots of; (note: i think there are supposed to be 2 each) 36 12 1.96 0.64 400 25/36

Goryan [66]

Answer:

36 : 6 and -6

12 = $2\sqrt{3} , -2\sqrt{3}$

1.96 =1.4 and -1.4

0.64 : 0.8 and -0.8

400 : 20 and -20

25/36 = 5/6 and -5/6

Step-by-step explanation:

we know that

(-x)^2 = x^2

ALSO

(x)^2 = x^2

thus, square of both negative and positive number is same positive number.

_________________________________________________

36 = 6*6

36 = -6*-6

hence

square roots of 36 is both -6 and 6

12 = 4*3 = $2^2*\sqrt{3} *\sqrt{3}$

$\sqrt{12} = 2\sqrt{3}$

also

12 = $-2\sqrt{3} *-2\sqrt{3}$

$\sqrt{12} = -2\sqrt{3}$

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1.96 = 196/100 = (-14/10)^2

hence

$\sqrt{1.96} = 14/10 \ or -14/10$

_______________________________

0.64 = 64/100 = (8/10)^2 = 0.8^2

0.64 = 64/100 = (-8/10)^2 = (-0.8)^2

Thus, square root of 0.64 = 0.8 and -0.8

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400 = 20^2

400 = (-20)^2

$\sqrt{400} = 20\\\sqrt{400} = -20\\$

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25/36 = (-5/6)^2

$\sqrt{ 25/36} = 5/6 \\\sqrt{ 25/36} = (-5/6$

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Step-by-step explanation:

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postnew [5]

Answer:

its 2

Step-by-step explanation:

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3 years ago

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