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3 years ago

What is the solution to the inequality?

Mathematics

1 answer:

Furkat [3]3 years ago

5 0

$17 - 9 > x \\ 8 > x \\ x < 8 \\ = = c \:$

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A particle moves on the hyperbola xy=18 for time t≥0 seconds. At a certain instant, y=6 and dydt=8. What is x that this instant?

professor190 [17]

Answer:

The value of x at this instant is 3.

Step-by-step explanation:

Let $x\cdot y = 18$ , we get an additional equation by implicit differentiation:

$x\cdot \frac{dy}{dt}+y\cdot \frac{dx}{dt} = 0$ (1)

From the first equation we find that:

$x = \frac{18}{y}$ (2)

By applying (2) in (1), we get the resulting expression:

$\frac{18}{y}\cdot \frac{dy}{dt}+y\cdot \frac{dx}{dt} = 0$ (3)

$y\cdot \frac{dx}{dt}=-\frac{18}{y}\cdot \frac{dy}{dt}$

$\frac{dx}{dt} = -\frac{18}{y^{2}} \cdot \frac{dy}{dt}$

If we know that $y = 6$ and $\frac{dy}{dt} = 8$ , then the first derivative of x in time is:

$\frac{dx}{dt} = -\frac{18}{6^{2}} \cdot (8)$

$\frac{dx}{dt} = -4$

From (1) we determine the value of x at this instant:

$x\cdot \frac{dy}{dt} = -y\cdot \frac{dx}{dt}$

$x = -y\cdot \left(\frac{\frac{dx}{dt} }{\frac{dy}{dt} } \right)$

$x = -6\cdot \left(\frac{-4}{8} \right)$

$x = 3$

The value of x at this instant is 3.

4 0

3 years ago

Please help!!!I'm confused

IceJOKER [234]

Any rhombus has the same length for all for sides, so:
x + 14 = 3x +4
So, we get x = 5

Now, we can write
x + 14 = 8y
Since x = 5,

19 = 8y
so y = 19/8 = 2.375

<span>You can take any one of the equations and substitute the value of x or y in. The length is 19</span>

7 0

3 years ago

Find the square root of 520409 by long division method]

bonufazy [111]

Answer:

721.39 to the nearest hundredth.

Step-by-step explanation:

7 2 1 . 3 9 <----- Quotient

| 52,04,09.0000

| 49

142 | 304

| 284

1441 | 2009

| 1441

14423 | 56800

43269

144269 | 1353100

1298421

54679

6 0

3 years ago

What is the slope of the line perpendicular to the equation y=3x+2?

vekshin1

The given equation of the line is in slope - intercept form where the slope is 3 and the y - intercept is 2. The line perpendicular to the given has a slope which is equal to its negative reciprocal. Thus, the slope of a line perpendicular to y = 3x + 2 is -1/3. The answer is letter D. -1/3

6 0

3 years ago

I need the number 7 please

antiseptic1488 [7]

Answer:

The answer would be 3*5*50 which equals 750 kilometers.

Step-by-step explanation:

6 0

4 years ago