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3 years ago

9

Which inequality will have a solid boundary line and a shaded region above its graph? x − y ≥ 3 2x − 3y ≤ 3 3y − x < 2 2x + y

< 7

1 answer:

LenKa [72]3 years ago

7 0

<span>x − y ≥ 3 ... > stands for above on a graph, and the line under it _ stands for shaded.</span>

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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

A ball is launched into the sky at 272 feet per second from the roof of a skyscraper 1,344 feet tall. The equation for the ball’

xz_007 [3.2K]

When the ball is in the ground, its height is basically equal to zero thus making our equation,

<span> -16t^2 + 272t + 1344 = 0</span>

Simplifying the equation will give us,

<span> - t^2 + 17t + 84 = 0 or t^2 – 17t – 84 = 0</span>

Factoring out the equation will give us,

<span> (t – 21)(t + 4) = 0</span>

Thus, t = 21 or t = -4. -4 is an extraneous root. Thus, the answer is t = 21.

<span>Answer: 21 seconds</span>

5 0

3 years ago

A color printer prints 31 pages in 9 minutes. How many pages does it print per minute?

djyliett [7]

According to my calculations, it would take approximately 3.4 (being in decimal form) pages PER minute or Just 3 minuets being rounded to the nearest tenth. If I am I correct please correct me. I used a calculator.

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2 years ago

4(3x+2)−7x simplified

baherus [9]

Answer:

19x+8

Step-by-step explanation:

1) distribute the term outside the parenthesis to each term inside:

4*3x=12x

4*2=8

12x+8-7x

2) 12x+7x=19x

19x+8

Hope this helps!

7 0

3 years ago

A parallelogram with sides lengths of 5 inches and 12 inches and a height of 3 inches. Question What is the perimeter of this pa

UkoKoshka [18]

The perimeter of a shape is the sum of its lengths. A parallelogram has four sides with two pairs of equal sides. In this case, those sides are 5 inches and 12 inches. So, the perimeter is 12*2+5*2=24+10=34 inches.

8 0

3 years ago