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3 years ago

If 4x < 24, then x < 6

Mathematics

1 answer:

Luda [366]3 years ago

6 0

Answer:

X, can not be less than 6.

Step-by-step explanation:

X has to be greater than 6 because 24/4=6,

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How do you solve 3X+2y=9,for y

AnnyKZ [126]

Answer and Explanation:

<em>Solving 3x + 2y = 9 for y gives y = -(3/2)x + (9/2). </em>

5 0

3 years ago

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 company making backpacks charges $29.99 for each backpack. It costs $6.45 to make each backpack. The company can make backpack

Ne4ueva [31]

A minimum of 220 backpacks must be produced to obtain the desired benefits.

Since a company making backpacks charges $ 29.99 for each backpack, and it costs $ 6.45 to make each backpack, and the company can make backpacks in multiples of 10 and there is $ 1,000 in fixed costs, and the company wants to make at least $ 4,000 profit each week, to determine how many backpacks should be produced, the following calculation must be performed: