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3 years ago

What is the solution to the inequality -3x - 42 > 3

Mathematics

1 answer:

garik1379 [7]3 years ago

4 0

$- 3x - 42 > 3\Leftrightarrow - 3x > 45\Leftrightarrow x < - 15$

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If the diameter is 21m what is the radius?<br><br> if the radius is 3.25mm what is diameter?

RoseWind [281]

Answer:

(a)

radius=diameter/2

=21/2=10.5m

(b)

radius=diameter/2

=3.25/2=1.625mm

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3 years ago

One week, Jason earned $404.70 at his job when he worked for 19 hours. If he is paid the same hourly wage, how many hours would

tensa zangetsu [6.8K]

Answer:

29 hours

Step-by-step explanation:

If he earned $404.70 per 19 hours, you do 404.70/19 to figure out the amount he earns per hour. 404.7/19 is 21.3. He earns $21.3 per hour. to solve, you find how many times 21.3 goes into 617.7 or 617.7/21.3. That is 29. He needs to work 29 hours to earn $617.70

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2 years ago

A rectangular storage container with an open top is to have a volume of 24 cubic meters. The length of its base is twice the wid

Mariana [72]

Answer:

419.25

Step-by-step explanation:

The calculation of the cost of materials for the cheapest such container is shown below:-

We assume

Width = x

Length = 2x

Height = h

where, length = $2 \times width$

Base area = lb

= $2x^2$

Side area = 2lh + 2bh

= 2(2x)h + 2(x)h

= 4xh + 2xh

Volume = 24 which is lbh = 24

$h = \frac{24}{2x^2} \\\\ h = \frac{12}{x^2}$

Now, cost is

$= 13(2x^2) + 9(4xh + 2xh)\\\\ = 13(2x^2) + 9(4x + 2x)\times \frac{12}{x^2} \\\\ = 26x^2 + \frac{648}{x}$

now we have to minimize C(x)

So, we need to compute the C'(x)

$= 52x - \frac{648}{x^2}$

C"(x) $= 52x - \frac{1,296}{x^3}$

now for the critical points, we will solve the equation C'(x) = 0

$= 52x - \frac{648}{x^2} = 0\\\\ x = \frac{648}{52}^{\frac{1}{3}}$

$C" = ((\frac{648}{52} ^{\frac{1}{3} } = 52 + \frac{1296}{(\frac{648}{52})^\frac{1}{3} )^3}\\\\ = 52 + \frac{1296}{\frac{648}{52} } >0$

So, x is a point of minima that is

= $(\frac{648}{52} )^\frac{1}{3}$

Now, Base material cost is

$= 13(2x^2)\\\\ = 26(\frac{648}{52} )^\frac{2}{3}$

= 139.75

Side material cost is

$= \frac{648}{x} \\\\ = \frac{648}{(\frac{648}{52})^\frac{1}{3} }$

= 279.50

and finally

Total cost is

= 139.75 + 279.50

= 419.25

4 0

3 years ago

Drag numbers to complete the table for missing values of x, x2, and x3.

natka813 [3]

Answer:

Values are:

x x²

10 100

7 0

3 years ago

Read 2 more answers

The total monthly profit for a firm is P(x)=6400x−18x^2− (1/3)x^3−40000 dollars, where x is the number of units sold. A maximum

wlad13 [49]

Answer:

Maximum profits are earned when x = 64 that is when 64 units are sold.

Maximum Profit = P(64) = 2,08,490.666667$

Step-by-step explanation:

We are given the following information: $P(x) = 6400x - 18x^2 - \frac{x^3}{3} - 40000$ , where P(x) is the profit function.

We will use double derivative test to find maximum profit.

Differentiating P(x) with respect to x and equating to zero, we get,

$\displaystyle\frac{d(P(x))}{dx} = 6400 - 36x - x^2$

Equating it to zero we get,

$x^2 + 36x - 6400 = 0$

We use the quadratic formula to find the values of x:

$x = \displaystyle\frac{-b \pm \sqrt{b^2 - 4ac} }{2a}$ , where a, b and c are coefficients of $x^2, x^1 , x^0$ respectively.

Putting these value we get x = -100, 64

Now, again differentiating

$\displaystyle\frac{d^2(P(x))}{dx^2} = -36 - 2x$

At x = 64, $\displaystyle\frac{d^2(P(x))}{dx^2} < 0$

Hence, maxima occurs at x = 64.

Therefore, maximum profits are earned when x = 64 that is when 64 units are sold.

Maximum Profit = P(64) = 2,08,490.666667$

6 0

3 years ago

What is the solution to the inequality -3x - 42 > 3​

What is the solution to the inequality -3x - 42 > 3