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mihalych1998 [28]

3 years ago

15

A shipping container will be used to transport several 100-kilogram crates across the country by rail. The greatest weight that

can be loaded into the container is 24000 kilograms. Other shipments weighing 12800 kilograms have already been loaded into the container. Write and solve an inequality which can be used to determine xx, the number of 100-kilogram crates that can be loaded into the shipping container.

1 answer:

snow_tiger [21]3 years ago

5 0

Answer:

$12800 + 100x \le 24000$

A maximum of 112 number of 100 - kilograms can be loaded in the container.

Step-by-step explanation:

Given that:

Weight of each crate = 100 kg

The greatest weight that can be loaded in the container = 24000 kg

Weight already loaded in the container = 12800 kg

To find:

The inequality to determine the value $x$ i.e. number of 100 - kilograms that can be loaded in the shipping container?

Solution:

Weight already loaded = 12800 kg

Let the number of 100 - kilograms that can be loaded in the container = $x$

Weight of $x$ = 100 $x$ kg

This combined weight nor be greater than the capacity of the container.

OR we can say, it must be lesser than or equal to greatest weight that can be loaded into the container.

$12800 + 100x \le 24000$

$100x \le 24000 - 12800\\\Rightarrow 100x \le 11200\\\Rightarrow x \le 112$

i.e. a maximum of <em>112</em> number of 100 - kilograms can be loaded in the container.

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Point <em>A</em> represents the complex conjugate z₁ and point L represents the complex conjugate of z₂ respectively

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Where in a complex number, we have;

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3 years ago

walnut grower estimates from past records that if 20 trees are planted per acre, then each tree will average 60 pounds of nuts p

laila [671]

Answer:

5 trees should be planted to maximize the yield per acre,

The maximum yield would be 1250

Step-by-step explanation:

Given,

The original number of trees per acre = 20,

Average pounds of nuts by a tree = 60,

Let x be the times of increment in number of trees,

So, the new number of trees planted per acre = 20 + x

∵ for each additional tree planted per acre, the average yield per tree drops 2 pounds,

So, the new number of pounds of nut = (60 - 2x)

Thus, the total yield per acre,

$Y(x) = (20+x)(60-2x)$

Differentiating with respect to t ( time ),

$Y'(x) = (20+x)(-2) + 60 - 2x = -40 - 2x + 60 - 2x = 20 - 4x$

Again differentiating with respect to t,

$Y''(x) = -4$

For maxima or minima,

$Y'(x) = 0$

⇒ 20 - 4x = 0

⇒ 20 = 4x

⇒ x = 5,

For x = 5, Y''(x) = negative,

Hence, Y(x) is maximum for x = 5,

And, maximum value of Y(x) = (20+5)(60 - 10) = 25(50) = 1250,

i.e. 5 trees should be planted to maximize the yield per acre,

and the maximum yield would be 1250 pounds

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3 years ago

What is the least common denominator used to add the fractions 1/18 and 5/12

Ne4ueva [31]

Answer:

6

Step-by-step explanation:

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I don't understand how to do find x and y, please help? thank yous.

pav-90 [236]

#8) There are THREE right-angle (90°) TRIANGLES.

The "big" triangle has legs "x" and "no designation - <em>so lets call it Z" </em>and hypotenuse "4+5"<em> = 9</em>

The "left" triangle has legs "4" and "y" and hypotenuse "x"

The "right" triangle has legs "5" and "y" and hypotenuse "no designation - <em>which we named Z</em>"

Now, you can create a system of equations - you have three unknown variables and can create an equation for each triangle using the Pythagorean Theorem.

Big: x² + Z² = 9² → x² + Z² = 81

Left: 4² + y² = x² → 16 + y² = x² → 16 = x² - y² → x² - y² = 16

Right: 5² + y² = Z² → 25 + y² = Z²

Next, let's eliminate Z by using substitution....use the Right equation to plug Z² into the Big equation to create a NEW Big equation.

NEW Big: x² + (25 + y² ) = 81 → x² + y² = 81 - 25 → x² + y² = 56

Now, we have two unknown variables (x and y) and two equations (NEW Big and Left). Solve the system using any method. <em>I am going to solve using the elimination method)</em>

NEW Big: x² + y² = 56

+ Left: <u>x² - y² = 16</u>

2x² = 72 <em>added the NEW Big and Left equations</em>

x² = 36 <em>divided both sides by 2</em>

x = 6 <em>took square root of both sides (NOTE: -6 is disregarded because we are solving for a length, which cannot be negative) </em>

The last step is to plug the "x" value (<em>that we just solved for)</em> into one of the equations to solve for "y". <em>I am choosing to use the Left equation.</em>

<em> </em>x² - y² = 16

36 - y² = 16<em> </em>

- y² = 16 - 36

- y² = -20

y² = 20

y = √20

y = 2√5

Answer: x = 6, y = 2√5

Try #9 on your own and then check your answers below:

Big: Z² + x² = 12², Left: 3² + y² = Z², Right: y² + 9² = x²

Answer: x = 6√3, y = 3√3

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