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3 years ago

What is the volume of the following rectangular prism?

Mathematics

1 answer:

NNADVOKAT [17]3 years ago

8 0

Answer:

1/10 units^3

Step-by-step explanation:

V=(Area of base)(height)

= 3/20 times 2/3

= 6/60

(simplified)= 1/10

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What is this simplified as a fraction

anyanavicka [17]

Step-by-step explanation:

35/48

this cannot be simplified any further

6 0

3 years ago

tasty yogurt manufacturing co. makes 10 cents per container of plain yogurt that it sells and 12 cents per container of vanilla

Ray Of Light [21]

32,000 - 15,000=17,000 thats how much

8 0

3 years ago

IM BEGGING PLEASE SOMEONE HELP

Rufina [12.5K]

156 because 12 times 13 is 156

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3 years ago

A container initially containing10 L of water in which there is 20 g of salt dissolved. A solution containing 4 g/L of salt is p

Kay [80]

Answer:

$A(40)= \frac{-200}{10+40} +4 (10 +40)=-4+200 = 196$

Step-by-step explanation:

For this case the solution flows at a rate of 2L/min and leaves at 1L/min. So then we can conclude the volume is given by $V= 10 +t$

Since the initial volume is 10 L and the volume increase at a rate of 1L/min.

For this case we can define A as the concentration for the salt in the container. And for this case we can set up the following differential equation:

$\frac{dA}{dt}= 4 \frac{gr}{L} *2 \frac{L}{min} - \frac{A}{10+t}$

Because at the begin we have a concentration of 8 gr/L and would be decreasing at a rate of $\frac{A}{10+t}$

So then we can reorder the differential equation like this:

$\frac{dA}{dt} +\frac{A}{10+t} =8$

We find the solution using the integration factor:

$\mu = -\int \frac{1}{10+t} dt = -ln(10+t)$

And then the solution would be given by:

$A = e^{-ln (10+t)} (\int e^{\int \frac{1}{10+t} dt})$

And if we simplify this we got:

$A= \frac{1}{10+t} (c + \int (10 +t) 8 dt)$

And after do the integral we got:

$A= \frac{c}{10+t} +4 (10 +t)$

And using the initial condition t=0 A= 20 we have this:

$20 = \frac{c}{10} +40$

$c= -200$

So then we have this function for the solution of A:

$A= \frac{-200}{10+t} +4 (10 +t)$

And now replacinf t= 40 we got:

$A(40)= \frac{-200}{10+40} +4 (10 +40)=-4+200 = 196$

8 0

3 years ago

Choose the graph that represents the following system of inequalities:

Licemer1 [7]

Answer:

FIRST.

64 square inches matches to a cross section parallel to the base of a right rectangle prism that is 3 inches long, 7 inches wide, and 11 inches tall

This is shown in the first figure below. A right rectangular prism where every edge connecting its base and the opposite face makes right angles with both faces. Since the tall is the side that measures 11 inches, then the base is formed by 3 inches long and 7 inches wide. Therefore, the area of this shape can be found as the area of a rectangle, which is: 21 in squared.

SECOND.

64 square inches matches to a cross section parallel to the base of a cube whose edges are 8 inches long.

This is shown in the second figure below. A cube is a prism whose sides all have the same length and in this case is 8 inches. We name cross section is to the slice that cuts through a solid. If the cross section is parallel to the base of a cube, then it forms a square with length . Therefore, the area of this shape can be found as the area of a square, which is: 64 in squared.

Third.

7 square inches matches to a cross section passing through the diagonal of opposite faces of a cube with edges that are 7 inches long and a diagonal that is approximately 10 inches

This is shown in the third figure below. As you can see, the cross section passes through the diagonals of the base and the top of the cube that are two opposite faces. This form a rectangle having sides where:

So: 70 in squared

FOURTH.

300 square inches matches to a cross section perpendicular to the base and passing through the diagonals of the base and opposite face of a right rectangular prism that is 24 inches wide, 7 inches long, and 12 inches tall and measures 25 inches along the diagonal of the base.

This is shown in the fourth figure below. The cross section passes through the diagonals of the base and the top of the right rectangular prism. They are opposite to each other, so the shape of the cross section is a rectangle whose sides are where:

So: 300 in squared.

Step-by-step explanation:

6 0

3 years ago