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2 years ago

For which of the following compound inequalities is there no solution?

Mathematics

1 answer:

Bess [88]2 years ago

8 0

Answer:

(a) $6m \le - 36$ and $m + 24 > 20$

Step-by-step explanation:

Required

Which of a to d has no solution

(a) $6m \le - 36$ and $m + 24 > 20$

We have: $m + 24 > 20$

Sole for m

$m >20 - 24$

$m >-4$

$6m \le - 36$

Divide by 6

$m \le -6$

So, we have:

$m \le -6$ and $m >-4$

$m \le -6$ implies that: m = -6,-7,-8,-9.....

$m >-4$ implies that m = -3,-2,-1,0.....

Hence, there is no solution

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Simplify the radical

katrin [286]

X^2 * 5,x^4 so B is the answer

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3 years ago

A company is making building blocks. Each building block is a cube and has volume 125/729 ft cubed . How long is each side of th

MariettaO [177]

Answer: The length of each side of the building block is 0.56 feet

Step-by-step explanation:

A company is making building blocks. Each building block is a cube and has volume 125/729 ft cubed . Each of the building blocks has 6 faces which are squares, 8 vertices and 12 edges.

Since a square has all sides to be equal sides,

The volume of the cube = the volume of the building block =

Product of length,L, width, W and height, H.

Volume of the building block = L × W × H

Since length = width = height,

Volume of cube = L^3

From the information given,

Volume of a building block = 125/729ft cubed

L^3 = 125 / 729

Taking cube root of both sides of the equation,

L = cube root of 125/729

L = 5/9

= 0.56 feet

4 0

3 years ago

What is the value of p so that the expession 6x+3-(8x-5) is equivalent to (px+8)?

kiruha [24]

Answer:

-2

Step-by-step explanation:

The first equation simplifies to -2x+8 so p should be replaced with -2

4 0

2 years ago

At time t=0 sec, a tank contains 15 oz of salt dissolved in 50 gallons of water. Then brine containing 88oz of salt per gallon o

maria [59]

Answer:

a) $s(t) =400- 385 e^{-\frac{1}{10} t}$

b) $s(t=25min) =400- 385 e^{-\frac{1}{10}25}=368.397$

Step-by-step explanation:

Part a

Assuming that the original concentration of salt is 8 oz/gal and that the rate of in is equal to the rate out = 5 gal/min.

For this case we know that the rate of change can be expressed on this way:

$Rate change = In-Out$

And we can name the rate of change as $\frac{ds}{dt}=rate change$

And our variable s would represent the amount of salt for any time t.

We know that the brine containing 8oz/gal and the rate in is equal to 5 gal/min and this value is equal to the rate out.

For the concentration out we can assume that is $\frac{s}{50gal}$

And now we can find the expression for the amount of salt after time t like this:

$\frac{dS}{dt}= 8 \frac{oz}{gal}(5\frac{gal}{min}) -\frac{s}{50gal} 5 \frac{gal}{min} =40\frac{oz}{min}- \frac{s}{10} \frac{oz}{min}$

And we have this differential equation:

$\frac{dS}{dt} +\frac{1}{10} s = 40$

With the initial conditions y(0)=15 oz

As we can see we have a linear differential equation so in order to solve it we need to find first the integrating factor given by:

$\mu = e^{\int \frac{1}{10} dt }= e^{\frac{1}{10} t}$

And then in order to solve the differential equation we need to multiply with the integrating factor like this:

$e^{\frac{1}{10} t} s = \int 40 e^{\frac{1}{10} t} dt$

$e^{\frac{1}{10} t} s = 400 e^{\frac{1}{10} t} +C$

Now we can divide both sides by $e^{\frac{1}{25} t}$ and we got:

$s(t) =400 + C e^{-\frac{1}{10} t}$

Now we can apply the initial condition in order to solve for the constant C like this:

$15 = 400+C$

$C=-385$

And then our function would be given by:

$s(t) =400- 385 e^{-\frac{1}{10} t}$

Part b

For this case we just need to replace t =25 and see what we got for the value of the concentration:

$s(t=25min) =400- 385 e^{-\frac{1}{10}25}=368.397$

7 0

2 years ago

A cuboid has a length of 25cm, a width of 5cm and height of (x-2)cm

mr Goodwill [35]

Step-by-step explanation:

Hi there!

From above question;

A cuboid has a length of 25cm, a width of 5cm and height of (x-2)cm.

Length (l) = 25cm

width (b) = 5cm

height (h) = (x-2)cm.

a).

Volume= l*b*h

V = 25*5*(x-2)

V = 125(x-2)

V = 125x - 250 → Answer

b).

(i)

V = 750cm³

V = 125x - 250

750 = 125x - 250..........(i)

(ii)

The equation (i) is: 750 = 125x - 250

or, 125x = 750+250

or, 125x = 1000

or, X = 1000/125

Therefore, X= 8cm.

(iii)

Height (h) = x-2

= 8-2

= 6

Therefore, height is 6cm.

Hope it helps!

6 0

3 years ago

For which of the following compound inequalities is there no solution? ​

For which of the following compound inequalities is there no solution?