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3 years ago

Choose Yes or No to tell if the fraction

Mathematics

1 answer:

Ivahew [28]3 years ago

8 0

Answer:

adding $\frac{3}{5}$ in the blank space makes the equation true.

Step-by-step explanation:

i) $\dfrac{7}{20}$ + $\dfrac{3}{5}$ = $\dfrac{7}{20}$ + $\dfrac{12}{20}$ = $\dfrac{7 + 12}{20}$ = $\dfrac{19}{20}$

ii) From the above equation we see that adding $\dfrac{3}{5}$ in the blank space makes the equation true.

iii) first the fraction of $\dfrac{3}{5}$ is multiplied by 4 on top and bottom which gives us the value of $\dfrac{12}{20}$ which now has the same denominator as $\dfrac{7}{20}$ and so the numerator of the two fractions can be added which gives the result $\dfrac{19}{20}$ which makes the equation true.

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mars1129 [50]

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3 years ago

Read 2 more answers

A tank contains 8000 L of pure water. Brine that contains 35 g of salt per liter of water is pumped into the tank at a rate of 2

OleMash [197]

Answer:

The concentration of salt in the tank approaches $35 \mathrm{g} / \mathrm{L},$

Step-by-step explanation:

Data provide in the question:

Water contained in the tank = 8000 L

Salt per litre contained in Brine = 35 g/L

Rate of pumping water into the tank = 25 L/min

Concentration of salt $\lim _{t \rightarrow \infty} C(t)=\lim _{t \rightarrow \infty} \frac{35 t}{320+t}$

Now,

Dividing both numerator and denominator by $t$ , we have

$\lim _{t \rightarrow \infty} \frac{\frac{1}{t} 35 t}{\frac{1}{t}(320+t)}=\lim _{t \rightarrow \infty} \frac{35}{\frac{320}{t}+1}=35$

Here,

The concentration of salt in the tank approaches $35 \mathrm{g} / \mathrm{L},$

3 0

4 years ago

Find the distance between a point (– 2, 3 – 4) and its image on the plane x+y+z=3 measured parallel to a line

Ber [7]

Answer:

The distance is:

$\displaystyle\frac{3\sqrt{142}}{10}$

Step-by-step explanation:

We re-write the equation of the line in the format:

$\displaystyle\frac{x+2}{3}=\frac{y+\frac{3}{2}}{2}=\frac{z+\frac{4}{3}}{\frac{5}{3}}$

Notice we divided the fraction of y by 2/2, and the fraction of z by 3/3.

In that equation, the director vector of the line is built with the denominators of the equation of the line, thus:

$\displaystyle\vec{v}=\left< 3, 2, \frac{5}{3}\right>$

Then the parametric equations of the line along that vector and passing through the point (-2, 3, -4) are:

$x=-2+3t\\y=3+2t\\\displaystyle z=-4+\frac{5}{3}t$

We plug them into the equation of the plane to get the intersection of that line and the plane, since that intersection is the image on the plane of the point (-2, 3, -4) parallel to the given line:

$\displaystyle x+y+z=3\to -2+3t+3+2t-4+\frac{5}{3}t=3$

Then we solve that equation for t, to get:

$\displaystyle \frac{20}{3}t-3=3\to t=\frac{9}{10}$

Then plugging that value of t into the parametric equations of the line we get the coordinates of the intersection:

$\displaystyle x=-2+3\left(\frac{9}{10}\right)=\frac{7}{10}\\\displaystyle y=3+2\left(\frac{9}{10}\right)=\frac{24}{5} \\\displaystyle z=-4+\frac{5}{3}\left(\frac{9}{10}\right)=-\frac{5}{2}$