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2 years ago

A circular garden has a diameter of 12 yards. What is the area of the garden? Use 3.14 for pi.

Mathematics

2 answers:

dimaraw [331]2 years ago

8 0

Answer:

$Solution,\\Diameter~of~the~circular~garden(d) = 12 yards\\Now,\\Area~of~the~circular~garden = \pi (\frac{d}{2})^2 = 3.14(6)^2= 113.04 sq. yard$

Katarina [22]2 years ago

3 0

Answer:

Step-by-step explanation:

113.04

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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:

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

Then to find the distance we just use the distance formula:

$\displaystyle d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2+(z_1-z_2)^2}$

So we get:

$\displaystyle d=\sqrt{\left(-2-\frac{7}{10}\right)^2+\left(3-\frac{24}{5}\right)^2+\left(-4 +\frac{5}{2}\right)^2}=\frac{3\sqrt{142}}{10}$

3 0

2 years ago

LMNP is a rectangle. Find the value of x and the length of each diagonal. LN= x and MP= 2x -8

loris [4]

Answer:

<h2>x = 8 (Verified) ✅</h2>

Step-by-step explanation:

If we visualize the figure, we can see that sides LN and MP are going to be parallel and of the same length.

So x = 2x - 8

Subtract x

0 = x - 8

x = 8

Check the answer

8 = 2(8) - 8

8 = 16 - 8

8 = 8 ✅

3 0

2 years ago

Help me pls. I need help with the question

likoan [24]

Answer:

$173.90

Step-by-step explanation:

The most obvious way to answer this question is to multiply $9.40 by 18.5

This would result in 173.90.

But I realize nobody like to deal with decimals in a multiplication problem, so here's the way I would do it (<em>especially if you don't have a calculator!</em>)

The strategy is to break it down!

Multiply $9.40 x 18 hours to start, since this is easier.

$9.4 x 18 = 169.2$