The a question is attached below

Mathematics

1 answer:

Stells [14]3 years ago

5 0

Answer:

22.2m

Step-by-step explanation:

vol of a sphere = 4/3 x pi x r^3

vol of a hemisphere is 1/2 the vol of a sphere, so vol of a hemisphere= 2/3 x pi x r^3

2/3pi x r^3 = 257

Divide both sides by 2/3pi

r^3 = 122.708

Cube root both sides.

r = 11.077

Diameter is twice the radius, so diameter = 22.154m

To the nearest 10th of a meter this is 22.2m.

Hope I helped x

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Is the point (1,3) a solution to the linear equation 5x-9y=32? explain

harina [27]

There are many ways to check if the point (1,3) is a solution to the linear equation $5x-9y=32$ .

Let us check it by expressing y in terms of x.

The given expression is 5x-9y=32. If we add -5x to both sides we will get:

$-9y=-5x+32$

Multiplying both sides by -1 we will get:

$9y=5x-32$

In order to isolate y, we will divide both sides by 9 to get:

$y=\frac{5}{9}x-\frac{32}{9}$

Now let us plug in the given value of x=1 from the point (1,3). This should give us y=3. Let us see if we get y=3 when we plug x=1 in the above equation.

$y=\frac{5}{9}\times 1-\frac{32}{9}=\frac{5-32}{9}$

$\therefore y=\frac{-27}{9}=-3$

Thus, we see that when x=1, y=-3 and that $y\neq 3$ and hence we conclude that the point (1,3) is not a solution to the original given linear equation 5x-9y=32.

For a better understanding of the explanation given here a graph has been attached. As can be seen from the graph, (1,3) does not lie on the straight line that represents 5x-9y=32, but (1,-3) does lie on it as we had just found out.