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2 years ago

PRECALCULUS HONORS HELP ME PLZ AND THANKS

Mathematics

1 answer:

Natalka [10]2 years ago

6 0

Inequalities are used to show the relationship between unequal expressions

The set notation of (5) and (6) are: $\{x : -6 > x \ge -2\}$ and $\{x:-4 < x \ge 6\}$ .
See attachment for the graphs

The following should be notated when plotting the graph of an inequality

< and > are represented with open circles, while $\leq$ and $\geq$ are represented with closed circles
The arrows of and $\le$ point to the left, while the arrows of $>$ and $\geq$ point to the right.

So, we have:

$(a)\ -8 < x$

Rewrite as:

$x > -8$

The graph of $x > -8$ will point to the right, and it will use an open circle

$(b)\ -6 > x \ge -2$

Split the inequality:

$-6 > x$ and $x \ge -2$

It is not possible for -6 to be less than x and at the same time, x is greater than or equal to -2.

Hence. $-6 > x \ge -2$ cannot be represented on a graph

$(c)\ -4$

Split the inequality:

$-4 < x$ and $x \ge 6$

$-4 < x$ means that -4 is less than x or x is greater than -4.

So, we have:

$x > -4$ and $x \ge 6$

If $x > -4$ and $x \ge 6$ , then we make use of $x > -4$ because it contains more values of x.

The graph of $x > -4$ will point to the right, and it will use an open circle

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Use the numbers 12 through 17. Place them in the connected circles so that the numbers along each line have a sum of 50. Do this

Furkat [3]

Answer:

[13, 15, 17, 16, 12]

[16, 12, 17, 13, 15]

[16, 15, 14, 13, 12]

[17, 13, 15, 12, 14]

Step-by-step explanation:

Writing a Python code, I got the answers given, reading from left to right to down. For example, for [13, 15, 17, 16, 12], 13 is the top left circle, 15 is the middle right, 17 is the far right, 16 is the bottom left, and 12 is the bottom right

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2 years ago

Sphere and a cylinder have the same radius and height. The volume of the cylinder is 64 meters cubed.

Mrrafil [7]

Answer:

C. 128/3 meters cubed

Step-by-step explanation:

The volume of a cylinder is denoted by: $V=\pi r^2h$ , where r is the radius and h is the height. We know it's equal to 64, so we can set that equal to V:

$V=\pi r^2h$

$64=\pi r^2h$

We know that the sphere and cylinder have the same height and radius. However, the "height" of a sphere is actually the same as its diameter, which is twice its radius. Then, we can replace h in the above equation with 2r:

$64=\pi r^2h$

$64=\pi r^2*2r=2\pi r^3$

$\pi r^3=64/2=32$

Now, the volume of a sphere is denoted by: $V=\frac{4}{3} \pi r^3$ , where r is the radius. From above, we know that $\pi r^3=32$ , so we can plug this into the equation: