An Internet service provider offers a plan that allows a subscriber to download 2 GB or less of content per month. Define a vari
able for the amount downloaded. Identify the inequality and the graph that represents the content that can be downloaded.
1 answer:
Answer: Choice C
Graph with filled in circles at d = 0 and d = 2, shading in between
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Explanation:
d = amount downloaded in gigabytes
The smallest amount is d = 0. We cannot download a negative amount of data, so this is why d = 0 is the smallest.
The largest amount allowed is d = 2. This is the cap that the ISP has set up.
So basically d can be anything between d = 0 and d = 2, including both endpoints. This means
We use filled in circles for both endpoints to show to the reader "include these endpoints". Shading is done in between to show the entire solution set of possible d values. For instance d = 1 is in that region so it is possible to have this solution. Something like d = 4 is outside the region and not possible.
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Answer:
The area of the shaded region is about 38.1 square centimeters.
Step-by-step explanation:
We want to find the area of the shaded region.
To do so, we can first find the area of the sector and then subtract the area of the triangle from the sector.
The given circle has a radius of 6 cm.
And the given sector has a central angle of 150°.
The area for a sector is given by the formula:
In this case, r = 6 and θ = 150°. Hence, the area of the sector is:
Now, we can find the area of the triangle. We can use an alternative formula:
Where a and b are the side lengths, and C is the angle between them.
Both side lengths of the triangle are the radii of the circle. So, both side lengths are 6.
And the angle C is 150°. Hence, the area of the triangle is:
The area of the shaded region is equivalent to the sector minus the triangle:
Therefore:
Use a calculator:
The area of the shaded region is about 38.1 square centimeters.
Answer:
A. 60 degrees
Step-by-step explanation:
Solution to sin(x/2)=(/2)
By looking at this equation, I can identify that the answer must be within the first quadrant since the numerator and denominator are both positive.
Since it is in the first quadrant, the range of the value of the answer must be between 0 degrees less than or equal to x less than or equal to 90 degrees.
I can also identify that this is a 30, 60, 90 degree triangle because it has a and 2 as the numerator and denominator; in this case this tells us that we are dealing with a 30, 60, 90 degree triangle because that is the only triangle with those 2 respective sides.
Once identifying those two pieces of information, we can then determine the answer.
Since sin is equal Opposite/Hypotenuse, we can then substitute the sides of the triangle (, 2) to find the angle (unknown).
So the equation would look like this,
Sinx/2=/2 (
representing the opposite side of the angle; 2 representing the Hypotenuse of the triangle)
We can then conclude that 60 degrees is the unknown angle, due to the nature of a 30 60 90 degree triangle.
*Use the attachment for reference
Therefore, the answer, 60 degrees, is a solution to the equation "sin(x/2)=(/2)"
