Your answer should be 0.3000
Answer:
<u>Option D: A cylinder with a circumference of about 50 units</u>
Step-by-step explanation:
The rest of the question is the attached figure.
The square shown has a perimeter of 32 units. The square is rotated about line k. What shape is created by the rotation and what is the approximate circumference of the base? Circumference of a circle: C = 2πr
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Given: the perimeter of the square = 32
perimeter of a square is four times the length of its side
So, the side length of square = 32/4 = 8 units
The square is rotated about line k.
So, it will form a cylinder with radius 8 units.
Circumference of a circle = 2 π r
Where, r is the radius of the circle.
Circumference of the base is C = 2 π * 8
∴ C = 16π = 16 * 3.14
∴ C = 50.26548 ≈ 50
The shape is created by the rotation is a cylinder with a circumference of about 50 units.
<u>So, the answer option is D.</u>
Answer:
Exponential decay.
Step-by-step explanation:
You can use a graphing utility to check this pretty quickly, but you can also look at the equation and get the answer. Since the function has a variable in the exponent, it definitely won't be a linear equation. Quadratic equations are ones of the form ax^2 + bx + c, and your function doesn't look like that, so already you've ruled out two answers.
From the start, since we have a variable in the exponent, we can recognize that it's exponential. Figuring out growth or decay is a little more complicated. Having a negative sign out front can flip the graph; having a negative sign in the exponent flips the graph, too. In your case, you have no negatives; just 2(1/2)^x. What you need to note here, and you could use a few test points to check, is that as x gets bigger, (1/2) will get smaller and smaller. Think about it. When x = 0, 2(1/2)^0 simplifies to just 2. When x = 1, 2(1/2)^1 simplifies to 1. Already, we can tell that this graph is declining, but if you want to make sure, try a really big value for x, like 100. 2(1/2)^100 is a value very very very veeery close to 0. Therefore, you can tell that as the exponent gets larger, the value of the function goes down and gets closer and closer to zero. This means that it can't be exponential growth. In the case of exponential growth, as the exponent gets bigger, your output should increase, too.
Answer:
20/49
Step-by-step explanation:
<span>D. She wrote articles and gave speeches about hate crimes against blacks in the south.</span>
