2-to the 4th power
2 to the 4th power is equal to 16.
What is the radius of the circle described by
the equation (x-6)2 + (y-4)2-64 = 0?
The equation of a circle with center (a, b) and radius r is given by:
(x - a)^2 + (y - b)^2 = r^2
We can rewrite the given equation in this form by rearranging the terms:
(x - 6)^2 + (y - 4)^2 = 64
Comparing this with the equation of a circle, we can see that the center of the circle is at (a, b) = (6, 4) and the radius is sqrt(64) = 8.
Therefore, the radius of the circle described by the equation (x-6)^2 + (y-4)^2-64 = 0 is 8.
In a construction paper pad, every 7th sheet of paper is red.
Every 2nd sheet of paper has a drawing on it. Starting at the beginning of the pad of construction paper, which is the first sheet that is both red and has a drawing on it?
We need to find the first sheet of paper that satisfies both conditions, i.e. is both red and has a drawing on it.
Let's start by finding the first red sheet of paper. We know that every 7th sheet of paper is red, so we can use division to find the first multiple of 7 that is greater than or equal to 1:
7 goes into 1 zero times with a remainder of 1
7 goes into 10 one time with a remainder of 3
So the first red sheet of paper is the 7th sheet.
Now let's find the first sheet of paper with a drawing on it. We know that every 2nd sheet of paper has a drawing, so we can use division to find the first even number that is greater than or equal to 1:
2 goes into 1 zero times with a remainder of 1
2 goes into 2 one time with no remainder
So the first sheet with a drawing on it is the 2nd sheet.
To find the first sheet that satisfies both conditions, we need to find the first multiple of 7 that is also an even number. We can do this by multiplying 7 by 2:
7 x 2 = 14
So the first sheet that is both red and has a drawing on it is the 14th sheet.
Estimate:
20 is 22% of what number?
To estimate, we can make use of the fact that 20 is approximately one-fifth (or 20%) of 100.
So if 20 is 20% of a number, that number is about 5 times larger than 20, which is 100.
We are looking for the number that 20 is 22% of, which means that the actual number will be smaller than 100 x 5 = 500.
To get an estimate, we can round 22% to 20% and use the same calculation.
20 is approximately 20% of 100, so the number that 20 is approximately 20% of is 5 times larger than 20, which is 100.
To adjust for the extra 2%, we can add 2% of 100, which is 2, to our estimate:
100 + 2 = 102
So an estimate for the number that 20 is 22% of is 102.
The volume of the rectangular pyramid is 360 cubic feet. The height, h, is 15 feet, and the width of the base, w, is 6 feet.
What is the length of the base, I, of the rectangular pyramid?
We can start by using the formula for the volume of a rectangular pyramid, which is:
V = (1/3)Bh
where B is the area of the base, h is the height, and V is the volume.
We are given that the volume is 360 cubic feet, the height is 15 feet, and the width of the base is 6 feet. We can substitute these values into the formula to get:
360 = (1/3)(B)(15)
Simplifying, we can divide both sides by 15 and multiply by 3 to solve for the area of the base:
360/15 x 3 = B
B = 72
Now we need to find the length of the base. We know that the area of the base is the product of the length and width:
B = lw
Substituting the values we know, we get:
72 = l(6)
Simplifying and solving for l, we get:
l = 12
Therefore, the length of the base of the rectangular pyramid is 12 feet.
Determine the vertex form and the maximum or minimum value of the function.
f(x) = 2xsecond power+ 8x + 3