Cannot see your image, but the formula for the volume of a sphere is
V=(4/3)πr³
to solve for r: r³=v÷(4/3)π=v*3/(4π)=3v/(4π) (three v out of 4 pi)
r=∛(3v/4π)
r equals the cubic root of (three v over 4π)
Perpendicular lines have slopes that are negative reciprocals. example: line a has a slope of 2/3, line b has a slope if -3/2 if they are perpendicular.
To answer the question above, we are simply to subtract the length of the gold ribbon which is 2 4/6 ft from the length of the silver ribbon, 5 2/6 feet. Mathematically,
5 2/6 feet - 2 4/6 feet = 8/3 feet
Therefore, Gina has 8/3 feet more of the silver ribbon than the golden ribbon.
Answer:
Step-by-step explanation:
We'll just work on solving both so you can see what's involved in solving an absolute value equation. Because an absolute value is a distance, we can have that distance being both to the right on the number line of the number in question or to the left. For example, from 2 on the number line, the numbers that are 5 units away are 7 and -3. Using that logic, we will simplify the equation down so we can set up the 2 basic equations needed to solve for x.
If 
then
What you need to remember here is that you cannot distribute into a set of absolute values like you would a set of parenthesis. The -2 needs to be divided away:
Now we can set up the 2 main equations for this which are
.5x + 1.5 = .5 and .5x + 1.5 = -.5
Knowing that an absolute value will never equal a negative number (because absolute values are distances and distances will NEVER be negative), once we remove the absolute value signs we can in fact state that the expression on the left can be equal to a negative number on the right, like in the second equation above.
Solving the first one:
.5x = -1 so
x = -2
Solving the second one:
.5x = -2 so
x = -4
Answer:
Option D
Step-by-step explanation:
The questions which involve calculating the angles and the sides of a triangle either require the sine rule or the cosine rule. In this question, the two sides that are given are adjacent to each other the given angle is the included angle. This means that the angle B is formed by the intersection of the lines a and c. Therefore, cosine rule will be used to calculate the length of b. The cosine rule is:
b^2 = a^2 + c^2 - 2*a*c*cos(B).
The question specifies that c=71, B=123°, and a=65. Plugging in the values:
b^2 = 65^2 + 71^2 - 2(65)(71)*cos(123°).
Simplifying gives:
b^2 = 14293.0182932.
Taking square root on the both sides gives b = 119.6 (rounded to the one decimal place).
This means that the Option D is the correct choice!!!
