Math › High School Math
What is if
and
?
In order to find we need to utilize the given information in the problem. We are given the opposite and adjacent sides. We can then, by definition, find the
of
and its measure in degrees by utilizing the
function.
Now to find the measure of the angle using the function.
If you calculated the angle's measure to be then your calculator was set to radians and needs to be set on degrees.
Find the length of an edge of the following cube:
The volume of the cube is .
The formula for the volume of a cube is
,
where is the length of the edge of a cube.
Plugging in our values, we get:
What is the circumference of a circle with a radius of ?
To find the circumference of a circle given the radius we must first know the equation for the circumference of a circle which is
We then plug in the number for the radius into the equation yielding
We multiply to find the value for the circumference is .
The answer is .
To the nearest tenth, give the area of a circle with diameter inches.
The radius of a circle with diameter inches is half that, or
inches. The area of the circle is
What is the area of a rectangle with a length of and a width of
?
The area of a rectangle is the length times the width:
Plug in our given values and solve:
How many radians are in ?
The conversion for radians is , so we can make a ratio:
Cross multiply:
Isolate :
What is the perimeter of a triangle with side lengths of ,
, and
?
To find the perimeter of a triangle you must add the three side lengths together.
In this case our equation would look like
Add the numbers together to get the answer .
What is the circumference of a circle with a radius of ?
To find the circumference of a circle given the radius we must first know the equation for the circumference of a circle which is
We then plug in the number for the radius into the equation yielding
We multiply to find the value for the circumference is .
The answer is .
Solve for :
To solve for in the equation
Square both sides of the equation
Set the equation equal to by subtracting the constant
from both sides of the equation.
Factor to find the zeros:
This gives the solutions
.
Verify that these work in the original equation by substituting them in for . This is especially important to do in equations involving radicals to ensure no imaginary numbers (square roots of negative numbers) are created.
To the nearest tenth, give the diameter of a circle with area 100 square inches.
The relationship between the radius and the area of a circle can be given as
.
We can substitute and solve for
:
Double this to get the diameter: , which we round to 11.3.