I do not understand most of these, Please help
To A
the area of the rhombus is $\displaystyle 4 \times _{area} \triangle UMW$
to find the area of the triangle use the $\displaystyle \frac {1}{2} \cdot base \cdot height$ formula (note, you have to find the height, use Pythagoras' theorem
got it?
do you know what a rhombus is? do you know the properties of a rhombus? see here
questions become easier when you know what you are dealing with
B is $\displaystyle 81 \sqrt {3}$
but i think that's what you meant to type... right?
double check question C. something is wrong with it
D is correct
clarify question E, what exactly is raised to the 4th power?
To F.
the circumference of a circle is given by:
$\displaystyle C = 2 \pi r$
For circle R, $\displaystyle 12 \pi = 2 \pi r_R \implies \boxed { r_R = 6 }$
For circle S, $\displaystyle 32 \pi = 2 \pi r_S \implies \boxed { r_S = 16 }$
Thus, the ratio of the radius of S to the radius of R is:
$\displaystyle r_S:r_R = \frac {r_S}{r_R} = \frac {16}{6} = \frac {8}{3} = 8:3$
4pir4, I think the r is to the 4th and to the 6th for 16pir6.
I have no clue about latex and there are no images with the other question
Here is how it looks after finding the symbols
Area of circle P is 4πr4 and area of circle Q is16πr6. Which is the ratio of a radius of Q to a radius of P
The last 4 and the 6 are the powers and I think they go with the r.
here it is:
E
Recall that the area of a circle is given by $\displaystyle A = \pi r^2$
So, for P: $\displaystyle P_{area} = 4 \pi r^4$
$\displaystyle \Rightarrow 4 \pi r^4 = \pi r_P^2$
$\displaystyle \Rightarrow 4r^4 = r_P^2$
$\displaystyle \Rightarrow r_P = \sqrt {4 r^4} = 2r^2$
For Q: $\displaystyle Q_{area} = 16 \pi r^6$
$\displaystyle \Rightarrow 16 \pi r^6 = \pi r_Q^2$
$\displaystyle \Rightarrow 16r^6 = r_Q^2$
$\displaystyle \Rightarrow r_Q = \sqrt {16r^6} = 4r^3$
So the ratio of the radius of Q to the radius of P is:
$\displaystyle r_Q : r_P = \frac {r_Q}{r_P} = \frac {4r^3}{2r^2} = 2r$
I want to thank you so much for this. You are GREAT! That just leaves A and C and I have tried to get them. I don't have any images for C just what I posted and those are the answers I can choose from. I think when I am trying to use the P theorem, I am putting the numbers in the wrong place in the formula for A.
i will look over C again and see if i can decipher what you want to say.
to A
see the diagram below:
Pythagoras theorem says: If the sides of a right-triangle have lengths $\displaystyle a$, $\displaystyle b$ and $\displaystyle c$, (where $\displaystyle c$ is the hypotenuse), then the sides can be related as follows:
$\displaystyle a^2 + b^2 = c^2$
In the triangle below, $\displaystyle c = 14$, $\displaystyle a = 10$, we want to find $\displaystyle b$ which is $\displaystyle x$ on the diagram.
$\displaystyle a^2 + b^2 = c^2$
$\displaystyle \Rightarrow b^2 = c^2 - a^2$
$\displaystyle \Rightarrow b = \sqrt { c^2 - b^2 }$
$\displaystyle \Rightarrow b = x = \sqrt {14^2 - 10^2} = \sqrt {96}$
So the area of the triangle is:
$\displaystyle A = \frac {1}{2}bh = \frac {1}{2} 10 \cdot \sqrt {96} = 5 \sqrt {96}$
the area of the rhombus is 4 times the area of one triangle.
so area of rhombus is: $\displaystyle A_R = 4 \times 5 \sqrt {96} = 20 \sqrt {96} = 80 \sqrt {6}$
Ratio of circumference of circle C to its radius is 12pi. Which is the area of the circle? 36pi,34pi,28pi, or 24pi
I found a place that says
The distance around a circle is called the circumference. The distance across a circle through the center is called the diameter. is the ratio of the circumference of a circle to the diameter. Thus, for any circle, if you divide the circumference by the diameter, you get a value close to .
C=2*pi*r
So 12pi=2*pi*r
Then what?