ANSWER
The length of a Diameter is 3.714
EXPLANATION
The circumscribed triangle is shown in the attachment.
We use the cosine ratio to find the altitude of the isosceles triangle.
![\cos(60 \degree) = \frac{altitude}{hypotenuse}](https://tex.z-dn.net/?f=%20%5Ccos%2860%20%5Cdegree%29%20%20%3D%20%20%5Cfrac%7Baltitude%7D%7Bhypotenuse%7D%20)
![\cos(60 \degree) = \frac{altitude}{8}](https://tex.z-dn.net/?f=%20%5Ccos%2860%20%5Cdegree%29%20%20%3D%20%20%5Cfrac%7Baltitude%7D%7B8%7D%20)
Altitude =8cos(60°)
Altitude=4cm
Let the upper half of the altitude be y cm.
Then the radius of the circle is (y-4)cm
The upper radius meets the tangent at right angles.
From the smaller right triangle,
![\sin(60 \degree) = \frac{4 - y}{y}](https://tex.z-dn.net/?f=%20%5Csin%2860%20%5Cdegree%29%20%20%3D%20%20%5Cfrac%7B4%20-%20y%7D%7By%7D%20)
![y\sin(60 \degree) = 4 - y](https://tex.z-dn.net/?f=%20y%5Csin%2860%20%5Cdegree%29%20%20%3D%204%20-%20y)
![y\sin(60 \degree) + y= 4](https://tex.z-dn.net/?f=y%5Csin%2860%20%5Cdegree%29%20%20%20%2B%20y%3D%204%20)
![(\sin(60 \degree) + 1)y= 4](https://tex.z-dn.net/?f=%28%5Csin%2860%20%5Cdegree%29%20%20%20%2B%201%29y%3D%204%20)
![y= \frac{4}{\sin(60 \degree) + 1}](https://tex.z-dn.net/?f=y%3D%20%20%5Cfrac%7B4%7D%7B%5Csin%2860%20%5Cdegree%29%20%20%20%2B%201%7D%20)
![y = 16 - 8 \sqrt{3}](https://tex.z-dn.net/?f=y%20%3D%2016%20-%208%20%5Csqrt%7B3%7D%20)
y=1.857
The diameter is 2y
![d = 32 - 16 \sqrt{3}](https://tex.z-dn.net/?f=d%20%3D%2032%20-%2016%20%5Csqrt%7B3%7D%20)
=2(1.875)
The length of a Diameter is 3.714
It depends on what the composite figure is, but use the formulas, such as A=1/2bh for the triangle and A=bh, for the square and the rectangle.
Answer:
Step-by-step explanation:
The two different rentals give rise to two equations. Let t and c represent the rental costs of a table and chair, respectively. The rentals are ...
5c +2t = 23
3c +8t = 58
Cramer's rule tells you ...
c = (2·58 -8·23)/(2·3-8·5) = -68/-34 = 2.00
t = (23·3 -58·5)/-34 = -221/-34 = 6.50
The cost to rent each chair is $2.00.
The cost to rent each table is $6.50.
_____
<em>Cramer's Rule</em> says the solution to
ax +by = c
dx +ey = g
is ...
x = (bg -ec)/(bd -ea)
y = (cd -ga)/(bd -ea)
When the equation's coefficients are not convenient to achieve elimination of a variable, Cramer's rule can get to the solution very quickly. The same number of math operations are involved, but they are expressed in terms of a formula that can be used with no guesswork.
Answer:
-6/5 x 5/3 x 11
Step-by-step explanation:
the commutative property states that x * y = y * x where "x" is a number and "y" is also a number and also x+y=y+x. also "*" is the multiplication symbol
-6/5*11*5/3 can be re-arranged into 11*-6/5*5/3 you can cancel the numbers to get 11*-2/3*5=55*-2/3=-110/3