Answer:
where the Question, i will help u i just need the work in order to help you
Step-by-step explanation:
Answer: ~54.54 units squared, or 25*pi - 24
Step-by-step explanation:
To find this, we need to find both the area of the triangle and circle, and then subtract the area of the triangle from the area of the circle.
Area of triangle: 
Area of circle: 
To find the radius, we first need to find the hypotenuse of the triangle, which happens to be the diameter of the circle.
Pythagorean Theorem: 
, where a and b are sides and c is the hypotenuse.
6^2 + 8^2 = c^2
36 + 64 = 100, c = 10
Knowing that the diameter is 10, we also know that the radius is 5.
Area of the circle with a radius of 5 is 25*pi, or 78.54~
Area of the triangle with side lengths of 6 and 8 is 24.
78.54 - 24 = 54.54 units squared.
The area of a rectangle is found using the formula A=LW. You need to express the length and width of this table using one variable. Since the length is described in terms of the width, let's call the width w. The length is 3m more than the width, so we can call the length w+3. Put these expressions of the length and width into the formula:
<span>A=LW, A=88m</span>²<span>, L= (w+3), w=w substitute: </span>
<span>88=w(w+3) (ok I did WL instead of LW but it's the same thing) Distribute the w: </span>
<span>88 = w</span>²<span>+3w subtract 88 from each side </span>
<span>0 = w</span>²<span>+3w-88 factor. w^2 can only be factored by w*w so set that up: </span>
<span>(w )(w ). Now look at the last term, it is -88. You need to find two factors of -88, and since factors multiply to get the number, you must have one positive and one negative factor to get -88, so go ahead and put them into your parentheses: </span>
<span>(w+ )(w- ). Now find factors of -88 that when added together give you 3, the coefficient of the middle term. -8 and 11 add up to 3, so put those into your factors: </span>
<span>(w+11)(w-8) and remember that this equals 0: </span>
<span>(w+11)(w-8)=0 Now when you multiply two numbers and get a product of 0, at least one of those numbers must equal 0 since any number times 0 equals 0. Either one can be 0, so set each equal to 0: </span>
<span>w+11=0 subtract 11 from each side </span>
<span>w= -11 </span>
<span>w-8=0 add 8 to each side </span>
<span>w=8 </span>
<span>Now you're asked to give the length and width of the table top. The table can't have a dimension that is negative, so we can discard the solution w= -11. We find that the width of the table is 8 feet. To find the length, go back to how we expressed the length, 3 more than the width: </span>
<span>L=3+w, w=8 substitute </span>
<span>L=3+8 add </span>
<span>L=11. </span>
<span>So the length of your table top is 11m and the width is 8m.</span>
Answer:
The coordinates of the circumcenter of triangle ABC is 
.
Step-by-step explanation:
The circumcenter of triangle ABC is the point of intersection of any two perpendicular bisectors of any two sides of the given triangle.
The equation of the perpendicular bisector of side B(3,0) and C(3,2) is 
.
Since the midpoint of AB is 
and its slope is undefined. The perpendicular bisector has a slope of zero. The equation of such line is 
.
Also the equation of the perpendicular bisector of A(0,0) and B(3,0) is 
. The reason is that the midpoint of AB is 
and its slope is zero. The perpendicular bisector will have an undefined slope. The equation of such line is given by 
.
These two perpendicular bisectors will intersect at . These are the coordinates of the circumcenter of the triangle.
