Answer:
24 mm^2
Step-by-step explanation:
length x width x 6 sides in a cube
(2)(2)(6)=24
If the equation of the circle is x^2+ y^2 = 41, we must first understand the parts of the equation.
A general circle's equation is (x-h)^2+(y-k)^2= r^2
(h.k) is the radius of the circle
r is the radius of the circle
Another useful fact to know is that tangent lines touch the circle at one point (4,5)
Since in our original equation there are no h or k values, we can assume that the center of the circle is (0,0).
The formula for slope is <u>Y1-Y2</u>
X1-X2
We can break this down with our two points (center and tangent)
(0,0) and (-4,-5)
(X1,Y1) and (X2,Y2)
therefore, we will put the equation as such
<u>0-(-5)= 5</u> = <em> </em><u><em>5</em></u>
0-(-4)= 4 <em> 4</em>
<em>this is our slope from the center to the point of tangency.</em>
We know that tangent lines are perpendicular to the radius, which we've already found the slope of. Perpendicular lines are opposite reciprocals of the line they are perpendicular to.
Therefore, we take our slope from center to the tangent, and make it opposite and then take the reciprocal of that slope, which will give us the slope of the tangent line itself. (note: reciprocal means flip the numerator and denominator)
<u>5</u> = <u>-5</u> = <u>-4</u><u>
</u>4 4 5
Now, we have a point on the line, and the line's slope. We can use slope-intercept equation to find the equation of the line.
Slope-int y=mx+b
(x,y) is a point,
m is the slope
b is the y intercept ( the point where x=0, or where its on the y axis)
now we plug things in
(-4,-5) is our point,
<u>-4</u> is our slope
5
-5=<u>-4</u>(-4)+b After we plug things in, solve for b
5
-5= 3.2+b
-1.8= b or b= <u />1 <u>4</u>
5
Now we just need to rewrite our equation with all our components.
(-4.-5) = point
<u>-4</u> = slope<u>
</u>5
1 <u>4</u> = y-intercept<u>
</u> 5
<em>y=</em><u><em>-4</em></u><em> x+ 1 </em><u><em>4</em></u><em> This is the equation of the tangent line</em><u>
</u><em> 5 5</em>
Hope that helped
Answer:
Degree of the polymonial is the highest of the degrees of the polynomial's monomials with non-zero coefficients.
Step-by-step explanation:
I think the equation is 4m² – 3
Therefore, degree of the polynomial is the sum of the powers of the variables,
2 + 6 + 4 = 12
Hope this helps!
Answer:
65.97
Step-by-step explanation:
volume of a cone is pi(r)^2(h)/3
hope this helps
Given that Jordan has a new puppy and she wants to put a fence around part of her yard to cover an area of 200 square feet.
Now we have to find what dimensions (length x width) should she make the rectangular area. None of the length or width are given so there can be lots of answers.
Since area is rectangular and we know that rectangle has different value of length and width so we just need to find two factors of given area 200 square feet.
For example 20 times 10 is 200.
So the dimension of the rectangular area will be:
Length = 20 feet and width = 10 feet
Now perimeter of the rectangle is given by formula:
Perimeter = 2(length+width) = 2(20+10)=2(30)=60
Hence perimeter is 60 feet.
