Parallel: the lines have = slopes. We thus need 5/6 to equal 2/p. then 5p must equal 12, and p = 12/5. (answer)
Check: Is 5/6 = 2 / (12/5)? YES
Perp.: The lines have slopes that are negative reciprocals of one another.
Then -6/5 = 2/p, or
-6 2
---- = ----
5 p Thus, -6p = 10, and p = -5/3 (answer)
Answer:
Step-by-step explanation:
18x² + 2 = 2 * 9x² + 2 *1
= 2*(9x² + 1)
Answer:
The rate of change in surface area when r = 20 cm is 20,106.19 cm²/min.
Step-by-step explanation:
The area of a sphere is given by the following formula:
In which A is the area, measured in cm², and r is the radius, measured in cm.
Assume that the radius r of a sphere is expanding at a rate of 40 cm/min.
This means that 
Determine the rate of change in surface area when r = 20 cm.
This is 
when 
. So
Applying implicit differentiation.
We have two variables, A and r, so:
The rate of change in surface area when r = 20 cm is 20,106.19 cm²/min.
1a. 21/3+32/5
((2*3)+1)/3+((3*5)+2)/5
7/3+17/5
(7*5+17*3)/15
86/15
1b. 2/3+3/5+2/5
(2*5+3*3+2*3)/15
(10+9+6)/15
25/15
5/3
2a. 57/10-22/5
(5*10+7)/10-(2*5+2)/5
57/10-12/5
(57*1-2*12)/10
33/10
2b. 5/12-1/4
(5*1-1*3)/12
2/12
1/6
3 say she has x stamps,she gave 2/9 and 1/5 to her frends so she is left with
X-2x/9-x/5
(9*5x-5*2x-9*1x)/45
(45x-10x-9x)/45
26x/45
4. 7/10+1/5
(1*7+2*1)/10
9/10
5. Brick 21/3kg
Stone (2*3+1)/3-(1*10+1)/10
7/3-11/10
(7*10-3*11)/30
(70-33)/30
37/30
Dilation refers to a non rigid motion where a figure is transform and its image has the same form but a different size measure.
Dilation is define by the rule (x,y)-- (kx, ky) where k represents the scale factor.
On this exercise is given that a triangle with vertices (-2,1), (8,4), and (3,0) was dilated by a scale factor of four, and it is asked to find the vertices of the image of the triangle after the dilation occurred.
Pre-image Image
(-2,1) -- (-2*4,1*4) -- (-8,4)
(8,4) -- (8*4,4*4) -- (32,16)
(3,0) -- (3*4,0*4) -- (12,0)
The coordinates representing the vertices of the triangle's image are (-8,4), (32,16), and (12,0); meaning that the ordered pair which is not a coordinate for a point in the triangle's image is (2,1).
