Answer:
-30(x-4) + 29 (y-1) -12(z-3) = 0
Step-by-step explanation:
You can find the perpendicular vector to both curves using the cross product between them, and that will give you all the information you need to find the equation of the tangent plane to the surface S.
Let's find the parameter of each curve for the specific point.
For the first curve notice that
And for the second curve notice that
Thus for the first curve we reach our point at 
and for the second curve we reach our point at 
Then we compute the tangent vector to our curves, and it would be given by the derivative so
and at 
we have that
Similarly
The the cross product between the two vectors would be
Since (-30,29,-12) would be the perpendicular vector to the tangent plane and (4,1,3) would be a point of the tangent then we would have that the equation of the tangent plane is given by
-30(x-4) + 29 (y-1) -12(z-3) = 0
Now to solve this problem, all we have to remember is the
formula for calculating the linear speed given the radial speed, that is:
v = r w
where,
v = is the linear velocity or linear speed
r = is the radius of the circular disk = (1 / 2) diameter
= (1/ 2) (2.5 inches) = 1.25 inches
w = is the radial velocity (must be in rad per time) =
7200 rev per minute
Calculating for v:
v = 1.25 inches (7200 rev per minute) (2 π rad / 1 rev)
v = 56,548.67 inches / minute
Converting to miles per hour:
v = 56,548.67 inches / minute (1 mile / 63360 inches) (60
min / hour)
<span>v = 53.55 mile / hour</span>
The simplified answer is 0.25-3x
3.4+0.4+4.17=7.97 you just have to try different combinations of different numbers with the decimals.
Answer: 251 stickers
Step-by-step explanation:
She had 27 stickers before she started her sticker buying spree 14 days ago (2 weeks)
She bought 3 stickers on the 1st day of those 14
Then she started increasing in by 2 each day
Total for those 14 days = 3+5+7+9+11+13+15+17+19+21+23+25+27+29
Adding the 27 she already had
3+5+7+9+11+13+15+17+19+21+23+25+27+29+27 = 251 stickers
