The cone equation gives
which means that the intersection of the cone and sphere occurs at
i.e. along the vertical cylinder of radius
when
.
We can parameterize the spherical cap in spherical coordinates by
where
and
, which follows from the fact that the radius of the sphere is 3 and the height at which the sphere and cone intersect is
. So the angle between the vertical line through the origin and any line through the origin normal to the sphere along the cone's surface is
Now the surface area of the cap is given by the surface integral,
-9 × 3 - 4² = -27 - 16 = -43
3² + 2² = 9 + 4 = 13
(-9 × 3 - 4²)/(3² + 2²) = -43/13 = -3 4/13
<span>Together they wrap 14+12 = 26 boxes per hour.
t hours × 26 boxes/hour = 65 boxes
C</span><span>
</span>
Answer:
(-5,0) and (4,0)
x= -5 and x= 4
Step-by-step explanation:
Going from top to bottom
A) All sides add up to 180 so just subtract the other angles from 180 to get the last ----- 180-(53+78)= 49. x=49
B) The little square means 90 and since the lines are equal the other two angles are equal. so ------2x+90=180 bring 90 over 2x=90 then divide by the 2 and get x=35
C) For this one since they all have a x you can say all of them added together is 180 so ----- 3x-11+6x-10+x=180 you can add like terms and have 10x-21=180 add 21 over 10x=201 then divide 201 by 10 and get x=20.1
D) This will take two different equations first do as you did in A for the right triangle ---- 180-(75+67) and get 38 now the angle on the other triangle that it is across from is the same. 38 now do it once again 180-(28+38) and get x=114
Exterior angles add up to the inside angle across from it to make 180.
A) Find out what the inside angle is first --- 180-(73+62)=45 now x+45= 180 so just subtract 45 over and get x=135
B) Same as above but the square is 90. 180-(31+90)=59 now x+59=180 subtract 59 over and have x=121
C)Because the two lines are equal (Indicated by the ticks) the angles at the end are as well. so now you have 98+2x= 180 subtract 98 over get 2x=82 then divide by the 2 and get x=41
D) This one requires some thinking. We know that all three angles inside equal 180 and the one outside and the one inside equal 180 but we don't know what the angle inside by the outside angle is. (sorry if that's confusing) but since the outside one minus 180 is the inside one then we can put that in x+28+4x-3+7x-15-180 = 180 (I put everything in but for the missing angle I put the outside one minus 180) you can first combine terms and have 12x-170=180 add 170 over and have 12x=350 then divide by 12 and get about 29.1 but that's just the missing angle! Next you can put that with the outside one and get 7x-15+29.1=180 combine 7x+14.1=180 subtract 14 7x=166.1 then divide and get x=23.7
I hoped this helped - all the answers are at the bottom of the explanation and the only one i'm not sure of is the last D
