(1)Identify the surface whose equation is r = 2cosθ by converting first to rectangular coordinates...(2)Identify the surface whose equation is r = 3sinθ by converting first to rectangular coordinates...(3)Find an equation of the plane that passes through the point (6, 0, −2) and contains the line x−4/−2 = y−3/5 = z−7/4...(4)Find an equation of the plane that passes through the point (−1,2,3) and contains the line x+1/2 = y+2/3 = z-3/-1...(5)Find a) the scalar projection of a onto b b) the vector projection of a onto b given = 〈2, −1,3〉 and = 〈1,2,2〉...(6)Find a) the scalar projection of a onto b b) the vector projection of a onto b given = 〈2,1,4〉 and = 〈3,0,1〉...(7)Find symmetric equations for the line of intersection of the planes x + 2 y + 3z = 1 and x − y + z = 1...(8)Find symmetric equations for the line of intersection of the planes x + y + z = 1 and x + 2y + 2z = 1...(9)Write inequalities to describe the region consisting of all points between, but not on, the spheres of radius 3 and 5 centered at the origin....(10)Write inequalities to describe the solid upper hemisphere of the sphere of radius 2 centered at the origin....(11)Find the distance between the point (4,1, −2) and the line x = 1 +t , y = 3 2−t , z = 4 3−t...(12)Find the distance between the point (0,1,3) and the line x = 2t , y = 6 2−t , z = 3 + t...(13)Find a vector equation for the line through the point (0,14, −10) and parallel to the line x=−1+2t, y=6-3t, z=3+9t<span>...</span>
Answer:
Step-by-step explanation:
given 
the factor (x - 3) can be cancelled from the numerator/ denominator leaving
8/x-7=7/2
16=7(x-7) cross multiply
16=7x-49
-7x=-49-16
-7x=-65 divides each side by -7
-7x/7=-65/7
X=65/7
Alternative form
X=92/7
Which is 1st options in your questions.
Hope this helps!
Let's start with x... Since angle AOE is a 90 degree angle, then we know the supplementary angle EOB is also 90 degrees. The 2 angles that make up angle EOB are given to us as expressions. Added together the must equal 90 degrees...
(x+8) + (2x-8) = 90
3x = 90
x = 30
Now if we look at y, we see it is an opposite angle from angle DOB. Because it is opposite, it is also congruent... so it has to be equal to angle DOB... and since angle DOB is 2x - 8, we can substitute x with the answer we found in the last step, 30, to find the angle.
2x - 8= y
2(30) - 8 = y
60 - 8 = y
y = 52 degrees
Since angle DOB equals 52 degrees, then y = 52 degrees
x = 30 degrees
y = 52 degrees
*Note, you can also find the value of angles GOF and EOD by plugging x (30) into the expressions.
Answer:
105
Step-by-step explanation:
LN = 6x
LN = LM + MN ➡ LN = 4x + 8 + 27 so 6x = 4x + 8 + 27
2x = 35 and x = 17.5
6 × 17.5 = 105
