The region is a right circular cylinder of radius 3 , with the bottom at −7 and top at 7 . find the limits of integration on the triple integral for the volume of the cylinder using cartesian, cylindrical, and spherical coordinates and the function to be integrated. for your answers θ= theta, ϕ= phi, and rho= rho. cartesianv=∫ba∫dc∫fep(x, y,z) dydxdzwhere a= , b= , c= , d= , e= , f= and p(x, y,z)= .cylindricalv=∫ba∫dc∫fep(r,θ,z)drdθ dzwhere a= , b= , c= , d= , e= , f= and p(r,θ,z)= .spherical (which is twice the top half)hint: here you must write the volume as the sum of two integrals 0≤ϕ≤arctan(3/7) and arctan(3/7)≤ϕ≤π/2v=2[∫b1a1∫d1c1∫f1e 1p(rho,θ,ϕ)drhodϕdθ+∫b2a2∫d2c2∫f2e2 p(rho,θ,ϕ)drhodϕdθ]where a1= , b1= , c1= , d1= , e1= , f1= and p(rho,θ,ϕ)= .andwhere a2= , b2= , c2= , d2= , e2= , f2= and p(rho,θ,ϕ)=

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.

X> -2 is the simplified version.