Match the integrals with the type of coordinates which make them the easiest to do. put the letter of the coordinate system to the left of the number of the integral.

1. z2 dv where e is: ? 2? z? 2, 1? x2+y2? 2
2. ? ? d 1x2+y2 da where d is: x2+y2? 4
3. dv where e is: x2+y2+z2? 4, x? 0, y? 0, z? 0
4. z dv where e is: 1? x? 2, 3? y? 4, 5? z? 6
5. ? 10? y20 1x dx dy

a. spherical coordinates
b. cylindrical coordinates
c. polar coordinates
d. cartesian coordinates

option a, c,d are correct.

step-by-step explanation:

from the given figure, it is given that z is equidistant from the sides of the triangle rst, then from triangle tzb and triangle szb, we have

tz=sz(given)

bz=zb(common)

therefore, by rhs rule,δtzb ≅δszb

by cpctc, sz≅tz

also, from δctz and δasz,

tz=sz(given)

∠tcz=∠saz(90°)

by rhs rule, δctz ≅ δasz, therefore by cpctc, ∠ctz≅∠asz

also,from δasz and δzsb,

zs=sz(common)

∠zbs=∠saz=90°

by rhs rule, δasz ≅δzsb, therefore, by cpctc, ∠asz≅∠zsb

hence, option a, c,d are correct.

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.

step-by-step explanation: