Rewrite the following integral using the order of integration dydxdz

Mathematics

1 answer:

Vlad [161]8 months ago

7 0

$y$ is bounded between the plane $y=z$ and the parabolic cylinder $y=1-x^2$ . The other variables are bounded by constants, $-1\le x\le1$ and $0\le z\le1$ , so the integral is

$\displaystyle \int_0^1 \int_{-1}^1 \int_z^{1-x^2} dy \, dx \, dz$

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The ice skating rink rents 25 pairs of skates each hour. Write an expression that represents the pairs of skates rented in h hou

Nookie1986 [14]

175 pairs of skates are rented for 7 hours.

Step-by-step explanation:

Given,

Pairs of skated rented each hour = 25

Let,

Number of hours = h

Total pairs rented = T

T = Pairs rented each hour * number of hours

T = 25h

Evaluate the expression for 7 hours.

h = 7

$T=25(7)\\T=175$

175 pairs of skates are rented for 7 hours.

Keywords: multiplication, linear expression

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2 years ago

In the diagram, VZ/YZ=WZ/XZ. To prove that △VWZ ~ △YXZ by the SAS similarity theorem, which other sides or angles should be used

Vitek1552 [10]

Answer:

The angles $\angle VZW\cong \angle YZX$ are used to prove the similarity of triangles VWZ and YXZ.

Step-by-step explanation:

Given information: $\frac{VZ}{YZ}=\frac{WZ}{XZ}$

Two triangles are called congruent if their corresponding sides are in same proportion or the corresponding angles are same.

If two corresponding sides of triangle have same proportion and their inclined angle is same, then by SAS rule of similarity both triangles are similar.

From the given figure it is noticed that the ∠VZW and ∠YZX are vertically opposite angles. The vertically opposite angles are always equal.

$\angle VZW=\angle YZX$ (Vertically opposite angles)