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3 years ago

I need help with this, ASAP.

Mathematics

1 answer:

Arada [10]3 years ago

7 0

This is the answer. Always remember SOH CAH TOA

Had fun solving this ngl

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Evaluate the integral. W (x2 y2) dx dy dz; W is the pyramid with top vertex at (0, 0, 1) and base vertices at (0, 0, 0), (1, 0,

In-s [12.5K]

Answer:

$\mathbf{\iiint_W (x^2+y^2) \ dx \ dy \ dz = \dfrac{2}{15}}$

Step-by-step explanation:

Given that:

$\iiint_W (x^2+y^2) \ dx \ dy \ dz$

where;

the top vertex = (0,0,1) and the base vertices at (0, 0, 0), (1, 0, 0), (0, 1, 0), and (1, 1, 0)

As such , the region of the bounds of the pyramid is: (0 ≤ x ≤ 1-z, 0 ≤ y ≤ 1-z, 0 ≤ z ≤ 1)

$\iiint_W (x^2+y^2) \ dx \ dy \ dz = \int ^1_0 \int ^{1-z}_0 \int ^{1-z}_0 (x^2+y^2) \ dx \ dy \ dz$

$\iiint_W (x^2+y^2) \ dx \ dy \ dz = \int ^1_0 \int ^{1-z}_0 ( \dfrac{(1-z)^3}{3}+ (1-z)y^2) dy \ dz$

$\iiint_W (x^2+y^2) \ dx \ dy \ dz = \int ^1_0 \ dz \ ( \dfrac{(1-z)^3}{3} \ y + \dfrac {(1-z)y^3)}{3}] ^{1-x}_{0}$

$\iiint_W (x^2+y^2) \ dx \ dy \ dz = \int ^1_0 \ dz \ ( \dfrac{(1-z)^4}{3}+ \dfrac{(1-z)^4}{3}) \ dz$

$\iiint_W (x^2+y^2) \ dx \ dy \ dz =\dfrac{2}{3} \int^1_0 (1-z)^4 \ dz$

$\iiint_W (x^2+y^2) \ dx \ dy \ dz =- \dfrac{2}{15}(1-z)^5|^1_0$

$\mathbf{\iiint_W (x^2+y^2) \ dx \ dy \ dz = \dfrac{2}{15}}$

7 0

3 years ago

Use synthetic division to divide x^3+5x^2−9x−7 by x−2 1 5 -9 -7 The quotient is: _____ The remainder is: ______

RoseWind [281]

Answer:

The quotient is x² + 6x +3

Remainder = -1

Step-by-step explanation:

Explanation:-

Given Polynomial equation

f(x) = x³+5x²−9x−7

By using synthetic division

x = 2 1 5 -9 -7

0 1 12 6

1 6 3  -1 

The quotient is x² + 6x +3

Remainder = -1

5 0

2 years ago

Elasticity is also called

balandron [24]

Another word for elasticity is also called D: responsiveness

7 0

3 years ago

The expression −8x3(7x6 − 3x5) is equivalent to?

Mama L [17]

Answer:

-56x^9+24x^8

Step-by-step explanation:

3 0

3 years ago

BIG POINTS ANSWER WITH DETAIL! Solve for x: 3x + 1 = 3x

Leni [432]

There are no solutions to this problem,

Let's solve your equation step-by-step.
3
x
+
1
=
3
x
Step 1: Subtract 3x from both sides.
3
x
+
1
−
3
x
=
3
x
−
3
x
1
=
0
Step 2: Subtract 1 from both sides.
1
−
1
=
0
−
1
0
=
−
1

There are no solutions

6 0

2 years ago