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3 years ago

How many equal parts does a ruler have?

Mathematics

1 answer:

svetoff [14.1K]3 years ago

7 0

Answer:

-inch distance on Ruler B is divided into two equal parts.

Step-by-step explanation:

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Use cylindrical coordinates to evaluate the triple integral ∭ where E is the solid bounded by the circular paraboloid z = 9 - 16

4vir4ik [10]

Answer:

$\mathbf{\iiint_E E \sqrt{x^2+y^2} \ dV =\dfrac{81 \ \pi}{80}}$

Step-by-step explanation:

The Cylindrical coordinates are:

x = rcosθ, y = rsinθ and z = z

From the question, on the xy-plane;

$9 -16 (x^2 + y^2) = 0 \\ \\ 16 (x^2 + y^2) = 9 \\ \\ x^2+y^2 = \dfrac{9}{16}$

$x^2+y^2 = (\dfrac{3}{4})^2$

where:

0 ≤ r ≤ $\dfrac{3}{4}$ and 0 ≤ θ ≤ 2π

∴

$\iiint_E E \sqrt{x^2+y^2} \ dV = \int^{2 \pi}_{0} \int ^{\dfrac{3}{4}}_{0} \int ^{9-16r^2}_{0} \ r \times rdzdrd \theta$

$\iiint_E E \sqrt{x^2+y^2} \ dV = \int^{2 \pi}_{0} \int ^{\dfrac{3}{4}}_{0} r^2 z|^{z= 9-16r^2}_{z=0} \ \ \ drd \theta$

$\iiint_E E \sqrt{x^2+y^2} \ dV = \int^{2 \pi}_{0} \int ^{\dfrac{3}{4}}_{0} r^2 ( 9-16r^2}) \ drd \theta$

$\iiint_E E \sqrt{x^2+y^2} \ dV = \int^{2 \pi}_{0} \int ^{\dfrac{3}{4}}_{0} ( 9r^2-16r^4}) \ drd \theta$

$\iiint_E E \sqrt{x^2+y^2} \ dV = \int^{2 \pi}_{0} ( \dfrac{9r^3}{3}-\dfrac{16r^5}{5}})|^{\dfrac{3}{4}}_{0} \ drd \theta$

$\iiint_E E \sqrt{x^2+y^2} \ dV = \int^{2 \pi}_{0} ( 3r^3}-\dfrac{16r^5}{5}})|^{\dfrac{3}{4}}_{0} \ drd \theta$

$\iiint_E E \sqrt{x^2+y^2} \ dV = \int^{2 \pi}_{0} ( 3(\dfrac{3}{4})^3}-\dfrac{16(\dfrac{3}{4})^5}{5}}) d \theta$

$\iiint_E E \sqrt{x^2+y^2} \ dV =( 3(\dfrac{3}{4})^3}-\dfrac{16(\dfrac{3}{4})^5}{5}}) \theta |^{2 \pi}_{0}$

$\iiint_E E \sqrt{x^2+y^2} \ dV =( 3(\dfrac{3}{4})^3}-\dfrac{16(\dfrac{3}{4})^5}{5}})2 \pi$

$\iiint_E E \sqrt{x^2+y^2} \ dV =(\dfrac{81}{64}}-\dfrac{243}{320}})2 \pi$

$\iiint_E E \sqrt{x^2+y^2} \ dV =(\dfrac{81}{160}})2 \pi$

$\mathbf{\iiint_E E \sqrt{x^2+y^2} \ dV =\dfrac{81 \ \pi}{80}}$

4 0

3 years ago

Which symbol creates a true sentence when x equals 2? 6 • 8 – 2x _____ 6(5 + x) < > = ?

34kurt

48－4=44,in the left
6×7=42,in the right
44＞42,so ＞ is the answer

5 0

3 years ago

Read 2 more answers

Can someone help me with this

VladimirAG [237]

Answer:

its red

Step-by-step explanation:

math. lol

8 0

3 years ago

How many solutions does the equation have?

SSSSS [86.1K]

Let's solve and find out.

4(2n - 4) + 3 = 8n - 19
8n - 16 + 3 = 8n - 19
8n - 13 = 8n - 19
-13 = -19

-13 and -19 are not equal, so the equation has no solutions.

Answer:
A. 0

6 0

3 years ago

Read 2 more answers

A tepee is designed to have a diameter of 10 ft and a volume of 393 ft. At

Citrus2011 [14]

Answer:

15 ft.

Step-by-step explanation:

The tepee is a cone and its volume

= 1/3 pi r^2 h where r = radius and h = height.

The radius r = 1/2 * 10 = 5 ft.

So we have the equation:

393 = 1/3*3.14* 5^2 * h

h = 393 / (1/3*3.14*25)

= 15.02 ft.

7 0

3 years ago

How many equal parts does a ruler have? ​

How many equal parts does a ruler have?