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4vir4ik [10]
3 years ago
12

A large cube has 5 layers, each with 5 rows of 5 small cubes. How many small cubes will the larger cube contain? Explain Please

Mathematics
1 answer:
boyakko [2]3 years ago
6 0
25 because you have to multiply 5✖️5 which equals 25. 5 is the 5 layers and the other 5 for the 5 rows.
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A guy wire 30 ft long supports an antenna at a point that is 24 ft above the base of the antenna.
GalinKa [24]
Use Pythagorean Theorem
c2 = a2 + b2
152 = a2 + 12
a2 = 152 - 122
=225 - 144 = 81
a = 9 ft
Distance from base of antenna = 9ft
4 0
2 years ago
4) The heat is turned on in a room. After 5 minutes, the temperature is 64 °F and after 25 minutes, the
damaskus [11]

Answer:

F=0.4t

Step-by-step explanation:

Find the slope using the formula rise over run or y2-y2 over x2-x1

y2=72 y1=64 x2=25 x1=5

72-64/25-5=8/20=0.4

6 0
2 years ago
Read 2 more answers
What is the area of this shape?
m_a_m_a [10]

Step-by-step explanation:

idk the answer but find the area of a circle with the radius of 45 m and then find the area of the rectangle then add them together.

5 0
3 years ago
Problem 4: Let F = (2z + 2)k be the flow field. Answer the following to verify the divergence theorem: a) Use definition to find
Viktor [21]

Given that you mention the divergence theorem, and that part (b) is asking you to find the downward flux through the disk x^2+y^2\le3, I think it's same to assume that the hemisphere referred to in part (a) is the upper half of the sphere x^2+y^2+z^2=3.

a. Let C denote the hemispherical <u>c</u>ap z=\sqrt{3-x^2-y^2}, parameterized by

\vec r(u,v)=\sqrt3\cos u\sin v\,\vec\imath+\sqrt3\sin u\sin v\,\vec\jmath+\sqrt3\cos v\,\vec k

with 0\le u\le2\pi and 0\le v\le\frac\pi2. Take the normal vector to C to be

\vec r_v\times\vec r_u=3\cos u\sin^2v\,\vec\imath+3\sin u\sin^2v\,\vec\jmath+3\sin v\cos v\,\vec k

Then the upward flux of \vec F=(2z+2)\,\vec k through C is

\displaystyle\iint_C\vec F\cdot\mathrm d\vec S=\int_0^{2\pi}\int_0^{\pi/2}((2\sqrt3\cos v+2)\,\vec k)\cdot(\vec r_v\times\vec r_u)\,\mathrm dv\,\mathrm du

\displaystyle=3\int_0^{2\pi}\int_0^{\pi/2}\sin2v(\sqrt3\cos v+1)\,\mathrm dv\,\mathrm du

=\boxed{2(3+2\sqrt3)\pi}

b. Let D be the disk that closes off the hemisphere C, parameterized by

\vec s(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec\jmath

with 0\le u\le\sqrt3 and 0\le v\le2\pi. Take the normal to D to be

\vec s_v\times\vec s_u=-u\,\vec k

Then the downward flux of \vec F through D is

\displaystyle\int_0^{2\pi}\int_0^{\sqrt3}(2\,\vec k)\cdot(\vec s_v\times\vec s_u)\,\mathrm du\,\mathrm dv=-2\int_0^{2\pi}\int_0^{\sqrt3}u\,\mathrm du\,\mathrm dv

=\boxed{-6\pi}

c. The net flux is then \boxed{4\sqrt3\pi}.

d. By the divergence theorem, the flux of \vec F across the closed hemisphere H with boundary C\cup D is equal to the integral of \mathrm{div}\vec F over its interior:

\displaystyle\iint_{C\cup D}\vec F\cdot\mathrm d\vec S=\iiint_H\mathrm{div}\vec F\,\mathrm dV

We have

\mathrm{div}\vec F=\dfrac{\partial(2z+2)}{\partial z}=2

so the volume integral is

2\displaystyle\iiint_H\mathrm dV

which is 2 times the volume of the hemisphere H, so that the net flux is \boxed{4\sqrt3\pi}. Just to confirm, we could compute the integral in spherical coordinates:

\displaystyle2\int_0^{\pi/2}\int_0^{2\pi}\int_0^{\sqrt3}\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=4\sqrt3\pi

4 0
3 years ago
Put the fractions in order smallest to largest<br> 7/10, 2/3 , 4/5, 11/15
Brrunno [24]

Answer:

Step-by-step explanation:

2/3, 7/10, 11/15, 4/5

8 0
3 years ago
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