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AlladinOne [14]
2 years ago
12

Volume of triangular prism​

Mathematics
1 answer:
Licemer1 [7]2 years ago
8 0

Answer:

48 cm^2

Step-by-step explanation:

The area of one of the triangular ends is A = (1/2)(4 cm)(3 cm) = 6 cm^2.

Multiply this "base area" by 8 cm, the length of the prism.  We get:

volume of triangular prism = (6 cm^2)(8 cm) = 48 cm^2

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If a cone has a volume of 60pi cubic meters then what is the radius, height, and diameter
algol [13]

Answer:

60pi = ⅓ × pi × r² × h

180 = r²h

Assuming r and h are whole numbers,

r = 3 m , h = 180/3² = 20 m

Diameter = 6 m

Or,

r = 6 m, h = 180/6² = 5 m

Diameter = 12 m

8 0
3 years ago
Read 2 more answers
:)
labwork [276]
Domain is the numbers you can use
range is the result of inputing the domain

an interesting fact is that the inverse of a function switches the domain and range

basically
the domain of f(x) becomes the range of f^-1(x)
the range of f(x) becomes the domain of f^-1(x)
so just find the domain and range of f(x)


f(x)=3x- \frac{1}{2}
there are no restrictions
all real numbers can be used
all real numbers can result


so the answer is domain and range for both is all real numbers

D is answer
7 0
3 years ago
Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of
tresset_1 [31]

Because I've gone ahead with trying to parameterize S directly and learned the hard way that the resulting integral is large and annoying to work with, I'll propose a less direct approach.

Rather than compute the surface integral over S straight away, let's close off the hemisphere with the disk D of radius 9 centered at the origin and coincident with the plane y=0. Then by the divergence theorem, since the region S\cup D is closed, we have

\displaystyle\iint_{S\cup D}\vec F\cdot\mathrm d\vec S=\iiint_R(\nabla\cdot\vec F)\,\mathrm dV

where R is the interior of S\cup D. \vec F has divergence

\nabla\cdot\vec F(x,y,z)=\dfrac{\partial(xz)}{\partial x}+\dfrac{\partial(x)}{\partial y}+\dfrac{\partial(y)}{\partial z}=z

so the flux over the closed region is

\displaystyle\iiint_Rz\,\mathrm dV=\int_0^\pi\int_0^\pi\int_0^9\rho^3\cos\varphi\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=0

The total flux over the closed surface is equal to the flux over its component surfaces, so we have

\displaystyle\iint_{S\cup D}\vec F\cdot\mathrm d\vec S=\iint_S\vec F\cdot\mathrm d\vec S+\iint_D\vec F\cdot\mathrm d\vec S=0

\implies\boxed{\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=-\iint_D\vec F\cdot\mathrm d\vec S}

Parameterize D by

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

with 0\le u\le9 and 0\le v\le2\pi. Take the normal vector to D to be

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

Then the flux of \vec F across S is

\displaystyle\iint_D\vec F\cdot\mathrm d\vec S=\int_0^{2\pi}\int_0^9\vec F(x(u,v),y(u,v),z(u,v))\cdot(\vec s_u\times\vec s_v)\,\mathrm du\,\mathrm dv

=\displaystyle\int_0^{2\pi}\int_0^9(u^2\cos v\sin v\,\vec\imath+u\cos v\,\vec\jmath)\cdot(-u\,\vec\jmath)\,\mathrm du\,\mathrm dv

=\displaystyle-\int_0^{2\pi}\int_0^9u^2\cos v\,\mathrm du\,\mathrm dv=0

\implies\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\boxed{0}

8 0
3 years ago
The first term of a geometric sequence is 300 and the common ratio is 2 What is the 7th term of the sequence
xxMikexx [17]

Step-by-step explanation:

s1 = 300

s2 = s1 × 2 = 300 × 2 = 600

s3 = s2 × 2 = s1 × 2² = 1200

sn = sn-1 × 2 = s1 × 2^(n-1)

s7 = 300 × 2⁶ = 300 × 64 = 19,200

3 0
2 years ago
If x = 11 units and h = 7 units, then what is the area of the triangle shown?
m_a_m_a [10]
The answer is A because of base times height
3 0
2 years ago
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