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Anton [14]
3 years ago
9

The area of each triangle is 4 square units the surface area of the triangle prism is what

Mathematics
1 answer:
e-lub [12.9K]3 years ago
3 0

Answer:

35

Step-by-step explanation:

The surface area of the given solid will be the sum of areas of all of its sides. From the given figure we can see that the sides(faces) of the solid are:

2 Equilateral Triangles

3 Squares

The Area of each triangle is 4 square units. So we need to calculate the area of the squares.

Side length of square = 3 units

Area of square = Length² = 3² = 9

Surface Area of Given Solid = Area of 2 Triangles + Area of 3 Squares

= 2(4) + 3(9)

= 8 + 27

= 35 square units

Surface Area of Given Solid = 35 square units

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A man throws a ball into the air with a velocity of 96 ft/s. Use the formula h=−16 t 2 + v 0 t to determine when the height of t
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Answer:

Assuming that v0 represents the initial velocity, then v0 = 96 ft/s. Substitute this value into h(t) and set the equation equal to 48. Then, write this quadratic equation in standard form, which is ax² + bx+ c = 0, where a, b, and c are constants. Either use factoring or the Quadratic Function to solve the equation for t. Remember that t must be positive, because it represents a unit of time.

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What is 3 ÷ 2\5 pls answer dis<br>​
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7 0
3 years ago
Calculate the flux of the vector field F⃗ (x,y,z)=(exy+9z+4)i⃗ +(exy+4z+9)j⃗ +(9z+exy)k⃗ through the square of side length 3 wit
ikadub [295]

The square (call it S) has one vertex at the origin (0, 0, 0) and one edge on the y-axis, which tells us another vertex is (0, 3, 0). The normal vector to the plane is \vec n=\vec\imath-\vec k, which is enough information to figure out the equation of the plane containing S:

(x\,\vec\imath+y\,\vec\jmath+z\,\vec k)\cdot(\vec\imath-\vec k)=0\implies x-z=0\implies z=x

We can parameterize this surface by

\vec s(x,y)=x\,\vec\imath+y\,\vec\jmath+x\,\vec k

for 0\le x\le\frac3{\sqrt2} and 0\le y\le3. Then the flux of \vec F, assumed to be

\vec F(x,y,z)=(e^{xy}+9z+4)\,\vec\imath+(e^{xy}+4z+9)\,\vec\jmath+(9ze^{xy})\,\vec k,

is

\displaystyle\iint_S\vec F(x,y,z)\cdot\mathrm d\vec S=\iint_S\vec F(\vec s(x,y))\cdot\vec n\,\mathrm dx\,\mathrm dy

=\displaystyle\int_0^3\int_0^{3/\sqrt2}\left((4+e^{xy}+9x)\,\vec\imath+(9+e^{xy}+4x)\,\vec\jmath+(e^{xy}+9x)\,\vec k\right)\cdot(\vec\imath-\vec k)\,\mathrm dx\,\mathrm dy

=\displaystyle\int_0^3\int_0^{3/\sqrt2}4\,\mathrm dx\,\mathrm dy=\boxed{18\sqrt2}

3 0
3 years ago
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