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Marrrta [24]
3 years ago
7

1. What is the volume of the prism that can be constructed from this net?

Mathematics
1 answer:
Irina-Kira [14]3 years ago
3 0
1. V = lwh
    V = (8)(4)(5)
    V = (32)(5)
    V = 160 units³

2. V = lwh + lwh
    V = (4)(2)(1) + (3)(1)(1)
    V = (8)(1) + (3)(1)
    V = 8 + 3
    V = 11 units³

3. V = leh + s³
    V = (9)(3)(4) + (3)³
    V = (27)(4) + 27
    V = 108 + 27
    V = 135 units³

4. V = lwh
    V = (3)(7)(2)
    V = (21)(2)
    V = 42 units³
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Frances has 4 square baking dishes. Each pan is 7 inches × 7 inches × 2 inches. Which expression will give her the total volume
julia-pushkina [17]

Answer:

D. (7^2 X2) x 4

The equation inside the parenthesis finds the volume of one pan and then that is multiplied by 4 which is the total number of pans. This will find the volume of all 4 pans.

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Set up a double integral for calculating the flux of the vector field ????⃗ (????⃗ )=????⃗ , where ????⃗ =⟨x,y,z⟩, through the p
Tema [17]

Answer:

-937.5π

Step-by-step explanation:

F (r) = r = (x, y, z) the surface equation z = 3(x^2 + y^2) z_x = 6x, z_y = 6y the normal vector n = (- z_x, - z_y, 1) = (- 6x, - 6y, 1)

Thus, flux ∫∫s F · dS is given as;

∫∫ <x, y, z> · <-z_x, -z_y, 1> dA

=∫∫ <x, y, 3x² + 3y²> · <-6x, -6y, 1>dA , since z = 3x² + 3y²

Thus, flux is;

= ∫∫ -3(x² + y²) dA.

Since the region of integration is bounded by x² + y² = 25, let's convert to polar coordinates as follows:

∫(θ = 0 to 2π) ∫(r = 0 to 5) -3r² (r·dr·dθ)

= 2π ∫(r = 0 to 5) -3r³ dr

= -(6/4)πr^4 {for r = 0 to 5}

= -(6/4)5⁴π - (6/4)0⁴π

= -937.5π

4 0
3 years ago
Write three different sentences that could describe the relationship between the quantities $27, $81
Olenka [21]
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8 0
3 years ago
Emily needs enough Fabric for 3 1/2 hats. Since she has half a hat done. If each bag requires 1 2/7 ft of Fabric, how much fabri
kow [346]

first off let's convert the mixed fractions to improper fractions.

\stackrel{mixed}{3\frac{1}{2}}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}} ~\hfill \stackrel{mixed}{1\frac{2}{7}}\implies \cfrac{1\cdot 7+2}{7}\implies \stackrel{improper}{\cfrac{9}{7}}

she already did half a hat, so we can say   \cfrac{7}{2}-\cfrac{1}{2}\implies \cfrac{7-1}{2}\implies 3

so she only needs enough fabric to make 3 more full hats, we know each one uses 9/7 ft, so

3\cdot \cfrac{9}{7}\implies \cfrac{27}{7}\implies 3\frac{6}{7}

5 0
2 years ago
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