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Whitepunk [10]
3 years ago
10

A supermarket had bags of grapes for $20.72 for 7. They also had bags of green grapes priced at 8.46 for 3. Which type of grapes

is most expensive?
Mathematics
1 answer:
emmasim [6.3K]3 years ago
6 0

Answer:

The grapes are more expensive than the green grapes.

Step-by-step explanation:

GRAPES: If you divide $20.72 by 7, to get one bag of grapes instead of seven, you get $2.96/bag.

GREEN GRAPES: If you divide $8.46 by 3, to get one bag of green grapes instead of three, you get $2.82/bag.

$2.82 is less than $2.96, therefore, the grapes are more expensive than the green grapes.

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Use spherical coordinates. Find the volume of the solid that lies within the sphere x^2 + y^2 + z^2 = 81, above the xy-plane, an
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Answer:

The volume of the solid is 243\sqrt{2} \ \pi

Step-by-step explanation:

From the information given:

BY applying sphere coordinates:

0 ≤ x² + y² + z² ≤ 81

0  ≤ ρ²   ≤   81

0  ≤ ρ   ≤  9

The intersection that takes place in the sphere and the cone is:

x^2 +y^2 ( \sqrt{x^2 +y^2 })^2  = 81

2(x^2 + y^2) =81

x^2 +y^2 = \dfrac{81}{2}

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This implies that:

z = \sqrt{x^2+y^2}

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Similarly; in the X-Y plane;

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So here; \dfrac{\pi}{4} \leq \phi \le \dfrac{\pi}{2}

Thus, volume: V  = \iiint_E \ d V = \int \limits^{\pi/2}_{\pi/4}  \int \limits ^{2\pi}_{0} \int \limits^9_0 \rho   ^2 \ sin \phi \ d\rho \   d \theta \  d \phi

V  = \int \limits^{\pi/2}_{\pi/4} \ sin \phi  \ d \phi  \int \limits ^{2\pi}_{0} d \theta \int \limits^9_0 \rho   ^2 d\rho

V = \bigg [-cos \phi  \bigg]^{\pi/2}_{\pi/4}  \bigg [\theta  \bigg]^{2 \pi}_{0} \bigg [\dfrac{\rho^3}{3}  \bigg ]^{9}_{0}

V = [ -0+ \dfrac{1}{\sqrt{2}}][2 \pi -0] [\dfrac{9^3}{3}- 0 ]

V = 243\sqrt{2} \ \pi

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