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2 years ago

A torch and a battery cost £2.50 altogether. The torch costs £2.00 more than the battery.

Mathematics

1 answer:

Hitman42 [59]2 years ago

6 0

Answer:

1/5

Step-by-step explanation:

To find what fraction of the total price the battery is, we need to find out how much the battery alone is first.

Since the battery and torch together are £2.50 and the torch is £2.00, we can find the price of the battery by subtracting the total price to the price of the torch.

Battery Price = £2.50 - £2.00

Battery Price = £0.50

The fraction value of the torch is:

2.00 of 2.50 = 4/5

That then leaves us with:

0.50 of 2.50 = 1/5

To check we need to add the two fractions together.

1/5 + 4/5 = 5/5 or 1

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3 years ago

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3 years ago

Rewrite the following integral in spherical coordinates.

lora16 [44]

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correspond to the upper and lower halves of a sphere with radius $\sqrt2$ . In spherical coordinates, this sphere is $\rho=\sqrt2$ .

$1 \le r \le \sqrt2$ means our region is between two cylinders with radius 1 and $\sqrt2$ . In spherical coordinates, the inner cylinder has equation

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This cylinder meets the sphere when

$x^2 + y^2 + z^2 = 1 + z^2 = 2 \implies z^2 = 1 \\\\ \implies \rho^2 \cos^2(\phi) = 1 \\\\ \implies \rho^2 = \sec^2(\phi) \\\\ \implies \rho = \sec(\phi)$

which occurs at

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where $n\in\Bbb Z$ . Then $\frac\pi4\le\phi\le\frac{3\pi}4$ .

The volume element transforms to

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Putting everything together, we have

$\displaystyle \int_0^{2\pi} \int_1^{\sqrt2} \int_{-\sqrt{2-r^2}}^{\sqrt{2-r^2}} r \, dz \, dr \, d\theta = \boxed{\int_0^{2\pi} \int_{\pi/4}^{3\pi/4} \int_{\csc(\phi)}^{\sqrt2} \rho^2 \sin(\phi) \, d\rho \, d\phi \, d\theta} = \frac{4\pi}3$

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2 years ago

I need e-learning help ugh ... ASAP

miskamm [114]

Answer:

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You know that she walks 1 meter in 1 second, but they're asking about minutes. Since 60 seconds are in 1 minute, it means she was 60 meters in 1 minute. Then multiply that by 10 (10 minutes).

She walked 600 meters, in 10 minutes.

I hope this helped!

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3 years ago