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Archy [21]
3 years ago
14

Jasmyn uses 42% of a gift card to buy groceries if she spent $67.20 on groceries, how much was on the gift card to begin with

Mathematics
1 answer:
lapo4ka [179]3 years ago
4 0

Answer:

The card was worth $160.

Step-by-step explanation:

It is given that:

Percent of gift card used = 42%

Cost of groceries = $67.20

Let,

x be the total amount on gift card.

42% of x = 67.20

\frac{42}{100}x=67.20

0.42x = 67.20

\frac{0.42x}{0.42}=\frac{67.20}{0.42}\\x=160

Therefore,

The card was worth $160.

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Leno4ka [110]

(a) See the attached sketch. Each shell will have a radius <em>y</em> chosen from the interval [2, 4], a height of <em>x</em> = 2/<em>y</em>, and thickness ∆<em>y</em>. For infinitely many shells, we have ∆<em>y</em> converging to 0, and each super-thin shell contributes an infinitesimal volume of

2<em>π</em> (radius)² (height) = 4<em>πy</em>

Then the volume of the solid is obtained by integrating over [2, 4]:

\displaystyle 4\pi \int_2^4 y\,\mathrm dy = 2\pi y^2\bigg|_{y=2}^{y=4} = 2\pi (4^2-2^2) = \boxed{24\pi}

(b) See the other attached sketch. (The text is a bit cluttered, but hopefully you'll understand what is drawn.) Each shell has a radius 9 - <em>x</em> (this is the distance between a given <em>x</em> value in the orange shaded region to the axis of revolution) and a height of 8 - <em>x</em> ³ (and this is the distance between the line <em>y</em> = 8 and the curve <em>y</em> = <em>x</em> ³). Then each shell has a volume of

2<em>π</em> (9 - <em>x</em>)² (8 - <em>x</em> ³) = 2<em>π</em> (648 - 144<em>x</em> + 8<em>x</em> ² - 81<em>x</em> ³ + 18<em>x</em> ⁴ - <em>x</em> ⁵)

so that the overall volume of the solid would be

\displaystyle 2\pi \int_0^2 (648-144x+8x^2-81x^3+18x^4-x^5)\,\mathrm dx = \boxed{\frac{24296\pi}{15}}

I leave the details of integrating to you.

3 0
3 years ago
Write three numbers greater than 20 that have 9 as a factor
Lubov Fominskaja [6]
We just need to find the multiples of 9 that are greater than 20.

9*1 = 9
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9*5 = 45

We can use 27,36, 45, .....
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6 0
3 years ago
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Bumek [7]

Answer:

The pattern is + 10.

Step-by-step explanation:

13 + 10 = 23

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I hope this helped! :-)

7 0
3 years ago
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AleksAgata [21]
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stepladder [879]

Answer:

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