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3 years ago

The linear scale factor of two shapes is 3:4. If the area of the smallest shape is 72^2 what is the area of the big shape?

Mathematics

1 answer:

Lorico [155]3 years ago

3 0

Answer:

$\boxed{6912 units^2}$

Step-by-step explanation:

Hey there!

Well using the given ratio,

3:4

And the area of the small shape we need to do,

72*72 = 5184

Now we can make the following fractions,

$\frac{3}{4}$ = $\frac{5184}{x}$

Now we can solve,

3*x = 3x

4 * 5184 = 20736

3x = 20736

20736 / 3

x = 6912

So the area of the bigger shape is 6912 units^2

Hope this helps :)

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A bad contains 15 balls of which X is red. Write an expression for the probability that a ball drawn from the bad is red. When 5

antoniya [11.8K]

Answer:

Step-by-step explanation:

The current probability of picking a red ball is $\frac{x}{15}$ . When 5 more balls are added, the probability is 3/4. We can write a ratio for this problem:

$\frac{x+5}{15+5} = \frac{3}{4}$

When using cross multiplication to solve this, you get 3 * 20 = 4(x+5).

60 = 4x + 20

40 = 4x

x = 10 red balls

5 0

2 years ago

Evaluate using integration by parts

PolarNik [594]

Rather than carrying out IBP several times, let's establish a more general result. Let

$I(n)=\displaystyle\int x^ne^x\,\mathrm dx$

One round of IBP, setting

$u=x^n\implies\mathrm du=nx^{n-1}\,\mathrm dx$

$\mathrm dv=e^x\,\mathrm dx\implies v=e^x$

gives

$\displaystyle I(n)=x^ne^x-n\int x^{n-1}e^x\,\mathrm dx$

$I(n)=x^ne^x-nI(n-1)$

This is called a power-reduction formula. We could try solving for $I(n)$ explicitly, but no need. $n=5$ is small enough to just expand $I(5)$ as much as we need to.