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3 years ago

HELLPPPPPP

Mathematics

2 answers:

Nady [450]3 years ago

4 0

<h3>Multiplication Property of Equality is the missing reason</h3>

Solution:

Given that,

five thirds times x plus 2 equals negative 3

Therefore,

$\frac{5}{3}x + 2 = -3$

Multiplication Property of Equality

The Multiplication Property of Equality means that, if both sides of an equation is multiplied by same number, the equation still remains equal

$\frac{5}{3}x + 2 = -3$

Multiply both sides by 3

$3(\frac{5}{3}x + 2) = -3 \times 3\\\\5x + 6 = -9$

Subtraction Property of Equality

The Subtraction Property of Equality means that, we can subtract the same number from both sides of equation and the equation will still be true

5x + 6 = -9

Subtract 6 from both sides

5x + 6 - 6 = -9 - 6

5x = -15

Division Property of Equality

The Division Property of Equality means that, if both sides of an equation is divided by same number, the equation still remains true

5x = -15

Divide both sides by 5

x = -3

joja [24]3 years ago

4 0

Answer: Multiplication Property Of Equality

Step-by-step explanation:

look at the image below

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$\displaystyle\int\frac{\sqrt{25-x^2}}x\,\mathrm dx$

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Now, $\sqrt{x^2}=|x|$ in general. But since we want our substitution $x=5\sin\theta$ to be invertible, we are tacitly assuming that we're working over a restricted domain. In particular, this means $\theta=\sin^{-1}\dfrac x5$ , which implies that $\left|\dfrac x5\right|\le1$ , or equivalently that $|\theta|\le\dfrac\pi2$ . Over this domain, $\cos\theta\ge0$ , so $\sqrt{\cos^2\theta}=|\cos\theta|=\cos\theta$ .

Long story short, this allows us to go from

$\displaystyle5\int\sqrt{\cos^2\theta}\dfrac{\cos\theta}{\sin\theta}\,\mathrm d\theta$

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$\displaystyle5\int\cos\theta\dfrac{\cos\theta}{\sin\theta}\,\mathrm d\theta$
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Computing the remaining integral isn't difficult. Expand the numerator with the Pythagorean identity to get

$\dfrac{\cos^2\theta}{\sin\theta}=\dfrac{1-\sin^2\theta}{\sin\theta}=\csc\theta-\sin\theta$

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$\displaystyle5\left(\int\csc\theta\,\mathrm d\theta-\int\sin\theta\,\mathrm d\theta\right)$
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and using basic trigonometric properties (e.g. Pythagorean theorem) this reduces to

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