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3 years ago

Explain why the square root of a number is defined to be equal to that number to the 1/2 power

Mathematics

2 answers:

Cloud [144]3 years ago

6 0

9514 1404 393

Answer:

(x^(1/2))^2 = x^(2/2) = x

Step-by-step explanation:

The square root of a number, when multiplied by itself, gives the original number.

(√x)(√x) = x

The rule for exponents is that powers of the same base, when multiplied, will be the base to the sum of those powers.

(a^b)(a^c) = a^(b+c)

Also, the first power of a number is that number itself.

$x^{\frac{1}{2}}\times x^{\frac{1}{2}}=x^{\frac{1}{2}+\frac{1}{2}}=x^1=x\\\\ \text{Compare to ...}\\\\ \sqrt{x}\times\sqrt{x}=x$

MAXImum [283]3 years ago

3 0

Answer:

Squaring and square root are inverses, so one should "undo" the other. That is, squaring the square root of a number results in the number. Using the power of a power rule, you multiply the exponents. Since a number to the first power is itself, the product of the exponents must equal 1. This means that the power of the square root must be the reciprocal of 2, or one half.

Step-by-step explanation:

EDGE 2020-2021

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Item 7

Mariulka [41]

Answer:

$A = 74.7^\circ$

$B = 42.5^\circ$

$C = 62.8^\circ$

Step-by-step explanation:

Given

$A = (-1,2) \to (x_1,y_1)$

$B = (2,8) \to (x_2,y_2)$

$C = (4,1) \to (x_3,y_3)$

Required

The measure of each angle

First, we calculate the length of the three sides of the triangle.

This is calculated using distance formula

$d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2$

For AB

$A = (-1,2) \to (x_1,y_1)$

$B = (2,8) \to (x_2,y_2)$

$d = \sqrt{(-1 - 2)^2 + (2 - 8)^2$

$d = \sqrt{(-3)^2 + (-6)^2$

$d = \sqrt{45$

So:

$AB = \sqrt{45$

For BC

$B = (2,8) \to (x_2,y_2)$

$C = (4,1) \to (x_3,y_3)$

$BC = \sqrt{(2 - 4)^2 + (8 - 1)^2$

$BC = \sqrt{(-2)^2 + (7)^2$

$BC = \sqrt{53$

For AC

$A = (-1,2) \to (x_1,y_1)$

$C = (4,1) \to (x_3,y_3)$

$AC = \sqrt{(-1 - 4)^2 + (2 - 1)^2$

$AC = \sqrt{(-5)^2 + (1)^2$

$AC = \sqrt{26$

So, we have:

$AB = \sqrt{45$

$BC = \sqrt{53$

$AC = \sqrt{26$

By representation

$AB \to c$

$BC \to a$

$AC \to b$

So, we have:

$a = \sqrt{53$

$b = \sqrt{26$

$c = \sqrt{45$

By cosine laws, the angles are calculated using:

$a^2 = b^2 + c^2 -2bc \cos A$

$b^2 = a^2 + c^2 -2ac \cos B$

$c^2 = a^2 + b^2 -2ab\ cos C$

$a^2 = b^2 + c^2 -2bc \cos A$

$(\sqrt{53})^2 = (\sqrt{26})^2 +(\sqrt{45})^2 - 2 * (\sqrt{26}) +(\sqrt{45}) * \cos A$

$53 = 26 +45 - 2 * 34.21 * \cos A$

$53 = 26 +45 - 68.42 * \cos A$

Collect like terms

$53 - 26 -45 = - 68.42 * \cos A$

$-18 = - 68.42 * \cos A$

Solve for $\cos A$

$\cos A =\frac{-18}{-68.42}$

$\cos A =0.2631$

Take arc cos of both sides

$A =\cos^{-1}(0.2631)$

$A = 74.7^\circ$

$b^2 = a^2 + c^2 -2ac \cos B$

$(\sqrt{26})^2 = (\sqrt{53})^2 +(\sqrt{45})^2 - 2 * (\sqrt{53}) +(\sqrt{45}) * \cos B$

$26 = 53 +45 -97.67 * \cos B$

Collect like terms

$26 - 53 -45= -97.67 * \cos B$

$-72= -97.67 * \cos B$

Solve for $\cos B$

$\cos B = \frac{-72}{-97.67}$

$\cos B = 0.7372$

Take arc cos of both sides

$B = \cos^{-1}(0.7372)$

$B = 42.5^\circ$

For the third angle, we use:

$A + B + C = 180$ --- angles in a triangle

Make C the subject

$C = 180 - A -B$

$C = 180 - 74.7 -42.5$

$C = 62.8^\circ$

8 0

3 years ago

there are 800 seats in the varsity theater. during regular preformances, all seats cost $12 each. It costs the owner $275 to pay

r-ruslan [8.4K]

Answer:

The correct answers are the following:

A) P=12n-275

B) 124

C) Decrease by $100

Step-by-step explanation:

A) P=12n-275  - Each person (n) pays $12, then the cost/expense ($275) is subtracted from the income to get the profit.

B) 1,213=12n-275 - Plug in the value for P ($1,213).

1,488=12n - Add $275 to both sides.

124=n - Divide both sides by $12.

n=124  - This the number (n) of people that attended.

C) P=12n-375 - Change the value for expense to $375.

P=12(124)-375 - Plug in the value for n (124).

P=1488-375 - Simplify and find the difference.

P=1,113 - This is your profit.

1,113-1,213=-100  - $100 reduction/decrease of profit (or -$100 to profit)

Hope this helps!

6 0

3 years ago

What is 39700.0947 in scientific notation ?

Elden [556K]

Answer: 3.97000947 × 10^4

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Alexeev081 [22]

Answer:

Me and my massive brain, among other massive things of mine, believe it to be -1

Step-by-step explanation:

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I don’t know how to work out this word problem for my math class

Len [333]

do you mind telling me the question?

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