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2 years ago

Find the mean proportional for each pair. SHOW YOUR SOLUTION 1. 6, 24

Mathematics

1 answer:

Bingel [31]2 years ago

5 0

Answer:

The mean proportional of 6, and 24 will be 12

Step-by-step explanation:

We know that the Mean proportional of two

numbers, x, and y : $\sqrt{xy}$

Therefore, the mean proportional of 6, and 24

$=\sqrt{6\times 24}$

$=\sqrt{144}$

$\mathrm{Factor\:the\:number:\:}\:144=12^2$

$=\sqrt{12^2}$

$\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{a^n}=a$

$\sqrt{12^2}=12$

$=12$

Therefore, the mean proportional of 6, and 24 will be 12.

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3 years ago

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Zepler [3.9K]

Answer:

Option B. 0.75 gallons is the right answer.

Step-by-step explanation:

Let the load of dishwasher used in house A = x gallons

Let the load of dishwasher used in house B is = y gallons

and similarly we assume for house C = z gallons

Now from the given question

On Friday amount of water used in all three houses = 17.5 gallons

From the table we will make the equation

x + 2y + 2z = 17.5-----(1)

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2x + 2y + 3z = 24.75 -----(3)

By subtracting equation 3 from 2

y + z = 31.5 - 24.75 = 6.75 ------(4)

Equation (1) multiplied by 2 - equation (2)

2×(x + 2y + 2z) - (2x + 3y + 4z) = 17.5×2 - 31.5

y = 35 - 31.5 = 3.5

By putting y = 3.5 in the equation (4)

z = 6.75 - 3.5 = 3.25

By putting y = 3.5 and z = 3.25 in the equation (1)

x + 7 + 6.5 = 17.5

x = 17.5 - 13.5 = 4

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Option B is the right answer.

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3 years ago

Write an equation of the circle with center (5, -7) and radius 9.

vagabundo [1.1K]

Answer:

(x - 5)² + (y + 7)² = 81

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

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Here (h, k) = (5, - 7) and r = 9, thus

(x - 5)² + (y - (- 7))² = 9², that is

(x - 5)² + (y + 7)² = 81 ← equation of circle

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3 years ago

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3 years ago

Prove this trigonometric equation;<br><br> - tan^2x + sec^2x = 1,

alekssr [168]

Hey there :)

- tan²x + sec²x = 1 or 1 + tan²x = sec²x

sin²x + cos²x = 1
Divide the whole by cos²x

$\frac{sin^2x}{cos^2x} + \frac{cos^2x}{cos^2x} = \frac{1}{cos^2x}$

$\frac{sinx}{cosx} = tanx$ so $\frac{sin^2x}{cos^2x} = tan^2x$
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Therefore,
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1 = - tan²x = sec²x or sec²x - tanx = 1

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3 years ago