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Tcecarenko [31]
3 years ago
6

The square root of a number consisting of two digits isequal

Mathematics
1 answer:
Gala2k [10]3 years ago
3 0

Answer:

81

Step-by-step explanation:

Let the digits that make up the number be a and b.

Given that the square root of the number is equal to the sum of the digits.

Then,

√(10a + b) = a + b

Also given that the square root of the number is less than the number obtained by  interchanging the digits by 9, then

√(10a +b) + 9  = 10b + a

Since √(10a + b) = a + b, then

a + b + 9 = 10b + a

a - a + 9 = 10b - b

9b = 9

b = 1

since √(10a + b) = a + b

√(10a + 1) = a + 1

10a + 1= (a + 1)²

10a + 1 = a² + 2a + 1

a²  + 2a - 10a + 1 - 1 = 0

a² - 8a = 0

a(a - 8) = 0

a = 0 or a = 8

Using a = 8 and b = 1,

the number 10a + b = 10(8) + 1 = 81.

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Answer:

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What are the solutions 2x^2 +7x=4
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8 0
2 years ago
Read 2 more answers
A source of laser light sends rays AB and AC toward two opposite walls of a hall. The light rays strike the walls at points B an
Nataly [62]

Answer:

The distance between the walls is 70 m.

Step-by-step explanation:

Given: A source of laser light is at point A on the ground between two parallel walls BE and CD . The walls are perpendicular to the ground that is

BE ⊥ ED and CD ⊥ ED

AB is a ray of light which strikes the wall on the left at point B which is 30 meters above the ground. that is BE = 30 m

AC is a ray of light which strikes the wall on the right at point C. The length of AC = 80 meters.

The ray AB makes an angle of 45 degrees with the ground that is m∠BAE = 45°

The ray AC makes an angle of 60 degrees with the ground that is m∠CAD = 60°

As shown is figure attached below.

WE have to find the distance between the walls that is Length of ED

Length of ED = EA + AD

Consider the Δ AEB,

Using trigonometric ratio,

\tan\theta=\frac{perpendicular}{base}

Here \theta=45^{\circ} , perpendicular = 30 m  and base we can find.

thus,

\tan 45^{\circ}=\frac{30}{EA}

We know \tan 45^{\circ}=1

thus, EA =  30 m

Consider the Δ AEB,

Using trigonometric ratio,

\cos\theta=\frac{base}{hypotenuse}

Here \theta=60^{\circ} , hypotenuse = 80 m  and base we can find.

thus, \cos 60^{\circ}=\frac{base}{80}

We know, \cos 60^{\circ}=\frac{1}{2}

thus, Base = 40 m

AD = 40 m

Thus, the distance between the walls that is the length of ED = 30 + 40 = 70 m

4 0
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V125BC [204]

The formula for compound interest

A = P( 1 + r/n) ^ (nt)

A is the amount in the account at the end

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A = 1800 ( 1.0375)^6

A = 2244.92138

Rounding to the nearest cent

A = 2244.92

7 0
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