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3 years ago

Find the sum: 4√3+11√12 15√15 15√3 26√3 48√3

Mathematics

2 answers:

Andreyy893 years ago

8 0

Answer:

$26\sqrt{3}$

Step-by-step explanation:

Simplify them:

$11\sqrt{12} = 22\sqrt{3}$

$22\sqrt{3}+4\sqrt{3}=26\sqrt{3}$

sasho [114]3 years ago

3 0

Answer:

26√3

Step-by-step explanation:

4√3+11√12

We know that sqrt(ab) = sqrt(a) sqrt(b)

4√3+11 $\sqrt{4} \sqrt{3}$

4√3+11* $2 \sqrt{3}$

4√3+22 $\sqrt{3}$

Combine like terms

26√3

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1)Convert the following binary numbwers into decimal number(only a,b,c,f,i)

kozerog [31]

Answer:

a) 3₁₀

b) 6₁₀

c) 7₁₀

f) 19₁₀

i) 181₁₀

Step-by-step explanation:

Binary to Decimal Conversion (Positional Notation Method)

Multiply each digit by the base (2) raised to the power dependent upon the position of that digit in the binary number.
Sum all the values obtained for each digit.
Express the number as a decimal number by placing subscript 10 after it.

For a binary number with 'n' digits:

The right-most digit is multiplied by 2⁰
The left-most digit is multiplied by $\sf 2^{n-1}$

For example, to convert the binary number 111001₂ into a decimal:

$\begin{array}{ c c c c c c}1 & 1 & 1 & 0 & 0 & 1\\\downarrow & \downarrow & \downarrow & \downarrow & \downarrow & \downarrow \\2^5 & 2^4 & 2^3 & 2^2 & 2^1 & 2^0\\\end{array}$

Multiply each digit by the base (2) raised to the power as indicated above and sum them:

$=(1 \times 2^5)+(1 \times 2^4)+(1 \times 2^3)+(0 \times 2^2)+(0 \times 2^1)+(1 \times 2^0)$

$= 32+16+8+0+0+1$

$= 57$

Finally, express as a decimal number ⇒ 111001₂ = 57₁₀

Question (a)

$\begin{aligned}\implies 11_2 & = (1 \times 2^1)+(1 \times 2^0)\\& = 2+1\\& = 3\end{aligned}$

Therefore, 11₂ = 3₁₀

Question (b)

$\begin{aligned}\implies 110_2 & = (1 \times 2^2)+(1 \times 2^1)+(0 \times 2^0)\\& = 4+2+0\\& = 6\end{aligned}$

Therefore, 110₂ = 6₁₀

Question (c)

$\begin{aligned}\implies 111_2 & = (1 \times 2^2) +(1 \times 2^1)+(1 \times 2^0)\\& =4+2+1\\& = 7\end{aligned}$

Therefore, 111₂ = 7₁₀

Question (f)

$\begin{aligned}\implies 10011_2 & =(1 \times 2^4)+(0 \times 2^3)+ (0 \times 2^2) +(1 \times 2^1)+(1 \times 2^0)\\& =16+0+0+2+1\\& = 19\end{aligned}$

Therefore, 10011₂ = 19₁₀

Question (i)

$\phantom{)))}10110101_2 \\\\=(1 \times 2^7)+(0 \times 2^6)+(1 \times 2^5)+(1 \times 2^4)+(0 \times 2^3)+ (1 \times 2^2) +(0 \times 2^1)+(1 \times 2^0)\\\\=128+0+32+16+0+4+0+1\\\\= 181$