Question

pls ans it is very urgent

Answer 1

Answer:

1st main 1st one the answer is 3

Step-by-step explanation:

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Answer 2

SECTION A

1. To find 'x' we need to use this property ⇒ $a^{0}=1$

So our equation now would be ⇒ $3^{x-2}=3^{0}$

Let's solve this equation step-by-step.

Since the bases are same we will take the exponents in our equation.

$x-2=0$

Step 1: Add 2 to both sides of the equation.

$x-2+2=0+2$

$x=2$

Verification if x = 2.

$3^{2-2}=1$

$3^{0}=1$

$1=1$

∴ The answer is c) 2.

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2. To find the least number by which 1375 should be divided to get a perfect cube we must do prime factorization first.

$\begin{array}{r | l} 5 & 1375 \\ \cline{2-2} 5 & 275 \\ \cline{2-2} 5 & 55\\ \cline{2-2} & 11\\ \end{array}$

Now we will have to group the product of primes in groups of three.

(5×5×5)×11 = 1375

∴ We must divide b) 11 by 1375 to obtain a perfect square.

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3. First we need to find the value of $1.5 \times 10^{-6}$

$10^{-6} = 0.000001$

$1.5 \times 0.000001 = 0.0000015$

Now we need to multiple 1500 to 0.0000015

$0.0000015\times 1500 = 0.00225$

Now we need to express 0.00225 in exponential form.

$0.00225 = 2.25\times 10^{-3}$

∴The computer will take a) $2.25\times 10^{-3}$ sec to perform 1500 such operations.

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SECTION B

4. To find the height we must find the cube root.

$\begin{array}{r | l} 5&42875 \\ \cline{2-2} 5 & 8575 \\ \cline{2-2} 5&1715 \\ \cline{2-2} 7 &343 \\ \cline{2-2} 7& 49 \\ \cline{2-2}&7 \end{array}$

Now we have to group the product of primes in groups of three.

(5×5×5)×(7×7×7)

To find the cube root we need to take one number from each group and multiply.

$\sqrt{42875} = 5\times 7$

$\sqrt{42875}=35$

∴The height of the cylinder tank is 35 m.

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5) $(\frac{-2}{3})^{-3}\times (\frac{1}{6})^{-3}$

Step 1: Apply this law of exponent ⇒ $a^{-m}=\frac{1}{a^{m}}$

$(\frac{-2}{3})^{-3}\times (\frac{1}{6})^{-3}$

$(\frac{-3}{2})^{3}\times ({6})^{3}$

Step 2: Apply this law of exponent ⇒ $a^m\times b^m = (ab)^m$

$(\frac{-3}{2})^{3}\times ({6})^{3}$

$(\frac{-3}{2}\times 6)^{3}$

$(-3\times 3)^{3}$

$(-9)^{3}$

Step 3: If required you can find the actual value without exponent.

$(-9)^{3}$

$(-9)^{3} = (-9)\times (-9) \times (-9)$

$-729$

∴ When we simplify $\bf (\frac{-2}{3})^{-3}\times (\frac{1}{6})^{-3}$ we get (-9)³ or (-729).

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SECTION C

6) Answer for this is attached.

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