DO NOT WRITE IN THIS AREA DO NOT WRITE I 1. (a) (i) Calculate the value of $$ \sqrt{(7.1)^{2}+(2.9)^{2}} $$, giving your answer correct to a) $$ \quad 2 $$ significant figures (1 mark) b) $$ \quad 2 $$ decimal places. (1 mark) (ii) Write the following quantities in ascending order. $$ \frac{12}{25}, \quad 0.46, \quad 47 \% $$ WRITE IN THIS AREA $$ \qquad $$ $$ \qquad $$ $$ \qquad $$ $$

Question

DO NOT WRITE IN THIS AREA DO NOT WRITE I 1. (a) (i) Calculate the value of $$ \sqrt{(7.1)^{2}+(2.9)^{2}} $$, giving your answer correct to a) $$ \quad 2 $$ significant figures (1 mark) b) $$ \quad 2 $$ decimal places. (1 mark) (ii) Write the following quantities in ascending order. $$ \frac{12}{25}, \quad 0.46, \quad 47 \% $$ WRITE IN THIS AREA $$ \qquad $$ $$ \qquad $$ $$ \qquad $$ $$ <. $$ $$ \qquad $$ (1 mark)

UpStudy AI · Accepted Answer

Calculate the value by following steps:
- step0: Calculate:
  $$\sqrt{7.1^{2}+2.9^{2}}$$
- step1: Convert the expressions:
  $$\sqrt{\left(\frac{71}{10}\right)^{2}+2.9^{2}}$$
- step2: Convert the expressions:
  $$\sqrt{\left(\frac{71}{10}\right)^{2}+\left(\frac{29}{10}\right)^{2}}$$
- step3: Add the numbers:
  $$\sqrt{\frac{2941}{50}}$$
- step4: Use the properties of radicals:
  $$\frac{\sqrt{2941}}{\sqrt{50}}$$
- step5: Simplify the expression:
  $$\frac{\sqrt{2941}}{5\sqrt{2}}$$
- step6: Multiply by the Conjugate:
  $$\frac{\sqrt{2941}\times \sqrt{2}}{5\sqrt{2}\times \sqrt{2}}$$
- step7: Multiply the numbers:
  $$\frac{\sqrt{5882}}{5\sqrt{2}\times \sqrt{2}}$$
- step8: Multiply the numbers:
  $$\frac{\sqrt{5882}}{10}$$
Calculate or simplify the expression $$ \sqrt((7.1)^2 + (2.9)^2) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\sqrt{7.1^{2}+2.9^{2}}$$
- step1: Convert the expressions:
  $$\sqrt{\left(\frac{71}{10}\right)^{2}+2.9^{2}}$$
- step2: Convert the expressions:
  $$\sqrt{\left(\frac{71}{10}\right)^{2}+\left(\frac{29}{10}\right)^{2}}$$
- step3: Add the numbers:
  $$\sqrt{\frac{2941}{50}}$$
- step4: Use the properties of radicals:
  $$\frac{\sqrt{2941}}{\sqrt{50}}$$
- step5: Simplify the expression:
  $$\frac{\sqrt{2941}}{5\sqrt{2}}$$
- step6: Multiply by the Conjugate:
  $$\frac{\sqrt{2941}\times \sqrt{2}}{5\sqrt{2}\times \sqrt{2}}$$
- step7: Multiply the numbers:
  $$\frac{\sqrt{5882}}{5\sqrt{2}\times \sqrt{2}}$$
- step8: Multiply the numbers:
  $$\frac{\sqrt{5882}}{10}$$
Calculate or simplify the expression $$ 12/25 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{12}{25}$$
Calculate or simplify the expression $$ 47/100 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{47}{100}$$
1. (a)
(i) To calculate $$ \sqrt{(7.1)^{2}+(2.9)^{2}} $$:

First, we compute the expression:
$$
\sqrt{(7.1)^{2}+(2.9)^{2}} = \sqrt{50.41 + 8.41} = \sqrt{58.82}
$$

Now, we find the approximate value:
- a) Correct to 2 significant figures: $$ \approx 7.7 $$
- b) Correct to 2 decimal places: $$ \approx 7.67 $$

(ii) To write the quantities in ascending order:
- $$ \frac{12}{25} = 0.48 $$
- $$ 0.46 $$
- $$ 47\% = 0.47 $$

Now, we can arrange them:
$$
0.46 < 0.47 < 0.48
$$

Thus, the final answer is:
$$
0.46 < 47\% < \frac{12}{25}
$$
1. (a) (i) - $$ \sqrt{(7.1)^{2}+(2.9)^{2}} = \sqrt{50.41 + 8.41} = \sqrt{58.82} $$ - a) $$ \approx 7.7 $$ (2 significant figures) - b) $$ \approx 7.67 $$ (2 decimal places) (ii) - $$ \frac{12}{25} = 0.48 $$ - $$ 0.46 $$ - $$ 47\% = 0.47 $$ In ascending order: $$ 0.46 < 47\% < \frac{12}{25} $$

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