Mathematics

Question

Please help!!! 100 points + brainliest PS: if you help and its right i have my own etsy busieness (jewerly) i will give 3 of my items for free you can pick
Please help!!! 100 points + brainliest PS: if you help and its right i have my own etsy busieness (jewerly) i will give 3 of my items for free you can pick

1 Answer

  • Answer:

    15)  47.48 and 47.52

    16) a)  27 cm²

         b)  6 cm

    Step-by-step explanation:

    Question 15

    When rounding a number, check the digit to the right of the one you're rounding to:

    • If it is 0, 1, 2, 3 or 4 round down.
    • If it is 5, 6, 7, 8 or 9 round up.

    [tex]\begin{array}{|c|c|c|}\cline{1-3} \vphantom{\dfrac12} \sf Given & \sf 1\;decimal\;place & \sf 2\; sig\; fig \\\cline{1-3} \vphantom{\dfrac12}47.38 & 47.4 &47\\\cline{1-3} \vphantom{\dfrac12}47.42 & 47.4 &47 \\\cline{1-3} \vphantom{\dfrac12}47.48 & 47.5 & 47\\\cline{1-3} \vphantom{\dfrac12}47.52 & 47.5 & 48 \\\cline{1-3} \vphantom{\dfrac12}47.58 & 47.6 &48\\\cline{1-3} \vphantom{\dfrac12}47.62 & 47.6& 48\\\cline{1-3} \end{array}[/tex]

    Therefore, the two numbers that are equal when they are rounded to one decimal place, and are not equal when rounded to two significant figures are:

    • 47.48 and 47.52

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    Question 16

    Part (a)

    [tex]\boxed{\begin{minipage}{4 cm}\underline{Area of a triangle}\\\\$A=\dfrac{1}{2}bh$\\\\where:\\ \phantom{ww}$\bullet$ $b$ is the base \\ \phantom{ww}$\bullet$ $h$ is the height\\\end{minipage}}[/tex]

    From inspection of the given diagram:

    • b = 9 cm
    • h = 6 cm

    Substitute the found values of b and h into the formula for area of a triangle:

    [tex]\begin{aligned}\implies \sf Area & = \frac{1}{2} \cdot 9 \cdot 6\\\\&=\frac{9}{2} \cdot 6\\\\&=27\;\; \sf cm^2\end{aligned}[/tex]

    Therefore, the area of the triangular cross-section of the prism is:

    • 27 cm²

    Part (b)

    [tex]\boxed{\text{$\vphantom{\dfrac12}$Volume of a prism = base area $\times$ height}}[/tex]

    The bases of a prism are the two congruent polygons.

    Therefore, the bases of a triangular prism are the triangles.

    Given:

    • Base area = 27 cm²  (from part a)
    • Height = 8 cm

    Substitute the found base area and height into the formula for volume:

    [tex]\begin{aligned}\implies \textsf{Volume of the triangular prism}& = 27 \times 8\\& = 216\;\; \sf cm^3\end{aligned}[/tex]

    Therefore, the volume of the triangular prism is:

    • 216 cm³

    [tex]\boxed{\begin{minipage}{4.5 cm}\underline{Volume of a cube}\\\\$V=s^3$\\\\where:\\ \phantom{ww}$\bullet$ $s$ is the side length \\\end{minipage}}[/tex]

    If the volume of the rectangular prism is the same as the volume of the cube:

    [tex]\implies s^3=216[/tex]

    [tex]\implies \sqrt[3]{s^3}=\sqrt[3]{216}[/tex]

    [tex]\implies s=6\;\; \sf cm[/tex]

    Therefore, the length of one side of the cube is:

    • 6 cm
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