Which three-dimensional object has the same shape for parallel, perpendicular, and diagonal cross sections?

Mathematics

1 answer:

GuDViN [60]3 years ago

3 0

This answer would be a cuboid because it has parallel,perpendicular,and diagonal cross sections

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Find the vector projection of B onto A if A = 5i + 11j – 2k,B = 4i + 7k

valkas [14]

Answer:

$\frac{3}{13} i+\frac{11}{130} j-\frac{6}{65} k\\$

Step-by-step explanation:

Given A = 5i + 11j – 2k and B = 4i + 7k, the vector projection of B unto a is expressed as $proj_ab = \dfrac{b.a}{||a||^2} * a$

b.a = (5i + 11j – 2k)*( 4i + 0j + 7k)

note that i.i = j.j = k.k =1

b.a = 5(4)+11(0)-2(7)

b.a = 20-14

b.a = 6

||a|| = √5²+11²+(-2)²

||a|| = √25+121+4

||a|| = √130

square both sides

||a||² = (√130)

||a||² = 130

$proj_ab = \dfrac{6}{130} * (5i+11j-2k)\\\\proj_ab = \frac{30}{130} i+\frac{11}{130} j-\frac{12}{130} k\\\\proj_ab = \frac{3}{13} i+\frac{11}{130} j-\frac{6}{65} k\\\\$

<em>Hence the projection of b unto a is expressed as </em> $\frac{3}{13} i+\frac{11}{130} j-\frac{6}{65} k\\$ <em></em>

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Find the volume of the solid figure shown below. The area of the base is 40 square inches, and the height of the figure is 7 inc

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Step-by-step explanation:

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What is the standard deviation of the following data set rounded to the nearest tenth?

tamaranim1 [39]

$Formula\ for\ standard\ deviation\ :\\\\
x=\sqrt{y^2}\\
y-variance\\\\
y^2=\frac{(a_1-a)^2+(a_2-a)^2...+(a_n-a)^2}{n}\\
n-amount\ of\ numbers\\
a-mean\\\
a=\frac{11+5+12+8+5+12+10}{7} =\frac{63}{7}=9\\\\
y^2=\frac{(11-9)^2+(5-9)^2+(12-9)^2+(8-9)^2+(5-9)^2(12-9)^2+(10-9)^2}{7}
\\y^2=\frac{(2)^2+(-4)^2+(3)^2+(-1)^2+(-4)^2+(3)^2+1^2}{7}=\\ \frac{4+16+9+1+16+9+1}{7}=\frac{56}{7}=8\\\\
x=\sqrt8=2\sqrt2
$