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3 years ago

Please help will give brainliest.

Mathematics

1 answer:

MAXImum [283]3 years ago

3 0

Answer:

V≈523.6

Step-by-step explanation:

V=4

3πr3=4

3·π·53≈523.59878

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Which on is not a function

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3 years ago

A mixture of concrete is made up of sand and cement in the ratio of 5:3.How many cubic centimeters of sand is needed to make 160

bazaltina [42]

Answer: $100\ cm^3$

Step-by-step explanation:

Given

The ratio of mixture of sand and cement is 5:3

If the total volume of mixture is $160\ cm^3$

Suppose there is 5x and 3x cubic centimeter of sand and cement respectively i.e.

$\Rightarrow 5x+3x=160\\\Rightarrow 8x=160\\\Rightarrow x=20\ cm^3$

Sand $5x=5\times 20=100\ cm^3$

So, there is $100\ cm^3$ of sand in the mixture

3 0

3 years ago

What is the best approximation of the projection of (5,-1) onto (2,6)?

Hatshy [7]

Answer:

Hence, the scalar projection of $\vec a$ onto $\vec b$ = $\frac{\sqrt{10} }{5}$ , and the vector projection of $\vec a$ onto $\vec b$ = $\frac{1}{5} \hat i+\frac{3}{5} \hat j$ .

Step-by-step explanation:

We have given two points $(5, -1)$ and $(2, 6)$ .

Let, $\vec a=5\hat {i}-\hat {j}$ and $\vec b= 2\hat {i}+6\hat{j}$ .

and we have calculate the projection of $\vec a$ onto $\vec b$ .

Now,

For the calculation of projection, first we need to calculate the dot product of $\vec a$ and $\vec b$ .

$\vec a.\vec b=(5\hat {i}-\hat{j}).(2\hat{i}+6\hat{j})$

$=10-6$

$=4$

then, we have to calculate the magnitude of $\vec b$ .

$\mid {\vec {b}}\mid$ = $\sqrt{2^{2}+6^{2} }$ = $\sqrt{40}$ = $2\sqrt{10}$ .

Now, the scalar projection of $\vec a$ onto $\vec b$ = $\frac{\vec a.\vec b}{\mid b\mid}$

= $\frac{4}{2\sqrt{10} }$ $\frac{2}{\sqrt{10} } \times\frac{\sqrt{10} }{\sqrt{10} } =\frac{2\sqrt{10} }{10} = \frac{\sqrt{10} }{5}$

and the vector projection of $\vec a$ onto $\vec b$ = $\frac{\vec a. \vec b}{\mid\vec b \mid^{2} } . \vec b$

= $\frac{4}{40} . (2\hat i+ 6\hat j)$

= $\frac{1}{5} \hat i+\frac{3}{5} \hat j$

Hence, the scalar projection of $\vec a$ onto $\vec b$ = $\frac{\sqrt{10} }{5}$ , and the vector projection of $\vec a$ onto $\vec b$ = $\frac{1}{5} \hat i+\frac{3}{5} \hat j$ .