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3 years ago

Find the magnitude of v. v = -3i+ 40 + 7k v =

Mathematics

1 answer:

kherson [118]3 years ago

5 0

Answer:

The magnitude of the given vector is 40.72 units.

Step-by-step explanation:

The given vector is $v=-3\widehat{i}+40\widehat{j}+7\widehat{k}$

We know that for any vector 'r' $\overrightarrow{r}=x\widehat{i}+y\widehat{j}+z\widehat{k}$ the magnitude is given by

$|r|=\sqrt{x^{2}+y^{2}+z^{2}}$

Comparing with the given vector we have

x = -3

y = 40

z = 7

Thus the magnitude equals

$|v|=\sqrt{(-3)^{2}+40^{2}+7^{2}}$

$|v|=40.72$

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Andre45 [30]

The answer is A: 4. This is easy once you know the order of operations, aka PEMDAS. Parentheses, exponents, multiplication/division, and addition/subtraction.

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3 years ago

») What is the volume of a ball with adiameter of 6 centimeters? Use 3.14for (pie)How is the volume of a sphere related tothe vo

Dahasolnce [82]

Volume of a sphere and a cone

We have that the equation of the volume of a sphere is given by:

$V=\frac{4}{3}\pi r^3$

We have that the radius of a sphere is half the diameter of it:

Then, the radius of this sphere is

r = 6cm/2 = 3cm

<h2>Finding the volume of a sphere</h2>

We replace r by 3 in the equation:

$\begin{gathered} V=\frac{4}{3}\pi r^3 \\ \downarrow \\ V=\frac{4}{3}\pi\cdot3^3 \end{gathered}$

Since 3³ = 3 · 3 · 3 = 27

$\begin{gathered} V=\frac{4}{3}\pi3^3 \\ \downarrow \\ V=\frac{4}{3}\pi\cdot27 \end{gathered}$

If we use π = 3.14:

$\begin{gathered} V=\frac{4}{3}\pi\cdot27 \\ \downarrow \\ V=\frac{4}{3}\cdot3.14\cdot27 \\ \downarrow \\ V=4.18\bar{6}\cdot27 \end{gathered}$

Rounding the first factor to the nearest hundredth (two digits after the decimal), we have:

4.18666... ≅ 4.19

Then, we have that:

$\begin{gathered} V=\frac{4}{3}\pi\cdot27 \\ \downarrow \\ V=4.19\cdot27 \\ =113.13 \end{gathered}$

Then, we have that:

<h2>Finding the volume of a cone</h2>

We have that the volume of a cone is given by:

$V=\frac{1}{3}\pi r^2h$

where r is the radius of its base and h is the height:

Then, in this case

r = 3

h = 6

and

π = 3.14

Replacing in the equation for the volume:

$\begin{gathered} V=\frac{1}{3}\pi r^2h \\ \downarrow \\ V=\frac{1}{3}\cdot3.14\cdot3^2\cdot6 \end{gathered}$

Then, we have:

3² = 9

$\begin{gathered} V=\frac{1}{3}\cdot3.14\cdot3^2\cdot6 \\ \downarrow \\ V=\frac{1}{3}\cdot3.14\cdot9\cdot6 \\ V=\frac{1}{3}\cdot3.14\cdot54 \\ V=56.52 \\ \end{gathered}$

Answer: the volume of the cone that has the same circular base and height is 56.52 cm³

5 0

1 year ago

PLEASEEEEE HELPPPPP!!!!

Dmitry_Shevchenko [17]

Step One

Find AM

Formula

AM = MN - AN

Givens

MN = 67.2

AN = 32

Solution

AM - 67,2 - 32

AM = 35.2

Step Two

Set up a solution

67.2/35.2 = 81.9/x Cross Muliply

67.2 * x = 81.9 * 35.2 Combine the right

67.2 * x = 2882.88 Divide by 67.2

x = 2882.88/67.2

x = 42.9 Answer

3 0

3 years ago

Help asap pleaseeee (if u do ily)))

n200080 [17]

Answer:

B) 120

Step-by-step explanation:

180 - 60 = 120

Hope that helps!

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3 years ago

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How is 7.54÷4= 1.88<br><br>I got 1.88 with the remainder of 2

Naddika [18.5K]

Answer:

I got 1.885 for the answer.

Maybe they wanted it rounded to just 2 decimal places.

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers