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lapo4ka [179]
3 years ago
12

Please answer the question below (ABOUT VECTORS AND MAGNITUDE)

Mathematics
1 answer:
coldgirl [10]3 years ago
4 0

(a) <em>v</em> appears to have a fixed direction along the positive <em>x</em>-axis. If ||<em>u</em>|| = 150 N, ||<em>v</em>|| = 220 N, then when <em>θ</em> = 30°, you have

<em>u</em> = (150 N) (cos(30°) <em>i</em> + sin(30°) <em>j</em> ) ≈ (129.904 <em>i</em> + 75 <em>j</em> ) N

<em>v</em> = (220 N) (cos(0°) <em>i</em> + sin(0°) <em>j</em> ) = (220 <em>i</em> ) N

(<em>i</em> and <em>j</em> are the unit vectors in the positive <em>x</em> and <em>y</em> directions)

and their sum is

<em>u</em> + <em>v</em> ≈ (349.904 <em>i</em> + 75 <em>j</em> ) N

with magnitude

||<em>u</em> + <em>v</em>|| ≈ √((349.904)² + (75)²) N ≈ 357.851 N ≈ 357.9 N

and at angle <em>φ</em> made with the positive <em>x</em>-axis such that

tan(<em>φ</em>) ≈ (75 N) / (349.904 N)   →   <em>φ</em> ≈ 12.098° ≈ 12.1°

(b) Letting <em>θ</em> vary from 0° to 180° would make <em>v</em> a function of <em>θ</em> :

<em>u</em> = (150 N) (cos(<em>θ</em>) <em>i</em> + sin(<em>θ</em>) <em>j</em> ) = (150 cos(<em>θ</em>) <em>i</em> + 150 sin(<em>θ</em>) <em>j</em> ) N

Then

<em>u</em> + <em>v</em> = ((220 + 150 cos(<em>θ</em>)) <em>i</em> + (150 sin(<em>θ</em>)) <em>j</em> ) N

→   <em>M</em> = ||<em>u</em> + <em>v</em>|| = √((220 + 150 cos(<em>θ</em>))² + (150 sin(<em>θ</em>))²) N

<em>M</em> = √(48,400 + 66,000 cos(<em>θ</em>) + 22,500 cos²(<em>θ</em>) + 22,500 sin²(<em>θ</em>)) N

<em>M</em> = 10 √(709 + 660 cos(<em>θ</em>)) N

(c) As a function of <em>θ</em>, <em>u</em> + <em>v</em> makes an angle <em>α</em> with the positive <em>x</em>-axis such that

tan(<em>α</em>) = (150 sin(<em>θ</em>) / (220 + 150 cos(<em>θ</em>))

→   <em>α</em> = tan⁻¹((15 sin(<em>θ</em>) / (22 + 15 cos(<em>θ</em>)))

(d) Filling in the table is just a matter of evaluating <em>M</em> and <em>α</em> for each of the given angles <em>θ</em>. For example, when <em>θ</em> = 0°,

<em>M</em> = 10 √(709 + 660 cos(0°)) N = 370 N

<em>α</em> = tan⁻¹((15 sin(0°) / (22 + 15 cos(0°))) = 0°

When <em>θ</em> = 30°, you get the same result as in part (a).

When <em>θ</em> = 60°,

<em>M</em> = 10 √(709 + 660 cos(60°)) N ≈ 323.3 N

<em>α</em> = tan⁻¹((15 sin(60°) / (22 + 15 cos(60°))) = 23.8°

and so on.

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The blood platelet counts of a group of women have a boll-shaped distribution with a mean of 261.1 and a standard deviation of 6
alexandr402 [8]

The variable is

X: blood platelet count of a woman

This variable has a bell shaped distribution (Normal)

With mean μ=261.1 and standard deviation σ=64.3

a.

The platelet count within 3 standard deviations of the mean can be calculated as

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You can symbolize it as

μ-3σ ≤ X ≤ μ+3σ

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Between μ ± σ you'll find the 68% of the distribution

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Between μ ± 3σ you'll find the 99% of the distribution

So following this rule you'll find 99% of the women with platelet count within 3 standard deviations of the mean.

b.

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Divide 0.97 by 2

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Each tail contains 0.485 of the distribtuion.

a and b represent the values within you'll find 3% of the population.

Until a you'll find 0.485 of the population and until b you'll find 0.485+0.03=0.515

To calculate both unknown values you have to use the standard normal distribution. This distribution is centered in zero, the left tail is negative and the right tail is positive.

a and b are at a equal distance from the mean but with different sign, so you only have to calculate on and then you invert the sign to get the other one.

I'll calculate the positive value:

Z= (X- μ )/σ~N(0,1)

P(Z≤ b)=0.515

Look in the body of the Z-table, rigth or positive entry and reach the margins for the value:

b= 0.038

Then using the values of the mean and the standard deviation you can calculate the corresponding valueof platelet count:

b= (X- μ )/σ

0.038= (X- 261.1 )/64.3

0.038*64.3=X-261.1

2.4434+261.1=X

X=263.5434=263.5

a=-b=-0.038

a= (X- μ )/σ

-0.038= (X- 261.1 )/64.3

-0.038*64.3=X-261.1

-2.4434+261.1=X

X=258.6566= 258.7

3% of the populations platelet count is between 258.7 and 263.5.

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10 months ago
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Step-by-step explanation:

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2 years ago
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The number of students in a math club decreased from 15 to 11. What is the percent decrease? Round to the nearest percent.
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Answer:

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3 years ago
I have 18 ones 15 hundreds 15 tens 8thousands what number am I
tankabanditka [31]
8 thousands is equal to 8000.
15 hundreds is equal to 1500.
15 tens is equal to 150.
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The number is 9668
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