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3 years ago

PLEASE HELP FAST

Mathematics

1 answer:

skad [1K]3 years ago

8 0

Answer:

The unit vector u is (-5/√29) i - (2/√29) j

Step-by-step explanation:

* Lets revise the meaning of unit vector

- The unit vector is the vector ÷ the magnitude of the vector

- If the vector w = xi + yj

- Its magnitude IwI = √(x² + y²) ⇒ the length of the vector w

- The unit vector u in the direction of w is u = w/IwI

- The unit vector u = (xi + yj)/√(x² + y²)

- The unit vector u = [x/√(x² + y²)] i + [y/√(x² + y²)] j

* Now lets solve the problem

∵ v = -5i - 2j

∴ IvI = √[(-5)² +(-2)²] = √[25 + 4] = √29

- The unit vector u = v/IvI

∴ u = (-5i - 2j)/√29 ⇒ spilt the terms

∴ u = (-5/√29) i - (2/√29) j

* The unit vector u is (-5/√29) i - (2/√29) j

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Through: (3, 3) and (-5, 4)

horsena [70]

Hi,

a line is define by the following equation : y = ax+b

where a is the slope, and b the value for x = 0

so you have : a*3 +b = 3 for the first point

a*(-5) +b = 4 for second point

so you have a system : 3a+b =3

-5a+b = 4

so : 3a+b -(-5a) -b = 3-4

3a+5a +b-b = -1

8a = -1

a = -1/8

then a = -1/8 so , in remplacing a by it's value in one equation , b is : 3(-1/8) +b = 3

-3/8 +b = 3

b = 3 +3/8

b = 24/8 +3/8

b = 27/8

let's check : 3 (-1/8) + 27/8 = -3/8 +27/8 = 24/8 = 3

first point is correct

-5( -1/8) + 27/8 = 5/8 +27/8 = 32/8 = 4

second point is correct

line is y = -1/8X +27/8

3 0

3 years ago

F(x) = x^2. What is g(x)?

Readme [11.4K]

G(x) = ax^2
y = ax^2
16 = a1^2
a = 16

Therefore, g(x) = 16x^2

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4 years ago

1. A company has $5826 to give out in bonuses. An amount is to be given out equally to each of the 29 employees.

pashok25 [27]

Answer:

a) Incorrect

b) $201

Step-by-step explanation:

$5826 need to be distributed equally among 29 employees . Hence we need to divide 5826 by 29 to know the amount each one will get. Since 58=29*2 and 26≈2, The manager can estimate that each one of the employee will get $201 as bonus. So his reason to estimate was correct but the estimated amount was incorrect.

Each employee will get

$\frac{5826}{29}$

= 200.89

Hence Each one will get

$201 rounded to nearest whole number

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3 years ago

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andrey2020 [161]

Answer:

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Step-by-step explanation:

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3 years ago

Read 2 more answers

PTC is a substance that has a strong bitter taste for some people and is tasteless for others. The ability to taste PTC is inher

umka21 [38]

Answer:

Sample size shouldbe atleast 60

Step-by-step explanation:

Given that PTC is a substance that has a strong bitter taste for some people and is tasteless for others. The ability to taste PTC is inherited and depends on a single gene that codes for a taste receptor on the tongue. Interestingly, though the PTC molecule is not found in nature, the ability to taste it correlates strongly with the ability to taste other naturally occurring bitter substances, many of which are toxins.

Proportion of Italians who taste PTC =0.75

Margin of error <0.11

Confidence level = 95%

Std error of proportion = $\sqrt{\frac{0.75*0.25}{n} }$

Margin of error = $1.96*\sqrt{\frac{0.75*0.25}{n} }$ <0.11

$\sqrt{n} >1.96*\sqrt{0.75*0.25} /0.11\\=17.81*0.4330\\=7.71\\n>59.47\\$

Sample size shouldbe atleast 60

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4 years ago