How do birds achieve take-off, gliding, dive, etc.? How do they modify their body shape?

This question is incomplete, the complete question is;

Given the complex numbers A₁ = 6∠30 and A₂ = 4 + j5;

(a) convert A₁ to rectangular form

(b) convert A₂ to polar and exponential form

(c) calculate A₃ = (A₁ + A₂), giving your answer in polar form

(d) calculate A₄ = A₁A₂, giving your answer in rectangular form

(e) calculate A₅ = A₁/([tex]A^{*}[/tex]₂), giving your answer in exponential form.

Answer:

a) A₁ in rectangular form is 5.196 + j3

b) value of A₃  in polar form is 12.19∠41.02°

The polar form of A₂ is 6.403 ∠51.34°, exponential form of A₂ = 6.403[tex]e^{j51.34 }[/tex]

c) value of A₃  in polar form is 12.19∠41.02°

d) A₄ in rectangular form is 5.784 + j37.98

e) A₅ in exponential form is 0.937[tex]e^{j81.34 }[/tex]

Explanation:

Given data in the question;

a) A₁ = 6∠30

we convert A₁ to rectangular form

so

A₁ = 6(cos30° + jsin30°)

= 6cos30° + j6cos30°

= (6 × 0.866) + ( j × 6 × 0.5)

A₁  =  5.196 + j3

Therefore, A₁ in rectangular form is 5.196 + j3

b) A₂ = 4 + j5

we convert to polar and exponential form;

first we convert to polar form

A₂ = √((4)² + (5)²) ∠tan⁻¹( [tex]\frac{5}{4}[/tex] )

= √(16 + 25) ∠tan⁻¹( 1.25 )

= √41 ∠ 51.34°

A₂ = 6.403 ∠51.34°

The polar form of A₂ is 6.403 ∠51.34°

next we convert to exponential form;

A∠β can be written as A[tex]e^{j\beta }[/tex]

so, A₂  in exponential form will be;

A₂ = 6.403[tex]e^{j51.34 }[/tex]

exponential form of A₂ = 6.403[tex]e^{j51.34 }[/tex]

c) A₃ = (A₁ + A₂)

giving your answer in polar form

so, A₁ = 6∠30 = 5.196 + j3 and A₂ = 4 + j5

we substitute

A₃ = (5.196 + j3) + ( 4 + j5)

= 9.196 + J8

next we convert to polar

A₃ = √((9.196)² + (8)²) ∠tan⁻¹( [tex]\frac{8 }{9.196}[/tex] )

A₃ = √(84.566416 + 64) ∠tan⁻¹( 0.8699)

A₃ = √148.566416 ∠41.02°    

A₃ = 12.19∠41.02°

Therefore, value of A₃  in polar form is 12.19∠41.02°

d) A₄ = A₁A₂

giving your answer in rectangular form

we substitute

A₄ = (5.196 + j3) ( 4 + j5)

= 5.196( 4 + j5) + j3( 4 + j5)

= 20.784 + j25.98 + j12 - 15

A₄ = 5.784 + j37.98

Therefore, A₄ in rectangular form is 5.784 + j37.98

e) A₅ = A₁/([tex]A^{*}[/tex]₂)

giving your answer in exponential form

we know that [tex]A^{*}[/tex]₂ is the complex  conjugate of A₂

so

[tex]A^{*}[/tex]₂ = (6.403 ∠51.34° )*

= 6.403 ∠-51.34°

we convert to exponential form

A∠β can be written as A[tex]e^{j\beta }[/tex]

[tex]A^{*}[/tex]₂  = 6.403[tex]e^{-j51.34 }[/tex]

also

A₁ = 6∠30

we convert to polar form

A₁ = 6[tex]e^{j30 }[/tex]

so A₅ = A₁/([tex]A^{*}[/tex]₂)

A₅ = 6[tex]e^{j30 }[/tex] / 6.403[tex]e^{-j51.34 }[/tex]

A₅  = (6/6.403) [tex]e^{j(30+51.34) }[/tex]

A₅  = 0.937[tex]e^{j81.34 }[/tex]

Therefore A₅ in exponential form is 0.937[tex]e^{j81.34 }[/tex]

Answer:

350×305π{^ not sure my answer please follow me

Answer: See explanation

Explanation:

Emerging technologies are simply referred to as the technical innovations which are done within a particular sector and typically brings about growth to such field or sector.

Some of the new and emerging technologies that are used in the electronics and telecommunications industry include:

1. Digital scent technology - This is a technology that is used for the sensing and the transmission of digital media such as video games, music etc that are event enabled.

2. Electronic nose - This refers to an electronic sensing device which is used in the detection of flavors.

3. Ambient intelligence - It is an electronic environments which shows sensitivity when there are people.

While changing a soil's basic texture is very difficult, you can improve its structure–making clay more porous, sand more water retentive–by adding amendments. The best amendment for soil of any texture is organic matter, the decaying remains of plants and animals.

Answer:

Resistance of copper = 1.54 * 10^18 Ohms

Explanation:

Given the following data;

Length of copper, L = 3 kilometers to meters = 3 * 1000 = 3000 m

Resistivity, P = 1.7 * 10^8 Ωm

Diameter = 0.65 millimeters to meters = 0.65/1000 = 0.00065 m

[tex] Radius, r = \frac {diameter}{2} [/tex]

[tex] Radius = \frac {0.00065}{2} [/tex]

Radius = 0.000325 m

To find the resistance;

Mathematically, resistance is given by the formula;

[tex] Resistance = P \frac {L}{A} [/tex]

Where;

First of all, we would find the cross-sectional area of copper.

Area of circle = πr²

Substituting into the equation, we have;

Area  = 3.142 * (0.000325)²

Area = 3.142 * 1.05625 × 10^-7

Area = 3.32 × 10^-7 m²

Now, to find the resistance of copper;

[tex] Resistance = 1.7 * 10^{8} \frac {3000}{3.32 * 10^{-7}} [/tex]

[tex] Resistance = 1.7 * 10^{8} * 903614.46 [/tex]

Resistance = 1.54 * 10^18 Ohms

Answer:

Get ready and comfortable.

List all of the tasks you need to accomplish over the next week. .

Next schedule everything.

Get a planner/calender.

Cut those tasks that do not fit into your

This question is incomplete, the complete question is;

Air entrainment is a process of entrapping tiny air bubbles in concrete mix in order to increase the durability of the hardened concrete in freeze-thaw climates. After 35 days, the breaking stress [in psi] was measured for concrete samples with and without air entrainment. Based on the data, does the air entrainment process increase the breaking stress of the concrete. { ∝ = 0.05 }, assuming population variances are equal.

Air Entrainment       No Air Entrainment

4479                                  4118

4436                                  4531

4358                                  4315

4724                                   4237

4414                                   3888

4358                                  4279

4487                                   4311

3984

4197

4327

Answer:

Since p-value ( 0.088) > significance level ( 0.05)

hence, Failed to reject Null hypothesis

It is then concluded that the null hypothesis H₀ is NOT REJECTED.

Therefore, there is no sufficient evidence to claim that population mean μ1 is greater than μ2 at 0.05 significance level.

We conclude that Air entrainment process can't increase the breaking stress of the concrete.

Explanation:

Given the data in the question;  

mean x" = (4479 + 4436 + 4358 + 4724 + 4414 + 4358 + 4487 + 3984 + 4197 + 4327) / 10

mean x"1 =  43764 / 10 = 4376.4

 x                 ( x - x" )             ( x - x" )²

4479              102.6              10526.76

4436              59.6               3552.16

4358             -18.4                 338.56

4724              347.6               120825.76

4414               37.6                 1413.76

4358             -18.4                 338.56

4487              110.6                 12232.36

3984            -382.4                153977.76

4197              -179.4                32184.36

4327             -49.4                  2440.36  

∑                                             337830.4

Standard deviation s1 = √( (∑( x - x" )²) / n -1  

Standard deviation s1 = √( 337830.4 / (10 - 1 ))

Standard deviation s1 = 193.74

 x2                 ( x2 - x"2 )           ( x2 - x"2 )²

4118                  -121.9               14859.61  

4531                   291.1               84739.21

4315                   75.1                5640.01

4237                  -2.9                 8.41    

3888                  -351.9            123833.61

4279                   39.1               1528.81

4311                     71.1                5055.21

∑                                              235664.87

mean x"2 = (4118 + 4531 + 4315 + 4237 + 3888 + 4279 + 4311) / 7

mean x"2 = 29679 / 7 = 4239.9  

Standard deviation s2 = √( (∑( x2 - x" )²) / n2 - 1  

Standard deviation s1 = √( 337830.4 / (7 - 1 ))

Standard deviation s1 = 198.19

so

Mean x"1 = 4376.4,   S.D1 = 193.74,  n1 = 10

Mean x"2 = 4239.9,   S.D2 = 198.19,   n2 = 7

so;

Null Hypothesis H₀ : μ1 = μ2

Alternative Hypothesis H₁ : μ1 > μ2

Lets determine our rejection region;

based on the data provided. the significance level ∝ = 0.005

with degree of freedom DF = n1 + n2 - 2 = 10 + 7 - 2 = 15

so, Critical Value = 1.753

The rejection region for this right -tailed is R = t:t > 1.753

Test statistics

since it is assumed that the population variances are equal, so we calculate pooled standard deviation;

Sp = √{ [ (n1 -1)S.D1² +  (n2 - 1)S.D2²] / [ n1 + n2 -2 ]

we substitute

Sp = √{ [ (10 -1)(193.74)² +  (7 - 1)(198.19)²] / [ 10 + 7 -2 ]

Sp = √ [ 573492.345 / 15 ]

Sp = 195.53

so the Test statistics will be;

t = (x"1 - x"2) / Sp√([tex]\frac{1}{n1}[/tex] + [tex]\frac{1}{n2}[/tex] )

t = (4376.4 - 4239.9) / 195.53√([tex]\frac{1}{10}[/tex] + [tex]\frac{1}{7}[/tex] )

t = 136.5 / 96.36

t = 1.42

so

P-value = 0.088

Since p-value ( 0.088) > significance level ( 0.05)

hence, Failed to reject Null hypothesis

It is then concluded that the null hypothesis H₀ is NOT REJECTED.

Therefore, there is no sufficient evidence to claim that population mean μ1 is greater than μ2 at 0.05 significance level.

We conclude that Air entrainment process can't increase the breaking stress of the concrete.

Answer:

mH275 units

Explanation: