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3 years ago

Find the conjugate and product of the following surds2i + 9

Mathematics

1 answer:

scZoUnD [109]3 years ago

6 0

Answer:

The conjugate of 2i + 9 = -2i + 9

Product of (2i+9) and (2i+9) is 36i + 77

Step-by-step explanation:

Given - 2i + 9

To find - Find the conjugate and product of the following surds

Proof -

We know that,

The sum and difference of two simple quadratic surds are said to be conjugate surds to each other.

To find a complex conjugate, simply change the sign of the imaginary part (the part with the i ).

So,

The conjugate of 2i + 9 = -2i + 9

Now,

Product of surd (2i+9) is

(2i+9)(2i+9) = 2i(2i) + 2i(9) + 9(2i) + 9(9)

= 4i² + 18i + 18i + 81

= -4 + 36i + 81 { because i² = -1 }

= 77 + 36i

⇒Product of (2i+9) and (2i+9) is 36i + 77

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Can someone help me on this

SCORPION-xisa [38]

Step-by-step explanation:

(a) n² + 3

First term = 1² + 3 = 4

Second term = 2² + 3 = 7

Third term = 3² + 3 = 12

Fourth term = 4² + 3 = 19

10th term = 10² + 3 = 103

(b) 2n²

First term = 2(1)² = 2

Second term = 2(2)² = 8

Third term = 2(3)² = 18

Fourth term = 2(4)²= 32

10th term = 2(10)² = 200

Hence, this is the required solution.

5 0

3 years ago

An experiment was performed to compare the abrasive wear of two different laminated materials. Twelve pieces of material 1 were

vladimir1956 [14]

Answer:

The calculated value Z= 4.8389> 1.96 at 0.05 level of significance.

The null hypothesis is rejected.

There is significance difference between that the abrasive wear of material 1 not exceeds that of material 2 by more than 2 units

Step-by-step explanation:

Step:-(1)

Given data the samples of material 1 gave an average (coded) wear of 85 units with a sample standard deviation of 4

Mean of the first sample x₁⁻ =85

standard deviation of the first sample S₁ = 4

Given data the samples of material 2 gave an average of 81 and a sample standard deviation of 5.

Mean of the first sample x₂⁻ =81

standard deviation of the first sample S₂ = 5

Step :-2

Null hypothesis: H₀: there is no significance difference between that the abrasive wear of material 1 exceeds that of material 2 by more than 2 units

Alternative hypothesis :H₁: there is significance difference between that the abrasive wear of material 1 exceeds that of material 2 by more than 2 units

Assume the populations to be approximately normal with equal variances.σ₁² =σ₂²

The test statistic

$Z= \frac{x_{1} -x_{2} }{\sqrt{\frac{S^2_{1} }{n_{1} } +\frac{S^2_{2} }{n_{2} } } }$

Given n₁=n₂=60.

$Z= \frac{85-81 }{\sqrt{\frac{(4)^2 }{60 } +\frac{5^2 }{60} } }$

On calculation, we get

Z = $\frac{4}{\sqrt{0.6833} }$

z = 4.8389

The tabulated value Z =1.96 at 0.05 level of significance.

The calculated value Z= 4.8389> 1.96 at 0.05 level of significance.

The null hypothesis is rejected.

Conclusion:-

there is significance difference between that the abrasive wear of material 1 not exceeds that of material 2 by more than 2 units.

3 0

3 years ago

1,666 divided by 7 PLEASE HELP

IRISSAK [1]

Answer:

The answer is 238 :)

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

2) find the area of each. Leave your answer in terms of Pi. 4) find the area of each.

Delvig [45]

Answer:

Area of circle= 81π

Area of triangle= 371.8 yards

Step-by-step explanation:

2) Area of circle = πr²

Area of circle = π*(18/2)²

Area of circle = 81π

Therefore, the area of circle is 81π.

4) Area of triangle = 1/2*base*height

Area of triangle = 1/2*22*33.8

Area of triangle = 371.8 yards

Therefore, the area of the triangle is 371.8 yards.

3 0

4 years ago

How would I get a answer?

tresset_1 [31]

Answer:

0.07kg

Step-by-step explanation:

1kg = 1000g

so grams/1000 =kg

70/1000 = 0.07kg

3 0

3 years ago