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3 years ago

Rewrite the expression 4+ the square root of 16-(4)(5) decided by 2 as a complex number in standard form a+bi

Mathematics

1 answer:

bija089 [108]3 years ago

8 0

Answer: $4 + \sqrt{4i}$

Step-by-step explanation:

$4+ \sqrt{16-(4)(5)} = 4 + \sqrt{16-20} =4 + \sqrt{-4} = 4 + \sqrt{4i}$

if it matters then simply further...

4 + \sqrt{4i} = $4 + 4i^{1/2}$

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Answer:

0.96592 or 0.97

Step-by-step explanation:

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The diameter of a car wheel is 60 cm, if the car travels at an average speed of 13.2m/s, find the number of revolutions made by

mixer [17]

The wheel has diameter 60 cm = 0.60 m, and thus circumference π(0.60 m) ≈ 5.923 m.

In one complete revolution, a point on the edge of the wheel covers this distance, so that the wheel has an angular speed of

(13.2 m/s) * (1/5.923 rev/m) ≈ 2.229 rev/s

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(2.229 rev/s) * (60 s/min) * (60 min/h) ≈ 8024 rev/h

3 0

3 years ago

Given: △ACM, m∠C=90°, CP ⊥ AM

larisa86 [58]

Answer: The answer is $3\dfrac{4}{7}.$

Step-by-step explanation: Given in the question that ΔAM is a right-angled triangle, where ∠C = 90°, CP ⊥ AM, AC : CM = 3 : 4 and MP - AP = 1. We are to find AM.

Let, AC = 3x and CM = 4x.

In the right-angled triangle ACM, we have

$AM^2=AC^2+CM^2=(3x)^2+(4x)^2=9x^2+16x^2=25x^2\\\\\Rightarrow AM=5x.$

Now,

$AM=AP+PM=AP+(AP+1)\\\\\Rightarrow 2AP=AM-1\\\\\Rightarrow 2AP=5x-1.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(A)$

Now, since CP ⊥ AM, so ΔACP and ΔMCP are both right-angled triangles.

So,

$CP^2=AC^2-AP^2=CM^2-MP^2\\\\\Rightarrow (3x)^2-AP^2=(4x)^2-(AP+1)^2\\\\\Rightarrow 9x^2-AP^2=16x^2-AP^2-2AP-1\\\\\Rightarrow 2AP=7x^2-1.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(B)$

Comparing equations (A) and (B), we have

$5x-1=7x^2-1\\\\\Rightarrow 5x=7x^2\\\\\Rightarrow x=\dfrac{5}{7},~\textup{since }x\neq 0.$

Thus,

$AM=5\times\dfrac{5}{7}=\dfrac{25}{7}=3\dfrac{4}{7}.$

8 0

3 years ago

The value of y varies directly with the value of x. When y = 15, x = 3. What is the value of x when y = 60?

Viefleur [7K]

The answer is B
because at first y was equal to 15 and x equaled to 3 the quotient of 15/3 = 5.
now the y is 60 so, 60/5 = 12

6 0

3 years ago