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3 years ago

Simplify the expression square root 4/(3+I)-(2+3i)

Mathematics

2 answers:

VladimirAG [237]3 years ago

8 0

$\cfrac{ \sqrt{-4} }{(3+i)-(2+3i)} = \cfrac{ 2i}{3+i-2-3i} = \cfrac{ 2i}{1-2i}= \cfrac{ 2i(1+2i)}{(1-2i)(1+2i)}= \\\\=\cfrac{ 2i-4}{1+4}= \cfrac{ -4+2i}{5}$

kolbaska11 [484]3 years ago

4 0

The answer is -⅘ + ⅖i

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The measure of a vertex angle of an isosceles triangle is 120° and the length of a leg is 8 cm. Find the length of a diameter of

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ANSWER

The length of a Diameter is 3.714

EXPLANATION

The circumscribed triangle is shown in the attachment.

We use the cosine ratio to find the altitude of the isosceles triangle.

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$\cos(60 \degree) = \frac{altitude}{8}$

Altitude =8cos(60°)

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Let the upper half of the altitude be y cm.

Then the radius of the circle is (y-4)cm

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From the smaller right triangle,

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3 years ago

Read 2 more answers

You throw a ball up and its height h can be tracked using the equation h=2x^2-12x+20.

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This problem seems to be wrong because no minimum point was found and no point of landing exists

Answer:

1) There is no maximum height

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Step-by-step explanation:

Derivatives

Sometimes we need to find the maximum or minimum value of a function in a given interval. The derivative is a very handy tool for this task. We only have to compute the first derivative f' and have it equal to 0. That will give us the critical points.

Then, compute the second derivative f'' and evaluate the critical points in there. The criteria establish that

If f''(a) is positive, then x=a is a minimum

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The function provided in the question is

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$h'(x)=4x-12$

solving h'=0:

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Computing h''

h''(x)=4

It means that no matter the value of x, the second derivative is always positive, so x=3 is a minimum. The function doesn't have a local maximum or the ball will never reach a maximum height

To find when will the ball land, we set h=0

$2x^2-12x+20=0$

Simplifying by 2

$x^2-6x+10=0$

Completing squares

$x^2-6x+9+10-9=0$

Factoring and rearranging

$(x-3)^2=-1$

There is no real value of x to solve the above equation, so the ball will never land.

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3 years ago

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3 years ago

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Answer:

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