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3 years ago

3i(4 - I) + i(6 + 2i)

Mathematics

1 answer:

kumpel [21]3 years ago

4 0

Answer:

-1 + 18i

Step-by-step explanation:

⟺ Distribute 3i and i in the expressions.

$12i-i^2+6i+2i^2\\i^2+18i$

⟺ The define of complex number is

$i^2=-1$

Thus, convert i² to -1

$-1+18i$

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Consider this scaled figure of a swimming pool. The dimensions of the original pool are 24 feet wide by 36 feet long. A rectangl

kozerog [31]

The scale factor used for scaling the actual rectangular pool was 4/15 and the length of the scaled rectangle is 9.6 feet.

<h3>How to calculate the scale factor?</h3>

Suppose the initial measurement of a figure was x units.

And let the figure is scaled and new measurement is of y units.

Since the scaling is done by multiplication of some constant, that constant is called scale factor. Let that constant be 's'.

Then we have:

$s \times x = y\\s = \dfrac{y}{x}$

Thus, scale factor is the ratio of the new measurement to the old measurement.

For this case, we're specified that:

Dimensions of the original pool = 24 feet wide by 36 feet long

The scaled rectangle's dimension: 6.4 feet width and L feet length (we assume the length be L units).

So, in scale drawing, 24 feet was converted to 6.4 feet. Let the scale factor be 's', then:

$6.4 = s \times 24\\\\s = \dfrac{6.4}{24} = \dfrac{4}{15}$

Thus, since length is also scaled by same factor(as the whole figure is scaled by constant scale factor assumingly), we get:

Scaled length = s times original length

$L = \dfrac{4}{15} \times 36 = 9.6 \: \rm feet$

Thus, the scale factor used for scaling the actual rectangular pool was 4/15 and the length of the scaled rectangle is 9.6 feet.

Learn more about scale factors here :

brainly.com/question/8765466

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2 years ago

A person gets on a Ferris wheel at the starting point. The starting point is 15 feet off the ground. The Ferris wheel has a radi

lisov135 [29]

<h2>Answer:</h2>

$\boxed{\frac{25}{2}(\sqrt{6}+\sqrt{2})+65}$

<h2>Explanation:</h2>

<em>The height of the rider from the ground after the Ferris wheel</em> equals <em>the starting point is 15 feet off the ground </em><em>plus </em><em>the radius of the Ferris wheel </em><em>plus </em><em>the opposite side of the triangle ΔABC </em>(See figure below).<em> </em>Hence our goal is to find this side. We have the angle $11\pi /2=165^{\circ}$ , therefore the angle ∠BAC = 165° - 90° = 75°. So this side can be found using trigonometry:

$\overline{BC}=\overline{AB}sin(75^{\circ})=50sin(75^{\circ})=\frac{25}{2}(\sqrt{6}+\sqrt{2})$

Finally, the height is:

$H=\frac{25}{2}(\sqrt{6}+\sqrt{2})+15+50 \\ \\ \boxed{H=\frac{25}{2}(\sqrt{6}+\sqrt{2})+65}$

6 0

3 years ago

A furniture company manufactures desks and chairs. Each desk uses four units of wood, and each chair uses three units of wood. A

Pavlova-9 [17]

Answer:

$180000

Step-by-step explanation:

Let's c be the number of chair and d be the number of desks.

The constraint functions:

- Unit of wood available 4d + 3c <= 2000 or d <= 500 - 0.75c

- Number of chairs being at least twice of desks c >= 2d or d <= 0.5c

c >= 0

d >= 0

The objective function is to maximize the profit function

P (c,d) = 400d + 250c

We draw the 2 constraint functions (500 - 0.75c and 0.5c) on a c-d coordinates (witch c being the horizontal axis and d being the vertical axis) and find the intersection point 0.5c = 500 - 0.75c

1.25c = 500

c = 400 and d = 0.5c = 200 so P(400, 200) = $250*400 + $400*200 = $180,000

The 500 - 0.75c intersect with c-axis at d = 0 and c = 500 / 0.75 = 666 and P(666,0) = 666*250 = $166,500

So based on the available zones in the chart we can conclude that the maximum profit we can get is $180000

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4 years ago

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Nesterboy [21]

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3 years ago

X:-13.8=x-4.3 Describe in words how to solve a one step equation

zimovet [89]

Answer:

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3 years ago