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3 years ago

How can you verify Euler's formula for this net of a cube?

Mathematics

1 answer:

navik [9.2K]3 years ago

5 0

I don't know what the Euler's Formula is..:(

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Find an nth-degree polynomial function with real coefficients satisfying the given conditions.

lesya692 [45]

Answer:

$\displaystyle f(x) = -2(x-2)(x^2+4)$

Step-by-step explanation:

We want to find a third degree polynomial with zeros x = 2 and x = 2i and f(-1) = 30.

First, note that by the Complex Root Theorem, since x = 2i is a root, x = -2i must also be a root.

Hence, we will have the three factors:

$\displaystyle f(x) = a(x-(2))(x-(2i))(x-(-2i))$

Where a is the leading coefficient.

Expand and simplify the second and third factors:

$\displaystyle \begin{aligned} (x-(2i))(x-(-2i)) &= (x-2i)(x+2i) \\ \\ &= x(x-2i)+2i(x-2i) \\ \\ &= (x^2 - 2ix) + (2ix - 4i^2) \\ \\ &=x^2 + 4\end{aligned}$

Hence:

$\displaystyle f(x) = a(x-2)(x^2+4)$

Since f(-1) = 30:

$\displaystyle \begin{aligned} f(x) &= a(x-2)(x^2+4) \\ \\ (30) &= a((-1)-2)((-1)^2+4) \\ \\ 30 &= -15a \\ \\ a&= -2\end{aligned}$

In conclusion, third degree polynomial function is:

$\displaystyle f(x) = -2(x-2)(x^2+4)$

5 0

3 years ago

emelia earns $8.74 per hour plus a gas allowence of $3.50 per day at her job how much does Emelia jobs pays in a day when she wo

trapecia [35]

Answer:

8.74 (3.50) + 3.50

= $51.57

Step-by-step explanation:

8 0

2 years ago

Find the midpoint between (-1+9i) and B=(5-3i)

sdas [7]

Answer:

2 + 3i, midpoint is (2,3)

Step-by-step explanation:

we need to find the midpoint between (-1+9i) and B=(5-3i)

To find the midpoint of two points (a+bi) and (c+di) in a complex plane,

we apply formula

$\frac{a+c}{2} + \frac{b+d}{2} i$

A = (-1+9i) and B=(5-3i)

Midpoint for AB is

$\frac{-1+5}{2} + \frac{9+(-3)}{2}i$

$\frac{4}{2} + \frac{6}{2}i$

2 + 3i , so midpoint is (2,3)

8 0

3 years ago

Read 2 more answers

……………………………………………..()1!-!/

alina1380 [7]

Answer:

A. a is where performance is minimal

Step-by-step explanation:

b is representing peak performance.

8 0

3 years ago

30 points Someone help im very confused.

Alchen [17]

Answer:

y=cotx

Step-by-step explanation:

5 0

2 years ago