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3 years ago

Write a polynomial equation of degree 3 such that two of its roots are 2 and an imaginary number

Mathematics

1 answer:

natta225 [31]3 years ago

5 0

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

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There are 27 performances in a dance recital. The ratio of hip hop to ballet is 5:4.

Aloiza [94]

Answer:

15 hip hop performances

12 ballet performances

Step-by-step explanation:

5:4 (multiply by 3)

15:12

6 0

3 years ago

A quadratic function has a vertex of (0,7) and passes through the point (2, 3). Which of

Arlecino [84]

Answer:

Y = -2X + 7

Step-by-step explanation:

Y = a(x-h)^2 + k

From (h,k) h = 0 k = 7 x = 2 y = 3

3 = a(2-0) + 7

3 = 2a - 0 + 7

Collect like terms

2a = 3 - 7

2a = -4

Divide both sides by 2

2a/2 = -4/2

a = -2

y = a(x-h) + k

y = -2(x-0) + 7

y = -2x + 0 + 7

y = -2x + 7 or

y + 2x - 7 = 0

8 0

3 years ago

The differential equation in Example 3 of Section 2.1 is a well-known population model. Suppose the DE is changed to dP dt = P(a

LuckyWell [14K]

Answer:

Decreases

Step-by-step explanation:

We need to determine the integral of the DE;

$dP/dt=P(aP-b)$

$dP=P(aP-b)dt$

$1/(dP^2-bP)dP=dt$

We can solve this by integration by parts on the left side. We expand the fraction 1/P²:

$1/(d-b/P)\cdot{P^2} dP$

let

$u=d-b/P$

$du/dP=b/P^2$

$dP=$ $\int\limits {P^2/b} \, du$

$P=lnu/b$

Substitute u in:

$P=ln(d-b/P)/b$

Therefore the equation is:

$ln(d-b/P)/b=t$

We simplify:

$d-b/P=e^b^t$

$P=b/(d-e^b^t)$

As t increases to infinity P will decrease

6 0

3 years ago

What if you magnified the image of a cluster fly by 9 times 10 to the third power?

densk [106]

It would either be 9*(10^3) which would be <em>9000</em>.

Or, it would be (9*10)^3, which equals <em>729000</em>.

Please try and get another answer to make sure!

6 0

3 years ago

Determine the nth term rule and find the 45th term for the arithmetic sequence with a10=1 and d-6

kari74 [83]

Answer: -209

Step-by-step explanation:

Formula for arithmetic progression

= a + (n - 1)d

Since a10 = 1 and d = -6

a10 = a + 9d

a + 9(-6) = 1

a - 54 = 1

a = 1 + 54

a = 55

Therefore, 45th term = a + (n - 1)d

= a + (45 - 1)d

= a + 44d

= 55 + 44(-6)

= 55 - 264

= -209

4 0

3 years ago