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alexandr1967 [171]
3 years ago
13

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. The roots of an equ

ation are x = -1 ± i. The equation is x2 + + 2 = 0.
Mathematics
1 answer:
Inessa [10]3 years ago
5 0

Answer:

If the roots of an equation are x = -1 ± i, it means that the factorized form of that equation is: (x + 1 + i)(x+ 1 - i) = 0.

Using the distributive property, we have:

(x + 1 + i)(x+ 1 - i) = x^2 + x - ix + x + 1 - i + ix + i + 1

Combining like-terms and simplifying:

⇒ x^2 + x + x + 1   + 1 = x^2 + 2x + 2 = 0

Therefore, the stament is correct. If the roots of an equation are x = -1 ± i, then the equation is: x^2 + 2x + 2 = 0.

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The number of trees in a forest follows the logistic growth function f(t)=32000/1+12.8e^-0.065t where t is the time in years. Wh
Vsevolod [243]

Answer:

Maximum number of trees will be 32000 as time grows to infinity

Step-by-step explanation:

Recall that the expression for logistic growth includes a quotient of a number (in our case 32000) divided by "1 + a number that approaches zero with time (in our case e^{-0.065\,t}". This is a decaying exponential function, that as "t" grows approaches zero.

Therefore, as the time increases, the denominator becomes closer and closer to 1 (one) due to the exponential factor approaching zero that is added to "1".

Then the maximum will be obtained when the quantity in the denominator becomes as small as possible, and that is as time grows. Reaching then its maximum as time goes to infinity. And that value is going to be approaching:\frac{32000}{1+0} =32000

7 0
3 years ago
Convert 83% into a decimal<br> can you guy help me to do that
PilotLPTM [1.2K]
To convert a percentage to decimal form, you need to divide the number in the percent by 100. In reality, that just looks like moving the decimal point to the left two places.

83% / 100 = 0.83

83% in decimal form is 0.83.
Hope that helped! =)
6 0
3 years ago
If a 6-foot tall man casts a 9-foot shadow, what is the approximate measure from the top of his head to the top of his shadow? 1
BartSMP [9]
I'd gotten 10.8 feet for the answer using the equation:

a^2+b^2=c^2
(a{squared}+b{squared}=c{squared})

Where 6 is your a variable, 9 is your b variable and you are looking for your c variable (hypotenuse).

a- 6^2 (6{squared}) or 6x6 giving you 36
b- 9^2(9{squared}) or 9x9 giving you 81
Adding those together you'll have 117.

117=c^2

You would have to get rid of the squared sign so you'll find the square root because finding the square root of something is the opposite of squaring it.

c=10.8 feet (rounding to 11 feet)
4 0
4 years ago
Read 2 more answers
Prove the identity of tan(pi - x) = - tan x
liq [111]

Two ways:

Step-by-step explanation:

1. First way. Using the trig unit circle.

tan (pi - x) = - tan x

2. Second way. Apply the identity:

tan(a-b)=tan a- tan b/ 1 - tan a×tan b

tan (π - x)= tan π - tanx/1 - tan(π)×tanx

Since tan (pi) = 0, therefor:

tan(π−x)=−tanx

8 0
3 years ago
What would the total account value be if i deposited 14,000 into a bank account earning 3.25% compounded quarterly for 4 years?
LUCKY_DIMON [66]
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7 0
3 years ago
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