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Ede4ka [16]
3 years ago
6

Noah and Lin are each trying to solve the equation x² - 6x + 10 = 0. They know that the solutions to x² = - 1 are i and -i, but

they are not sure how to use this information to solve for x in their equation.
Here is Noah's work:
x² - 6x + 10 = 0
x² - 6x = -10
x² - 6x + 9 = -10 + 9
(x-3)² = -1

Show how Noah can finish his work using complex numbers.​
Mathematics
1 answer:
Leviafan [203]3 years ago
8 0

Answer:

Solving the equation x^2 - 6x + 10 = 0 we get x=3+i \ , \ x=3-i

Step-by-step explanation:

Noah's step to solve the equation x^2 - 6x + 10 = 0 are:

x^2 - 6x + 10 = 0\\x^2 - 6x = -10\\x^2 - 6x + 9 = -10 + 9\\(x-3)^2 = -1

The next step is to take square root on both sides because: \sqrt{x^2}=x

\sqrt{(x-3)^2}=\sqrt{-1}  \\x-3=\pm\sqrt{-1} \\x=\pm(\sqrt{-1})+3 \\

Now, we know that: \sqrt{-1}=i

x=\pm(i)+3\\x=3+i \ , \ x=3-i

So, Solving the equation x^2 - 6x + 10 = 0 we get x=3+i \ , \ x=3-i

You might be interested in
What are prime and composite numbers
alexgriva [62]

Answer:

A prime number is a number ( greater than 1) and it cannot be found/formed by multiplying two smaller numbers.

A composite number is a positive number/integer that can be found/formed by multiplying two smaller numbers/integers.

Hope this helps! Have a great day/night! :)

8 0
3 years ago
measurement error that is continuous and uniformly distributed from millivolts is added to the true voltage of a circuit. then t
satela [25.4K]

Question has missing details (Full question below)

Measurement error that is continuous and uniformly distributed from –3 to +3 millivolts is added to a circuit’s true voltage. Then the measurement is rounded to the nearest millivolt so that it becomes discrete. Suppose that the true voltage is 219 millivolts. What is the mean and variance of the measured voltage

Answer:

Mean = 219

Variance = 4

Step-by-step explanation:

Given

Let X be a random variable measurement error.

X has a discrete uniform distribution as follows

a = 219 - 3 = 216

b = 219 + 3 = 222

Mean or Expected value is calculated as follows;

E(x) = ½(216+222)

E(x) = ½ * 438

E(x) = 219

Variance is calculated as follows;

Var(x) = ((b-a+1)²-1)/12

Var(x) = ((222-216+1)²-1)/12

Var(x) = (7²-1)/12

Var(x) = 48/12

Var(x) = 4

8 0
2 years ago
An automobile manufacturer sold 30,000 new cars, one to each of 30,000 customers, in a certain year. The manufacturer was intere
snow_lady [41]
A) In order to create a sampling plan, you need to follow the following 5 steps:
    1) Define the sample population: who are the customers you want to contact?
       The costumers who bought a new car on a certain year.
    2) Define the size of population: how many customers are you going to contact?
       Of the 30000 customers who bought a car, you want to contact 1000 customers.
    3) Define the contact options: how are you going to contact the customers?
       You have a list of names and addresses, therefore you can send a questionnaire via mail.
    4) Form a sampling frame: what is the time or contact frame to get in touch with your customers? 
       You will send the questionnaires and you will wait two months for the answer.
    5) Define the analysis method: is yours a qualitative or quantitative research?
     In your case, you want a quantitative research and therefore a probabilistic sampling.

B) The 32.5% probability refers to customers having issues with the power doors locks among the costumers who had problems, it does not consider the customers who did not have any problem or those who had problems after the first 5000 miles.

C) In order to find the probability of a power door lock problem if there have been problems within the first 5000 miles, we need to consider the whole sample:
P = 13 / 1000
   = 0.013

Therefore, 
N = <span>0.013 </span>× 30000
   = 390

Hence, the number of new cars sold that experienced a problem with the power door locks within the first 5000 miles will be 390.
         
4 0
3 years ago
We are standing on the top of a 320 foot tall building and launch a small object upward. The object's vertical altitude, measure
STALIN [3.7K]

Answer:

The highest altitude that the object reaches is 576 feet.

Step-by-step explanation:

The maximum altitude reached by the object can be found by using the first and second derivatives of the given function. (First and Second Derivative Tests). Let be h(t) = -16\cdot t^{2} + 128\cdot t + 320, the first and second derivatives are, respectively:

First Derivative

h'(t) = -32\cdot t +128

Second Derivative

h''(t) = -32

Then, the First and Second Derivative Test can be performed as follows. Let equalize the first derivative to zero and solve the resultant expression:

-32\cdot t +128 = 0

t = \frac{128}{32}\,s

t = 4\,s (Critical value)

The second derivative of the second-order polynomial presented above is a constant function and a negative number, which means that critical values leads to an absolute maximum, that is, the highest altitude reached by the object. Then, let is evaluate the function at the critical value:

h(4\,s) = -16\cdot (4\,s)^{2}+128\cdot (4\,s) +320

h(4\,s) = 576\,ft

The highest altitude that the object reaches is 576 feet.

6 0
3 years ago
Emelio wants to solve this equation.
Ludmilka [50]

Answer:

Answer is 175

:)

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
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