Answer:
B.23-14i
Step-by-step explanation:
(3x5)+(3x2i)-(4ix5)-(4ix2i)
15+6i-20i-8(-1)
15+6i-20i+8
23-14iฟ
Answer:
the distance is 4
Step-by-step explanation:
Answer:
Step-by-step explanation:
Given that,
f(3) = 2
f'(3) = 5.
We want to estimate f(2.85)
The linear approximation of "f" at "a" is one way of writing the equation of the tangent line at "a".
At x = a, y = f(a) and the slope of the tangent line is f'(a).
So, in point slope form, the tangent line has equation
y − f(a) = f'(a)(x − a)
The linearization solves for y by adding f(a) to both sides
f(x) = f(a) + f'(a)(x − a).
Given that,
f(3) = 2,
f'(3) = 5
a = 3, we want to find f(2.85)
x = 2.85
Therefore,
f(x) = f(a) + f'(a)(x − a)
f(2.85) = 2 + 5(2.85 - 3)
f(2.85) = 2 + 5×-0.15
f(2.85) = 2 - 0.75
f(2.85) = 1.25
There are several ways you can solve this problem if you're trying to solve for m and n. You can substitute, or systems of equations. However, I'm going to use substitution:
2m + n = 0 => n = -2m
We can input that in for the other equation:
m + 2n = 3 now becomes: m + 2(-2m) = 3
Now we can solve:
m + 2(−2m) = 3
m + −4m = 3
(m + −4m) = 3 (Combine Like Terms)
−3m=3
m = -1
Now we can input that value in to solve for n:
We said that n = -2m, and m = -1, so n = -2(-1):Answer:
n = 2
Your final answer is m = -1, and n = 2, which can also be written as (m,n) = (-1,2)
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However, if you were solving for m+n:
You would add the two equations!:
2m + n = 0
m + 2n = 3
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3m + 3n = 3
Now, you can take 3 common:
3(m+n) = 3
m + n = 1
Your final answer for what m + n equals 1!
The lengths of the other two sides of the right triangle are 12 and 13
<h3>Pythagorean theorem </h3>
From the question, we are to determine the lengths of the other sides of the triangle
From the given information,
The other sides have lengths that are consecutive integers
Thus,
If the length of the other side is x
Then,
The hypotenuse will be x + 1
By the <em>Pythagorean theorem</em>, we can write that
(x+1)² = x² + 5²
(x+1)(x+1) = x² + 25
x² + x + x + 1 = x² + 25
x² - x² + x + x = 25 - 1
2x = 24
x = 24/2
x = 12
∴ The other leg of the right triangle is 12
Hypotenuse = x + 1 = 12 + 1 = 13
Hence, the lengths of the other two sides are 12 and 13
Learn more on Pythagorean theorem here: brainly.com/question/4584452
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