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MAXImum [283]
3 years ago
7

PLS HELP!! If f(x) = 2x^2-4x and g(x) =5-2x, evaluate f(x)-g(x) for x=5

Mathematics
1 answer:
anastassius [24]3 years ago
6 0
To solve this equation you need to first start by writing out the f(x)-g(X).
The equation should be 2x^2-4x-5+2x. 
You then want to simplify the equation, I got 2x^2-2x-5.
You then want to plug in the x=5 for all the x's in the equation. 
2(5)^2-2(5)-5 would be the equation. 
The answer you get should be 35.
You might be interested in
Let z=3+i, <br>then find<br> a. Z²<br>b. |Z| <br>c.<img src="https://tex.z-dn.net/?f=%5Csqrt%7BZ%7D" id="TexFormula1" title="\sq
zysi [14]

Given <em>z</em> = 3 + <em>i</em>, right away we can find

(a) square

<em>z</em> ² = (3 + <em>i </em>)² = 3² + 6<em>i</em> + <em>i</em> ² = 9 + 6<em>i</em> - 1 = 8 + 6<em>i</em>

(b) modulus

|<em>z</em>| = √(3² + 1²) = √(9 + 1) = √10

(d) polar form

First find the argument:

arg(<em>z</em>) = arctan(1/3)

Then

<em>z</em> = |<em>z</em>| exp(<em>i</em> arg(<em>z</em>))

<em>z</em> = √10 exp(<em>i</em> arctan(1/3))

or

<em>z</em> = √10 (cos(arctan(1/3)) + <em>i</em> sin(arctan(1/3))

(c) square root

Any complex number has 2 square roots. Using the polar form from part (d), we have

√<em>z</em> = √(√10) exp(<em>i</em> arctan(1/3) / 2)

and

√<em>z</em> = √(√10) exp(<em>i</em> (arctan(1/3) + 2<em>π</em>) / 2)

Then in standard rectangular form, we have

\sqrt z = \sqrt[4]{10} \left(\cos\left(\dfrac12 \arctan\left(\dfrac13\right)\right) + i \sin\left(\dfrac12 \arctan\left(\dfrac13\right)\right)\right)

and

\sqrt z = \sqrt[4]{10} \left(\cos\left(\dfrac12 \arctan\left(\dfrac13\right) + \pi\right) + i \sin\left(\dfrac12 \arctan\left(\dfrac13\right) + \pi\right)\right)

We can simplify this further. We know that <em>z</em> lies in the first quadrant, so

0 < arg(<em>z</em>) = arctan(1/3) < <em>π</em>/2

which means

0 < 1/2 arctan(1/3) < <em>π</em>/4

Then both cos(1/2 arctan(1/3)) and sin(1/2 arctan(1/3)) are positive. Using the half-angle identity, we then have

\cos\left(\dfrac12 \arctan\left(\dfrac13\right)\right) = \sqrt{\dfrac{1+\cos\left(\arctan\left(\dfrac13\right)\right)}2}

\sin\left(\dfrac12 \arctan\left(\dfrac13\right)\right) = \sqrt{\dfrac{1-\cos\left(\arctan\left(\dfrac13\right)\right)}2}

and since cos(<em>x</em> + <em>π</em>) = -cos(<em>x</em>) and sin(<em>x</em> + <em>π</em>) = -sin(<em>x</em>),

\cos\left(\dfrac12 \arctan\left(\dfrac13\right)+\pi\right) = -\sqrt{\dfrac{1+\cos\left(\arctan\left(\dfrac13\right)\right)}2}

\sin\left(\dfrac12 \arctan\left(\dfrac13\right)+\pi\right) = -\sqrt{\dfrac{1-\cos\left(\arctan\left(\dfrac13\right)\right)}2}

Now, arctan(1/3) is an angle <em>y</em> such that tan(<em>y</em>) = 1/3. In a right triangle satisfying this relation, we would see that cos(<em>y</em>) = 3/√10 and sin(<em>y</em>) = 1/√10. Then

\cos\left(\dfrac12 \arctan\left(\dfrac13\right)\right) = \sqrt{\dfrac{1+\dfrac3{\sqrt{10}}}2} = \sqrt{\dfrac{10+3\sqrt{10}}{20}}

\sin\left(\dfrac12 \arctan\left(\dfrac13\right)\right) = \sqrt{\dfrac{1-\dfrac3{\sqrt{10}}}2} = \sqrt{\dfrac{10-3\sqrt{10}}{20}}

\cos\left(\dfrac12 \arctan\left(\dfrac13\right)+\pi\right) = -\sqrt{\dfrac{10-3\sqrt{10}}{20}}

\sin\left(\dfrac12 \arctan\left(\dfrac13\right)+\pi\right) = -\sqrt{\dfrac{10-3\sqrt{10}}{20}}

So the two square roots of <em>z</em> are

\boxed{\sqrt z = \sqrt[4]{10} \left(\sqrt{\dfrac{10+3\sqrt{10}}{20}} + i \sqrt{\dfrac{10-3\sqrt{10}}{20}}\right)}

and

\boxed{\sqrt z = -\sqrt[4]{10} \left(\sqrt{\dfrac{10+3\sqrt{10}}{20}} + i \sqrt{\dfrac{10-3\sqrt{10}}{20}}\right)}

3 0
3 years ago
Read 2 more answers
PLEASE HELP!! DUE SOON!!
ryzh [129]

Answer:

Do you still need help??

Step-by-step explanation:

5 0
3 years ago
Can you help me please??
dusya [7]

Answer:

y = \frac{4}{5}x+\frac{54}{5}

Step-by-step explanation:

Equation of a line has been given as,

y=\frac{4}{5}x+\frac{3}{5}

Here, slope of the line = \frac{4}{5}

y-intercept = \frac{3}{5}

"If the two lines are parallel, there slopes will be equal"

By this property slope of the parallel line to the given line will be equal.

Therefore, slope 'm' = \frac{4}{5}

Since, slope intercept form of a line is,

y = mx + b

Therefore, equation of the parallel line will be,

y = \frac{4}{5}x+b

Since, this line passes through a point (-6, 6),

6 = \frac{4}{5}(-6)+b

6 = -\frac{24}{5}+b

b = 6+\frac{24}{5}

b = \frac{30+24}{5}

b = \frac{54}{5}

Equation of the parallel line will be,

y = \frac{4}{5}x+\frac{54}{5}

4 0
3 years ago
Uber charges a $5 pickup fee and $0.25 per mile. define variables and write an equation to model this situation.
Degger [83]

Answer:

See below

Step-by-step explanation:

<h3>Uber</h3>
  • $5 pickup fee
  • $0.25 per mile

<u>Equation</u>

  • y = 0.25x + 5

<u>Cost of 5 miles:</u>

  • y = 0.25(5) + 5 = $6.25
<h3>KC yellow Cab Co.</h3>
  • $1.75 pickup fee
  • $0.75 per mile

<u>Equation</u>

  • y = 0.75x + 1.75

<u>Cost of 5 miles:</u>

  • y = 0.75(5) + 1.75 = $5.5

Comparing the cost we see KC yellow Cab Co. is better value for a 5 mile ride.

8 0
3 years ago
Help ASAP will mark Brainly to who ever answers 1st
ch4aika [34]

Answer:

Step-by-step explanation:

the bottom left is the answer. I hope this helps.

4 0
2 years ago
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