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3 years ago

I WILL GIVE BRAINLIST AND 5 STARS Show that (2x + i)(2x – i) = 4x² + 1

Mathematics

1 answer:

sladkih [1.3K]3 years ago

8 0

Answer:

see below

Step-by-step explanation:

(2x + i)(2x – i)

FOIL

first 2x*2x =4x^2

outer -i * 2x = 2x i

inner i * 2x = 2x i

last i * -i = -i^2 and i^2 = -1 so - (i^2 ) = - (-1) = 1

Add together

4x^2 + 2xi -2x i +1

Combine like terms

4x^2 +1

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Solve for x please :-<br> 3(9+x)-31=20

Zolol [24]

27+3x-31=20
-4+3x=20
+4 +4
3x=24
X=8

6 0

3 years ago

Read 2 more answers

Given that the series kcoskt kº +2 k=1 converges, suppose that the 3rd partial sum of the series is used to estimate the sum of

3241004551 [841]

Answer:

Step-by-step explanation:

Given that:

$\sum \limits ^{\infty}_{k=1} \dfrac{kcos (k\pi)}{k^3+2}$

since cos (kπ) = $-1^k$

Then, the series can be expressed as:

$\sum \limits ^{\infty}_{k=1} \dfrac{(-1)^kk)}{k^3+2}$

In the sum of an alternating series, the best bound on the remainder for the approximation is related to its $(n+1)^{th$ term.

∴

$\sum \limits ^{\infty}_{k=1} \dfrac{(-1)^{(3+1)}(3+1))}{(3+1)^3+2}$

$\sum \limits ^{\infty}_{k=1} \dfrac{(-1)^{(4)}(4))}{(4)^3+2}$

$= \dfrac{4}{64+2}$

$=\dfrac{2}{33}$

5 0

3 years ago

You bought a car 3 years ago for $12000. If its value decreases by 17% each year, how much is your car worth now?

Mrac [35]

Answer: $‭6,861.44

Step-by-step explanation:

Car was bought 3 years ago for $12,000.

Value decreases by 17% every year.

Current value is:

= 12,000 * (1 - 17%)³

= $‭6,861.44

8 0

3 years ago

HELP WITH VOLUME AND SURFACE AREA!!!!!! WILL MARK BRAINLIEST!!!!!

ArbitrLikvidat [17]

Answer:

Volume is 48 yards cubed

surface area is 96 yards squared

4 0

3 years ago

State the linear programming problem in mathematical terms, identifying the objective function and the constraints. A firm makes

Sedbober [7]

Answer:

Maximum profit at (3,0) is $27.

Step-by-step explanation:

Let quantity of products A=x

Quantity of products B=y

Product A takes time on machine L=2 hours

Product A takes time on machine M=2 hours

Product B takes time on machineL= 4 hours

Product B takes time on machine M=3 hours

Machine L can used total time= 8hours

Machine M can used total time= 6hours

Profit on product A= $9

Profit on product B=$7

According to question

Objective function Z= $9x+7y$

Constraints:

$2x+3y\leq 6$

$2x+4y\leq 8$

Where $x\geq 0, y\geq 0$

I equation $2x+3y\leq 6$

I equation in inequality change into equality we get

$2x+3y=6$

Put x=0 then we get

y=2

If we put y=0 then we get

x= 3

Therefore , we get two points A (0,2) and B (3,0) and plot the graph for equation I

Now put x=0 and y=0 in I equation in inequality

Then we get $0\leq 6$

Hence, this equation is true then shaded regoin is below the line .

Similarly , for II equation

First change inequality equation into equality equation

we get $2x+4y=8$

Put x= 0 then we get

y=2

Put y=0 Then we get

x=4

Therefore, we get two points C(0,2)a nd D(4,0) and plot the graph for equation II

Point A and C are same

Put x=0 and y=0 in the in inequality equation II then we get

$0\leq 8$

Hence, this equation is true .Therefore, the shaded region is below the line.

By graph we can see both line intersect at the points A(0,2)

The feasible region is AOBA and bounded.

To find the value of objective function on points

A (0,2), O(0,0) and B(3,0)

Put A(0,2)

Z= $9\times 0+7\times 2=14$

At point O(0,0)

Z=0

At point B(3,0)

Z= $9\times3+7\times0=27$

Hence maximum value of z= 27 at point B(3,0)

Therefore, the maximum profit is $27.

6 0

3 years ago