All categories

2 years ago

Show all work to multiply (6+square root -64)(3-square root -16)

Mathematics

2 answers:

Tpy6a [65]2 years ago

8 0

Answer:

Step-by-step explanation:

Given expression,

$(6+\sqrt{-64})\times (3-\sqrt{-16})$

$=(6+\sqrt{-(8^2)})\times (3-\sqrt{-(4^2)})$

$=(6+8\sqrt{-1})\times (3-4\sqrt{-1})$

$=(6+8i)(3-4i)$ ( ∵ √-1 = i )

$=6(3-4i)+8i(3-4i)$

$=18-24i+24i-32i^2$

$=18+32$ ( ∵ i² = -1 )

$=50$

Hunter-Best [27]2 years ago

7 0

Answer:

Step-by-step explanation:

- 8i = √-64

8i + 6

- -4i = -√-16

-4i + 3

[8i + 6][-4i + 3] → FOIL

>> -32i² + [24i - 24i] + 18

↑ ↑

-1 0

>>> 32 + 18 = 50

Information on Imaginary Numbers

√-1 = i

-1 = i²

-i = i³

1 = i⁴ [And every other exponent that is a multiple of 4; this cycle then repeats itself every time you go up one number at a time]

If you are ever in need of assistance, do not hesitate to let me know by subscribing to my You-Tube channel [USERNAME: MATHEMATICS WIZARD], and as always, I am joyous to assist anyone at any time.

You might be interested in

A Mallard duck flies 5 6 of a mile in 1 60 of a hour. Compute the unit rate by setting up a complex fraction and simplifying.

seropon [69]

Important: Please express fractions properly: use the " / " symbol to represent division. Your question should read:

"A Mallard duck flies 5/6 of a mile in 1/60 of a hour. Find the rate (speed) at which it flies."

To do this, divide the distance flown by the elapsed time:
5
5/6 mile -----
----------------- = -------6------------- miles / hr
1/60 hour 
1
-----
60

to divide 5/6 by 1/60, write 5/6 and multiply that by the reciprocal of 1/60.

In other words, write 5/6, invert (1/60) and then multiply.

This comes out to (5)(60)
---------- mph
(6)(1)

Do not multiply here. Instead, reduce 60/6 to 10/1.

Can you now write out the final answer, in mph? (miles per hour)

8 0

2 years ago

Read 2 more answers

Jane is taking two courses. The probablity she passes the first course is 0,7. The probablity she passes the second course is 0.

makkiz [27]

Answer:

a. 0.6

b. not independent

c. 0.1

d. 0.4

e. 0.3

Step-by-step explanation:

P(passing first course)=P(C1)=0.7

P(passing second course)=P(C2)=0.8

P(passing at least one course)=P(C1∪C2)=0.9

P( passes both courses)=P(C1∩C2)=?

We know that

P(A∪B)=P(A)+P(B)-P(A∩B)

P(A∩B)=P(A)+P(B)-P(A∪B)

So,

P( passes both courses)=P(C1∩C2)=P(C1)+P(C2)-P(C1∪C2)

P( passes both courses)=P(C1∩C2)=0.7+0.8-0.9

P( passes both courses)=P(C1∩C2)=0.6

Thus, the probability she passes both courses is 0.6.

The event of passing one course is independent of passing another course if

P(C1∩C2)=P(C1)*P(C2)

P(C1)*P(C2)=0.7*0.8=0.56

P(C1∩C2)=0.6

As,

0.6≠0.56

P(C1∩C2)≠P(C1)*P(C2),

So, the event of passing one course is dependent of passing another course.

P(not passing either course)=P(C1∪C2)'=1-P(C1∪C2)

P(not passing either course)=P(C1∪C2)'=1-0.9

P(not passing either course)=P(C1∪C2)'=0.1

Thus, the probability of not passing either course is 0.1.

P(not passing both courses)=P(C1∩C2)'=1-P(C1∩C2)

P(not passing both courses)=P(C1∩C2)'=1-0.6

P(not passing both courses)=P(C1∩C2)'=0.4

Thus, the probability of not passing both courses is 0.4.

P(passing exactly one course)=?

P(passing exactly course 1)=P(C1)-P(C1∩C2)=0.7-0.6=0.1

P(passing exactly course 2)=P(C2)-P(C1∩C2)=0.8-0.6=0.2

P(passing exactly one course)=P(passing exactly course 1)+P(passing exactly course 2)

P(passing exactly one course)=0.1+0.2

P(passing exactly one course)=0.3

Thus, the probability of passing exactly one course is 0.3.

3 0

2 years ago

In a small town, 50% of single family homes have a front porch. 48 single family homes are randomly selected. Let X represent th

Reil [10]

Answer:

N(24, 3.46)

Step-by-step explanation:

We are given the following in the question:

Percentage of family homes having front poach = 50%

$p = 50\% = 0.50$

Sample size, n = 48

Normal approximation to the given distribution:

$\mu = np = 48(0.50) = 24$

$\sigma = \sqrt{np(1-p)} = \sqrt{48(0.50)(1-0.50)} = 3.46$

Thus, the distribution of single family homes is best approximated by the normal distribution N(24, 3.46) where mean is 24 and standard deviation is 3.46

6 0

2 years ago

Use the alternative curvature formula K=|a x v|/|v|^3 to find the curvature of the following parameterized curves.

neonofarm [45]

Answer:

$K=\frac{2}{(4t^{2}+1)^{\frac{3}{2}}}$

Step-by-step explanation:

First of all, we calculate v and a as:

$v(t)=\frac{dr(t)}{dt}=(2t,1,0)$

$a(t)=\frac{dv(t)}{dt}=(2,0,0)$

after that, we compute the cross product and we replace in the formula for k

a(t) X v(t) = (0,0,2)

| a(t) X v(t) | = 2

$| v |^{3} = (4t^{2}+1)^{\frac{3}{2}}$

Hence we have

$K=\frac{2}{(4t^{2}+1)^{\frac{3}{2}}}$

I hope this is useful for you

regards

8 0

2 years ago

If you have drums that hold 60 gallons and you need to ship 5,300 liters of liquid how many drums will you need remeber 1 liter=

alina1380 [7]

5300 liters x .26 liter/gallon = 1378 gallons. This is what you need to hold in gallons
Then 1378 gallons/ 60 gallons/drum= 22.96 drums. 
Since each can only hold 60 gallons maximum you round up to 23 drums

hope this helped!!

6 0

2 years ago