Questions posted in Mathematics

Express the complex number 6 in complex trigonometric form.

Answer:

6(cos 0° + sin 0° . i)

Step-by-step explanation:

The trigonometric form formula is a combination of the following formulas:

Binomic: a + bi

Polar: rα

Giving as a result the formula: r (cos α + sin α · i)

Where,

r = module

α = angle

In the given case, the complex number is 6, where

Binomic form: 6 + 0i

Where a = 6 and b = 0

We must calculate the module (r) and the angle (α).

r=\sqrt{a^{2} +b^{2}} =\sqrt{6^{2} +0^{2}}=\sqrt{36}=6

α = tan^{-1}(0) = 0°

Since r=6 and α=0°, then the trigonometric form is

r(cos α + sin α · i)  = 6(cos 0° + sin 0° . i)

Hope this helps!

ANSWERED AT 24/01/2020 - 11:58 PM


QUESTION POSTED AT 24/01/2020 - 11:58 PM

What is 40% simplified in a fraction

You want to start by putting 40 over 100 like a fraction and then you would take off the last zero in the hundred and the zero on forty and then that would give you 4/10 and then from there you would take 2 and divide too and bottom and that would give you 2/5 which will be your answer

ANSWERED AT 24/01/2020 - 11:57 PM


QUESTION POSTED AT 24/01/2020 - 11:57 PM

Somebody please explain absolute value and whatever the frick it has to do with math and adding and stuff

The answer to an absolute value must be positive
here are examples of simple ones
ex1:|-5|=5
ex2:|-3|=3
ex3:|3|=3

ANSWERED AT 24/01/2020 - 11:57 PM


QUESTION POSTED AT 24/01/2020 - 11:57 PM

The function g(x) is defined as shown. What is the value of g(3)? 2 3 9 14

Answer:

3


Step-by-step explanation:

This is a piece-wise function. The domain [x-values] is broken down into parts.

To evaluate this type of functions, we see in WHICH PART of the DOMAIN does the questions ask to look for.

The question asks for g(3) , the value of the function at  x=3

In which of the 3 parts does  x=3  fall into?


The domain condition,  x\geq3  , in the last part tells us that it is GREATER THAN OR EQUAL TO 3. So  x=3  falls in this part of the function, which is  6-x

We can simply substitute 3 in x of that part and get our desired answer. So,

6-x\\6-(3)\\3

The value of g(3)=3

ANSWERED AT 24/01/2020 - 11:56 PM


QUESTION POSTED AT 24/01/2020 - 11:56 PM

Help please Calculate the product of 8/15, 6/5, and 1/3.

To find this answer, multiply the numerators across: (8 x 6 x 1) = 48, and the denominators in the same fashion: (15 x 5 x 3) = 225. This gives a non-reduced fraction of 48/225, which, when reduced by 3s, gives a product of 16/75.

ANSWERED AT 24/01/2020 - 11:55 PM


QUESTION POSTED AT 24/01/2020 - 11:55 PM

Help please Calculate the product of 8/15, 6/5, and 1/3.

Hey there!

Great question:)


8/15 * 6/5 * 1/3 = 16/75

Simply multiply!

8*6*1=48

15*3*5=155


I hope this helps;)

ANSWERED AT 24/01/2020 - 11:55 PM


QUESTION POSTED AT 24/01/2020 - 11:55 PM

Help please Calculate the product of 8/15, 6/5, and 1/3.

Hey there!

Great question:)


8/15 * 6/5 * 1/3 = 16/75


I hope this helps;)

ANSWERED AT 24/01/2020 - 11:55 PM


QUESTION POSTED AT 24/01/2020 - 11:55 PM

Lydia writes the equation below with a missing value. y=5x - __ She puts a value in the box and says that the equation represents a direct variation. Which explains whether the equation could represent a direct variation? A. If she puts 0 in the box she would have a direct variation. B. If she puts 5 in the box she would have a direct variation. C. The equation is not of the form y=kx, so it cannot represent a direct variation. D. The equation has a minus sign, so it cannot represent a direct variation.

Answer:

Option (a) is correct.

If she puts 0 in the box she would have a direct variation.

Step-by-step explanation:

 Given : Lydia writes the equation y = 5x - __ with a missing value.

She puts a value in the box and says that the equation represents a direct variation.

We have to choose the correct option from the given options that explain that  the equation could represent a direct variation.

When two variables are such that one is a constant multiple of other, we said they are in Direct variation.

That is in form of y = ax , here y and x are in direct variation.

Consider the given equation y = 5x  - __

For the equation to be in direct variation the value of missing term has to be 0.

then equation becomes,

y = 5x

Thus, If she puts 0 in the box she would have a direct variation.

Option (a) is correct.

ANSWERED AT 24/01/2020 - 10:56 PM


QUESTION POSTED AT 24/01/2020 - 10:56 PM

Money is invested into an account earning 4.25% interest compounded annually. If the accumulated value after 18 years will be $25,000, approximately how much money is presently in the account?

Answer: $11,820

Step-by-step explanation:

The formula to calculate the compound amount after x years is given by :-

A=P(1+r)^x, where r is the rate of interest.

Given: The accumulated value A= $25000

The rate of interest r= 4.25%=0.0425

Let P be the present value invested in the account.

Now,according to the question,we have

25000=P(1+0.0425)^{18}\\\\\Rightarrow\ 25000=P(2.11528624641)\\\\\Rightarrow\ P=\frac{25000}{2.11528624641}\\\\\Rightarrow\ P=11818.7314092\approx\$11820......[\text{to the nearest tens}]

Hence, the amount of money presently in the account =$11,820

ANSWERED AT 24/01/2020 - 10:56 PM


QUESTION POSTED AT 24/01/2020 - 10:56 PM

What is the percentage formula

15 is what percent 150 ? In equation form is 15/150 = P% 15/150 = 0.10. We now need to convert the decimal to an percentage so we end up with a percentage. Converting a decimal to a percentage we multiply by 100 and append a percentage sign to the result.

ANSWERED AT 24/01/2020 - 10:56 PM


QUESTION POSTED AT 24/01/2020 - 10:56 PM

The area of a rectangle is 48. If the width is 8 less than its length, what is its length? I got 6 but that isnt right PLEASE Help

OK.... here we go....

The width is 8 less than the length, so that means: w = L - 8.

So, since the area of a rectangle is: A = L x W ...

Therefore, 48 = L(L - 8)...

48 = L^2 - 8L...

continuing from there .... you get width = 4 and length = 12

48 = 4 x 12   (and notice that the width is 8 less than the length)



ANSWERED AT 24/01/2020 - 10:56 PM


QUESTION POSTED AT 24/01/2020 - 10:56 PM

The area of a trapezoid is 100 square feet. The sum of the two bases is 25 feet. What is the height of the trapezoid? I kept getting 4 but that isn't correct

Well I don't know !
Let's slow down, relax, and work it out together.

The formula for the area of a trapezoid is

                          Area  =  (1/2) · (height) · (the sum of the bases)

Fill in
the numbers
that we know:    100 sq ft  =  (1/2) · (height) · (25 ft)

Divide each side
by  (25 ft) :            (100 sq ft) / (25 ft)  =  (1/2) · (height)

                                         4 ft            =  (1/2) · (height)

Multiply each side by  2 :      8 ft          =            height

So what was the major difficulty ?
Did you forget the  (1/2)  in the formula ?

ANSWERED AT 24/01/2020 - 10:56 PM


QUESTION POSTED AT 24/01/2020 - 10:56 PM

The number of milligrams of a certain medicine a veterinarian gives to a dog varies directly with the weight of the dog. If the veterinarian gives a 30-pound dog 3/5 milligram of the medicine, which equation relates the weight, w, and the dosage, d? A. d=1/50w B. d=3/5w C. d=18w D. d=50w

Answer:

Option A is correct

d = \frac{1}{50}w

Step-by-step explanation:

Direct variation says that:

y \propto x then;

the equation is in the form of

y=kx, where k is the constant of variation

As per the statement:

The number of milligrams of a certain medicine a veterinarian gives to a dog varies directly with the weight of the dog.

Here, w represents the weight and d represents the dosage

then ,by definition of direct variation we have;

d =kw         .....[1]

It is also given that if the veterinarian gives a 30-pound dog 3/5 milligram of the medicine

⇒w = 30 pound and d = 3/5 milligram

Substitute in [1] we have;

\frac{3}{5} = 30k

Multiply both sides by 5 we have;

3 = 150k

Divide both sides by 150 we have;

\frac{3}{150}=k

Simplify:

k = \frac{1}{50}

d = \frac{1}{50}w

therefore, equation relates the weight, w, and the dosage, d is:

d = \frac{1}{50}w

ANSWERED AT 24/01/2020 - 10:56 PM


QUESTION POSTED AT 24/01/2020 - 10:56 PM

If postage costs $.54 for the first ounce and $.22 for each additional ounce, calculate the cost of mailing a 10-ounce envelope.

Answer:

$251

Step-by-step explanation:

Let x be the number of ounces for the additional cost, we can write an expression to determine the cost of 10-ounce envelope. The first ounce is $54 therefore the remaining 9 ounces wiht cost $22.

53+22\cdot{x}=53+22\cdot{9}=53+198=251

The cost of mailing 10 ounces envelope is $251

ANSWERED AT 24/01/2020 - 10:56 PM


QUESTION POSTED AT 24/01/2020 - 10:56 PM

What is the capacity of a building

I think u will find it is 222,500 tonnes may be 222,000

ANSWERED AT 24/01/2020 - 10:56 PM


QUESTION POSTED AT 24/01/2020 - 10:56 PM

If postage costs $.54 for the first ounce and $.22 for each additional ounce, calculate the cost of mailing a 10-ounce envelope.

Answer:

$2.52

Step-by-step explanation:

Mass of envelope = 10 ounce

Now, it has been given that postage costs $.54 for the first ounce and $.22 for each additional ounce.

Therefore, the cost of first ounce =$ 0.54

Now, we are left with 9 more ounces. hence cost of 9 ounces should be 9×0.22 = $1.98

Therefore, total cost of mailing a 0- ounce envelope is

0.54 + 1.98

= $2.52

ANSWERED AT 24/01/2020 - 10:56 PM


QUESTION POSTED AT 24/01/2020 - 10:56 PM

With similar triangles the rates of all three pairs of corresponding sides are equal. True or false

False that is not true

ANSWERED AT 24/01/2020 - 10:55 PM


QUESTION POSTED AT 24/01/2020 - 10:55 PM

Firefly211 what is the length to memphis to Alaska

Hello,

The length from Memphis to Alaska is approximately 3,946 miles.

Hope this helps!

ANSWERED AT 24/01/2020 - 10:55 PM


QUESTION POSTED AT 24/01/2020 - 10:55 PM

What are the formulas for trigonometry and pythagoras?

That's not a good question at all.  It's a lot like asking
"What are the statements for News and President Obama ?"

There are at least a hundred formulas that are useful in trigonometry.
One of the most useful is:

       In a right triangle, the square of the length of the hypotenuse
       is equal to the sum of the squares of the two short sides.

Pythagoras is the name of the ancient Greek mathematician who
discovered that formula.  The formula is so useful that it's known
by his name, in his honor.

ANSWERED AT 24/01/2020 - 10:55 PM


QUESTION POSTED AT 24/01/2020 - 10:55 PM

What is the sum of the first five terms of a geometric series with a1=6 and r=1/3

The sum of n terms of a geometric series is found using the following formula:
S _{n} = \frac{a(1-r^{n})}{1-r}
where a is the first term and r is the common ratio.
In your question, a = 6 and r = 1/3, so we have:
 S_{5} =\frac{6(1-(\frac{1}{3})^5)}{1-\frac{1}{3}}
which simplifies to:S_{5}=\frac{6(1-\frac{1}{243})}{\frac{2}{3}}

ANSWERED AT 24/01/2020 - 10:55 PM


QUESTION POSTED AT 24/01/2020 - 10:55 PM

Firefly211 what is 30765796368×2315206

The correct answer is 71229156345971808
this was actually simple lol all you need is a calculator 
well i hope i helped you out in some type of way :)))
see you in another life brother 

ANSWERED AT 24/01/2020 - 10:55 PM


QUESTION POSTED AT 24/01/2020 - 10:55 PM

Amy drove her car 241 miles. The car used 8.07 gallons of gasoline on the drive. Estimate the cars gasoline mileage in miles per gallon. Which conversion ratio could you multiply by the number of miles to convert the distance to kilometers

Miles driven in 8.07 gallons = 241 miles
Miles driven in 1 gallons      = (241/8.07) * 1
                                            = 29.86 miles

ANSWERED AT 24/01/2020 - 10:54 PM


QUESTION POSTED AT 24/01/2020 - 10:54 PM

I need help on one of my math questions. It would be most helpful to get the answer as well as an explanation on how to do these types of problems.Thank you in advance.

This is a very interesting problem.  What makes it so interesting is that
there's so little actual math to it.  The only big Math thing you need to know
in order to work with this question is the definition of "perimeter".

  "Perimeter" means

                 "the distance all the way around the edge of something".

The problem GIVES you the length of all the sides of both triangles.
To find the perimeter of one triangle, just take the lengths of its three
sides and addum up.

The perimeter of the blue one is    (7x+7) + (5x-4) + (4x+2)  .
That's it !  That's the perimeter.  Of course, they want you to write
it in simplest form, so you have to clean it up.  Remove all of the
parentheses, add up all the 'x's, and add up all the plain numbers,
and you'll have a short, pretty expression.

Then do the same thing for the red one, and get its perimeter.

In part-b, they want you to find the difference between the two perimeters.
No problem.  Just write  (the blue perimeter) minus (the red perimeter),
and simplify THAT expression.

Now they want the actual perimeters when 'x' is 3.
No big deal.  Just take each separate perimeter, write '3' in place of 'x',
and find the number that the expression becomes.

Just now, looking at the picture without writing anything down,
I got  53  for the blue one and  17  for the red one.
I could easily be wrong, so you definitely have to work them
out for yourself.

ANSWERED AT 24/01/2020 - 10:54 PM


QUESTION POSTED AT 24/01/2020 - 10:54 PM

What is the mean of the following numbers? (to the nearest tenth)21, 23, 76, 47, 55, 135, 45, 30, 17

The mean is the average, and you can find the average by adding ALL the numbers together, and divide the sum by the number of numbers in the set (which is 9), so you would solve (21+23+76+47+55+135+45+30+17)/9

Give me a second to get your answer

ANSWERED AT 24/01/2020 - 10:54 PM


QUESTION POSTED AT 24/01/2020 - 10:54 PM

What is the formula in finding the distance of circle

Hey there!

Great question=)

Area= \pi r^{2}

Circumference=  2 \pi r


I hope this helps=)

ANSWERED AT 24/01/2020 - 10:54 PM


QUESTION POSTED AT 24/01/2020 - 10:54 PM

Derive the equation of the parabola with a focus at (0, −4) and a directrix of y = 4

We are given with the focus coordinates of (0,-4) and a directrix equation of y=4,. we are asked for the equation of the parabola. The vertex of the parabola should lie in between the directrix and the focus. Hence, vertex should be at (0,0). the curve goes downwards. and the length of the latus rectum is 4. Hence the equation is x2=-16y

ANSWERED AT 24/01/2020 - 10:54 PM


QUESTION POSTED AT 24/01/2020 - 10:54 PM

Working together, Rocco and Giulia can paint a room in 3 hours. It would have taken Rocco 7 hours to do the job alone. Which equation can be used to determine r, Giulia’s rate of work in parts per hour

Rocco and Guilia can paint and finish together in 3 hours while Rocco alone can do it alone in 7 hours. Guilia at the rate of 1/r can finish the job expressed in the following equation. 1/3= 1/7+1/r. Getting r, r is equal to 5.25 hrs. Hence, Guilia can do painitng alone in 5.25 hrs.

ANSWERED AT 24/01/2020 - 10:54 PM


QUESTION POSTED AT 24/01/2020 - 10:54 PM