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meriva
2 years ago
12

Write -4i+(1/4-5i)-(-3/4+8i)+17i as a complex number in the standard for

Mathematics
1 answer:
KatRina [158]2 years ago
8 0

Answer:

1+ 0i

Step-by-step explanation:

A complex number is a number which has some real part and some imaginary part.

Standard form of a complex number is represented as

a +bi

Where a is the real part,

and bi is the imaginary part.

And i = \sqrt{-1}

Given complex number:

-4i+\dfrac{1}{4}-5i)-(-\dfrac{3}{4}+8i)+17i\\\Rightarrow -4i+\dfrac{1}{4}-5i + \dfrac{3}{4}-8i+17i\\\Rightarrow  \dfrac{3}{4}+\dfrac{1}{4}-4i -5i-8i+17i\\\Rightarrow  \dfrac{3+1}{4}-17i+17i\\\Rightarrow \dfrac{4}{4}+0i\\\Rightarrow 1 + 0i

Hence, the standard form is 1+ 0i.

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Misha Larkins [42]

Answer:

Step-by-step explanation:

3 0
2 years ago
8n^2-4(7m^3+5n^2)<br> help
Rasek [7]
Hello there!


8m² - 4(7m³ + 5n²)

You wanna start by using the distributive property

=8n² - (-4)(7m³) + (-4)(5n²)

= 8n² - 28m³ - 20n²

= -28m³ - 12m²
7 0
2 years ago
A denotes an mn matrix. Determine whether the statement is true or false. Justify your answer. The row space of AT is the same a
ziro4ka [17]

Answer: true

Step-by-step explanation:

For an m*n matrix, the column space of A will be a space formed by the lineal combination of all the columns of A.

column space = a1*c1 + a2*c2 + ...

                       

where a1, a2, ... are scalars, and c1 is the vector of column 1.

Then we should write:

Column space = a1*(A₁₁, A₂₁, A₃₁, ...) + a2*(A₁₂, A₂₂, A₃₂, ...) + ...

Now, the transpose is defined as:

[At]₁₃ = A₃₁

Here i used the element with subindex 3 and 1, but is the same for every subindex.

Notice that if A is m*n, then [At] is n*m

Now, the row space of [At] will be, same as before.

Row space = b1*r1 + b2*r2 + ...

Where b1, b2, ... are scalars and the r's are the vector of each row.

                   = b1*( [At]₁₁ , [At]₁₂, [At]₁₃, ...) + b2*([At]₂₁, [At]₂₂, [At]₂₃, ...) + ...

Now we replace each term of the transpose by the associated element in the original matrix.

                   = b1*( A₁₁, A₂₁, A₃₁, ...) + b2*(A₂₁, A₂₂, ...) + ....

If we take:

b1 = a1, b2 = a2, b3 = a3, ...

We will have that the row space of [At] is the same as the column space of A.

4 0
2 years ago
The admission fee at an amusement park is $1.50 for children and $4 for adults. On a certain day 333 people enter the park, the
liberstina [14]

Answer:

<u>188 children</u> and <u>145 adults</u> were admitted in the park.

Step-by-step explanation:

Given:

The admission fee at an amusement park is $1.50 for children and $4 for adults.

Total $862 collected on a certain day when 333 people enter the park.

Now, to find the children and adults admitted in the park.

<u><em>Let the number of children admitted be </em></u>x.<u><em /></u>

<u><em>And the the number of adults admitted be </em></u>y.<u><em /></u>

So, the total people enter the park:

x+y=333\\\\x=333-y\ \ \ ...(1)

Thus, the total amount collected of the admission fee:

1.50(x)+4(y)=862\\\\

Substituting the value of x from equation (1):

1.50(333-y)+4(y)=862\\\\499.50-1.50y+4y=862\\\\499.50+2.50y=862\\\\Subtracting\ both\ sides\ by\ 499.50\ we\ get:\\\\2.50y=362.50\\\\Dividing\ both\ sides\ by\ 2.50\ we\ get:\\\\y=145.

<u><em>Thus, the number of adults = 145.</em></u>

Now, to get the number of children by substituting the value of y in equation (1) we get:

x=333-y\\\\x=333-145\\\\x=188.

<u><em>Hence, the number of children = 188.</em></u>

Therefore, 188 children and 145 adults were admitted in the park.

4 0
3 years ago
E^2x -2e^x -8=0<br><img src="https://tex.z-dn.net/?f=%20%7Be%7D%5E%7B2x%7D%20-%20%20%7B2e%7D%5E%7Bx%7D%20-%208%20%3D%200" id="Te
vovikov84 [41]
E^2x -2e^x -8=0   =>    e<span>^(2x)  -2e^x -8=0

Temporarily replace e^x with y.

Then (y)^2 - 2y - 8 = 0.  Factors are (y-4) and (y+2).

Roots are y = 4 and y= -2.

Now remembering that we temporarily replaced e^x with y, we let 
y=4 = e^x.  We need to solve for x.  Taking the natural log of both sides, we get:

ln 4 = x (answer)

We have to discard the other root (y= -2), because we cannot take the ln of a negative number.


</span>
8 0
3 years ago
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