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3 years ago

Write the expression 2i^15-i^7 in the standard form a + bi

1 answer:

7 0

$\bf 2i^{15}-i^7\qquad 
\begin{cases}
i^2=\sqrt{-1}\cdot \sqrt{-1}\implies \sqrt{(-1)^2}\implies -1\\\\
i^4=i^2\cdot i^2\implies -1\cdot -1\implies 1
\end{cases}\\\\
-----------------------------\\\\
2i^{4+4+4+2+1}-i^{4+2+1}\implies 2i^4i^4i^4i^2i^1-i^4i^2i^1
\\\\\\
(2\cdot 1\cdot 1\cdot 1\cdot -1\cdot i)-(1\cdot -1\cdot i)\implies -2i-(-i)
\\\\\\
-2i+i\implies -i\implies \boxed{0-i}$

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How to solve b/2= -4

kobusy [5.1K]

Answer:

b = -8

Step-by-step explanation:

crossmultiply

6 0

3 years ago

A landscape architect wished to enclose a rectangular garden on one side by a brick wall costing $20/ft and on the other three s

makvit [3.9K]

Answer:

The dimensions of the garden that minimize the cost is 9.018 feet(length) and 13.528 feet(width)

Step-by-step explanation:

Let the length of garden be x

Let the breadth of garden be y

Area of Rectangular garden = $Length \times Breadth = xy$

We are given that the area of the garden is 122 square feet

So, $xy=122$ ---A

A landscape architect wished to enclose a rectangular garden on one side by a brick wall costing $20/ft

So, cost of brick along length x = 20 x

On the other three sides by a metal fence costing $10/ft.

So, Other three side s = x+2y

So, cost of brick along the other three sides= 10(x+2y)

So, Total cost = 20x+10(x+2y)=20x+10x+20y=30x+20y

Total cost = 30x+20y

Substitute the value of y from A

Total cost = $30x+20(\frac{122}{x})$

Total cost = $\frac{2440}{x}+30x$

Now take the derivative to minimize the cost

$f(x)=\frac{2440}{x}+30x$

$f'(x)=-\frac{2440}{x^2}+30$

Equate it equal to 0

$0=-\frac{2440}{x^2}+30$

$\frac{2440}{x^2}=30$

$\sqrt{\frac{2440}{30}}=x$

$9.018 =x$

Now check whether it is minimum or not

take second derivative

$f'(x)=-\frac{2440}{x^2}+30$

$f''(x)=-(-2)\frac{2440}{x^3}$

Substitute the value of x

$f''(x)=-(-2)\frac{2440}{(9.018)^3}$

$f''(x)=6.6540$

Since it is positive ,So the x is minimum

Now find y

Substitute the value of x in A

$(9.018)y=122$

$y=\frac{122}{9.018}$

$y=13.528$

Hence the dimensions of the garden that minimize the cost is 9.018 feet(length) and 13.528 feet(width)

4 0

3 years ago

Julia is going to the store to buy candies. Small candies cost $4 and extra-large candies cost $12.She needs to purchase at leas

BartSMP [9]

Answer:

Small candies $=9$

Extra large candies $=12$

Step-by-step explanation:

Let small candies $=x$

Extra large candies $=y$

the number of candies is at least $20$ .

$x+y\geq20$

Cost of $1$ small candy $=\$4$

Cost of $1$ extra large candy $=\$12$

but she has only $\$180$ to spend

$4x+12y\leq180$

Solve for

$x+y=20.......(1)\\4x+12y=180.....(2)\\eqn(2)-eqn(1)\times4\\8y=100\\y=\frac{100}{8} \\y=\frac{25}{8} \\from\ eqn(1)\\x+\frac{25}{2}=20\\ x=20-\frac{25}{2} \\x=\frac{15}{2}$

Since number of candies should be integer.

let $x=7,y=13$

total spend $4\times7+12\times13=184$ which is more than $\$180$ , so this combination is not possible.

$let\ x=8,y=12\\8\times4+12\times12=176$

She has $\$4$ more so she can buy $1$ more small candy.

Hence small candy $=9$

extra large candy $=12$

4 0

3 years ago

Whats the diffrence of 2 2/3 - 1 2/5 write answer in simplest form

Fofino [41]

$2 \frac{2}{3}-1 \frac{2}{5}=2 \frac{2 \times 5}{3 \times 5}-1 \frac{2 \times 3}{5 \times 3}=2 \frac{10}{15}-1 \frac{6}{15}=\boxed{1\frac{4}{15}}$

3 0

3 years ago

Read 2 more answers

Can you help with this. Thanks!

Ierofanga [76]

92 males buy tickets so
200-92=108
so 108 females buy tickets

30 males buy business and a total of 44 people (female and male) but business so 44-30=14
14 females buy business

108-14(business ticket) = 94 females left.
62 of those 94 females buy economy tickets
so therefore 94-62=32. 32 females left over

14 females = business
62 females = economy
14 + 62 = 76
108 - 76 = 32
32 remaining females buy premium

it says a total of 60 people buy premium so 60 - 32 = 28

so 28 males buy premium

hope this helped

3 0

3 years ago