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3 years ago

Find three positive numbers x, y, and z that satisfy the given conditions. the sum is 180 and the product is maximum.

1 answer:

8 0

I don't know of any algebraic way to answer this, but 59,60,61 add up to 180, and 60^3 would be the greatest product of 3 numbers, so 59,60,61 yield the greatest product.

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Read 2 more answers

Which expression represents the number 2i4−5i3+3i2+−81‾‾‾‾√ rewritten in a+bi form?

vichka [17]

Answer:

The expression $-1+14i$ represents the number $2i^4-5i^3+3i^2+\sqrt{-81}$ rewritten in a+bi form.

Step-by-step explanation:

The value of $i$ is $i=\sqrt{-1}[tex] or [tex]i^{2}=-1[\tex].Now [tex]i^{4}$ in term of $i^{2}[\tex] can be written as, [tex]i^{4}=i^{2}\times i^{2}$

Substituting the value,

$i^{4}=\left(-1\right)\times \left(-1\right)$

Product of two negative numbers is always positive.

$\therefore i^{4}=1$

Now $i^{3}$ in term of $i^{2}[\tex] can be written as, [tex]i^{3}=i^{2}\times i$

Substituting the value,

$i^{3}=\left(-1\right)\times i$

Product of one negative and one positive numbers is always negative.

$\therefore i^{3}=-i$

Now $\sqrt{-81}$ can be written as follows,

$\sqrt{-81}=\sqrt{\left(81\right)\times\left(-1\right)}$

Applying radical multiplication rule,

$\sqrt{ab}={\sqrt{a}}\sqrt{b}$

$\sqrt{\left(81\right)\times\left(-1\right)}={\sqrt{81}}\sqrt{-1}$

Now, $\sqrt{\left(81\right)=9$ and $\sqrt{-1}}=i$

$\therefore \sqrt{\left(81\right)\times\left(-1\right)}=9i$

Now substituting the above values in given expression,

$2i^4-5i^3+3i^2+\sqrt{-81}=2\left(1\right)-5\left(-i\right)+3\left(-1\right)+9i$

Simplifying,

$2+5i-3+9i$

Collecting similar terms,

$2-3+5i+9i$

Combining similar terms,

$-1+14i$

The above expression is in the form of a+bi which is the required expression.

Hence, option number 4 is correct.

5 0

3 years ago

The bar graph below shows the attendance at school dances. The ticket per price for each dance is $5 per student. Which two danc

topjm [15]

It's B because all the students that attended added together is 320 and 37.5 of 320 is 120

6 0

3 years ago

What value, written as a decimal, should Lena use as the common ratio?

inn [45]

Answer:

an=1*2.5^(n-1)

=2.5^(n-1)

Step-by-step explanation:

Complete question below:

What value, written as a decimal, should Lena use as the common ratio? Lena is asked to write an explicit formula for the graphed geometric sequence. On a coordinate plane, 3 points are plotted. The points are (1, 1), (2, 2.5), (3, 6.25).

Solution

Point (1, 1), (2, 2.5), (3, 6.25).

a=1

ar=2.5

ar^2=6.25

From ar and ar^2

r=6.25/2.5

=2.5

r=2.5

an=ar^(n-1)

Therefore, the explicit formula is

an=1*2.5^(n-1)

=2.5^(n-1)

7 0

3 years ago