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3 years ago

I need help on how to simplify this problem.

Mathematics

1 answer:

guajiro [1.7K]3 years ago

6 0

Simplify the radical by breaking the radicand up into a product of known factors
Exact Form:
2√10 + 5

Decimal Form:
11.32455532 . . .

Answer: 2√10 + 5

Hope this helps! :)
~Zain

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avanturin [10]

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5 0

3 years ago

Read 2 more answers

If alvin sold 60% of his baseball cards, gave away 30% of those that were left, and still had 40 baseball cards in his possessio

kipiarov [429]

Answer:

The number of baseball card to begin with is 143

Step-by-step explanation:

Let The number of baseball cards = x

The number of sold baseball card = 60% of x

= 0.6 x

The number of left baseball card = x - 0.6 x = 0.4 x

The number of card gave away = 30 % of left cards

= 0.3 × 0.4 x = 0.12 x

The number of card left in his possession = 40

So, 0.6 x + 0.12 x + 40 = x

Or, 40 = x - 0.6 x - 0.12 x

Or, 40 = 0.28 x

∴ x = $\frac{40}{0.28}$ = 142.85 ≈ 143

Hence The number of baseball card to begin with is 143 Answer

3 0

3 years ago

Which of the following options is the last step in calculating your net worth?

mestny [16]

Answer:

Step-by-step explanation:

subtracting your liabilities from your assets

5 0

3 years ago

You have a wire that is 20 cm long. You wish to cut it into two pieces. One piece will be bent into the shape of a square. The o

Aleksandr [31]

Answer:

Therefore the circumference of the circle is $=\frac{20\pi}{4+\pi}$

Step-by-step explanation:

Let the side of the square be s

and the radius of the circle be r

The perimeter of the square is = 4s

The circumference of the circle is =2πr

Given that the length of the wire is 20 cm.

According to the problem,

4s + 2πr =20

⇒2s+πr =10

$\Rightarrow s=\frac{10-\pi r}{2}$

The area of the circle is = πr²

The area of the square is = s²

A represent the total area of the square and circle.

A=πr²+s²

Putting the value of s

$A=\pi r^2+ (\frac{10-\pi r}{2})^2$

$\Rightarrow A= \pi r^2+(\frac{10}{2})^2-2.\frac{10}{2}.\frac{\pi r}{2}+ (\frac{\pi r}{2})^2$

$\Rightarrow A=\pi r^2 +25-5 \pi r +\frac{\pi^2r^2}{4}$

$\Rightarrow A=\pi r^2\frac{4+\pi}{4} -5\pi r +25$

For maximum or minimum $\frac{dA}{dr}=0$

Differentiating with respect to r

$\frac{dA}{dr}= \frac{2\pi r(4+\pi)}{4} -5\pi$

Again differentiating with respect to r

$\frac{d^2A}{dr^2}=\frac{2\pi (4+\pi)}{4}$ > 0

For maximum or minimum

$\frac{dA}{dr}=0$

$\Rightarrow \frac{2\pi r(4+\pi)}{4} -5\pi=0$

$\Rightarrow r = \frac{10\pi }{\pi(4+\pi)}$

$\Rightarrow r=\frac{10}{4+\pi}$

$\frac{d^2A}{dr^2}|_{ r=\frac{10}{4+\pi}}=\frac{2\pi (4+\pi)}{4}>0$

Therefore at $r=\frac{10}{4+\pi}$ , A is minimum.

Therefore the circumference of the circle is

$=2 \pi \frac{10}{4+\pi}$

$=\frac{20\pi}{4+\pi}$

4 0

3 years ago

1 L of a 78% acid solution was mixed with 6 L of a 64% acid solution. Find the concentration of the new mixture.

JulijaS [17]

The first solution contributes 0.78*1 = 0.78 L of acid.

The second contributes 0.64*6 = 3.84 L of acid.

There will be 7 L total of the new solution, and 3.84 + 0.78 = 4.62 total L of acid in it. So the new solution has a concentration of 4.62/7 = 0.66, or about 66%.

8 0

3 years ago