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2 years ago

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Paula puts an initial $600 into a savings account. The account has a 7% annual compound interest rate. Find the amount of money

in her account after nine years.

1 answer:

Alexxandr [17]2 years ago

3 0

$600*0.07*9 years= $10

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2 years ago

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What is the volume of this cone?

olchik [2.2K]

Answer:

The volume of the cone is approximately 453.0 cm³

Step-by-step explanation:

The volume of a cone is one third that of a cylinder with the same height and radius. That gives us 1/3 πr²h, where r is radius and h is height.

However, we are not given the height of the cone, but the side length. We can work out the height using the Pythagorean theorem, as we have a right triangle with the height, base radius, and length. You may recall that the Pythagorean theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of it's other two sides:

$a^2 = b^2 + c^2$

So we can find the height of the cone with that:

$10.8^2 = 7.4^2 + h^2\\h^2 = 10.8^2 - 7.4^2\\h^2 = 116.64 - 54.76\\h^2 = 61.88\\h = \sqrt{61.88}\\h \approx 7.9$

Now that we have the cone's height, we can solve for its volume:

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3 years ago

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Rewrite the expression 4+<img src="https://tex.z-dn.net/?f=%5Csqrt%7B16-%284%29%285%29%7D" id="TexFormula1" title="\sqrt{16-(4)(

Inessa05 [86]

Answer:

$2+i$

Step-by-step explanation:

Given the expression:

$\dfrac{4+\sqrt{16-(4)(5)}}{2}$

To find:

The expression of above complex number in standard form $a+bi$ .

Solution:

First of all, learn the concept of $i$ (pronounced as <em>iota</em>) which is used to represent the complex numbers. Especially the imaginary part of the complex number is represented by $i$ .

Value of $i =\sqrt{-1}$ .

Now, let us consider the given expression:

$\dfrac{4+\sqrt{16-(4)(5)}}{2}\\\Rightarrow \dfrac{4+\sqrt{16-(4\times 5)}}{2}\\\Rightarrow \dfrac{4+\sqrt{16-20}}{2}\\\Rightarrow \dfrac{4+\sqrt{-4}}{2}\\\Rightarrow \dfrac{4+\sqrt{(-1)(4)}}{2}\\\Rightarrow \dfrac{4+\sqrt{(-1)}\sqrt4}{2}\\\Rightarrow \dfrac{4+\sqrt4i}{2} \ \ \ \ \ (\because \sqrt{-1} =i) \\\Rightarrow \dfrac{4+2i}{2}\\\Rightarrow 2+i$

So, the given expression in standard form is $2+i$ .

Let us compare with standard form $a+bi$ so we get $a =2, b =1$ .

$\therefore$ The standard form of

$\dfrac{4+\sqrt{16-(4)(5)}}{2}$

is: $\bold{2+i}$

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2 years ago