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nikdorinn [45]
2 years ago
7

Find the length of the second leg of the triangle round to the nearest hundredth

Mathematics
1 answer:
horsena [70]2 years ago
7 0

Answer:

\displaystyle \frac{3\sqrt{230}}{5}

Step-by-step explanation:

Use the Pythagorean Theorem:

\displaystyle a^2 + b^2 = c^2 \\ \\ 9,7^2 + b^2 = 13,3^2; \sqrt{82,8} = \sqrt{b^2} \\ \\ \frac{3\sqrt{230}}{5}\:[or\:9,0994505329...] = b

So, you have this:

\displaystyle 9,1 ≈ b

I am joyous to assist you at any time.

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An investment of P dollars increased to A dollars in t years. If interest was compounded continuously, find the interest rate. (
Gemiola [76]

Answer: the interest rate is 6%

Step-by-step explanation:

The formula for continuously compounded interest is

A = P x e (r x t)

Where

A represents the future value of the investment after t years.

P represents the present value or initial amount invested

r represents the interest rate

t represents the time in years for which the investment was made.

e is the mathematical constant approximated as 2.7183.

From the information given,

A = $4482

P = 1000

t = 25 years

Therefore,

4482 = 1000 x 2.7183^(r x 25)

4482/1000 = 2.7183^25r

4.482 = 2.7183^25r

Taking ln of both sides, it becomes

Ln 4.482 = 25rLn2.7183

1.5 = 25r

r = 1.5/25 = 0.06

r = 0.06 × 100 = 6%

5 0
3 years ago
Which is equivalent to V180x11 after it has been simplified completely?
inna [77]

Question:

Which is equivalent to \sqrt{180x^{11}} after it has been simplified completely?

Answer:

\sqrt{180x^{11}} = 6x^{5}\sqrt{5x}

Step-by-step explanation:

Given

\sqrt{180x^{11}}

Required

Simplify

We start by splitting the square root

\sqrt{180x^{11}} = \sqrt{180} * \sqrt{x^{11}}

Replace 180 with 36 * 5

\sqrt{180x^{11}} = \sqrt{36 * 5} *  \sqrt{x^{11}}

Further split the square roots

\sqrt{180x^{11}} = \sqrt{36} *\sqrt{5} *  \sqrt{x^{11}}

\sqrt{180x^{11}} = 6*\sqrt{5} *  \sqrt{x^{11}}

Replace power of x; 11 with 10 + 1

\sqrt{180x^{11}} = 6*\sqrt{5} *  \sqrt{x^{10 + 1}}

From laws of indices; a^{m+n} = a^m * a^n

So, we have

\sqrt{180x^{11}} = 6*\sqrt{5} *  \sqrt{x^{10} * x^1}

\sqrt{180x^{11}} = 6*\sqrt{5} *  \sqrt{x^{10} * x}

Further split the square roots

\sqrt{180x^{11}} = 6*\sqrt{5} *  \sqrt{x^{10}} * \sqrt{x}

From laws of indices; \sqrt{a} = a^{\frac{1}{2}}

So, we have

\sqrt{180x^{11}} = 6*\sqrt{5} *  x^{10*\frac{1}{2}} * \sqrt{x}

\sqrt{180x^{11}} = 6*\sqrt{5} *  x^{\frac{10}{2}} * \sqrt{x}

\sqrt{180x^{11}} = 6*\sqrt{5} *  x^{5} * \sqrt{x}

Rearrange Expression

\sqrt{180x^{11}} = 6 *  x^{5} * \sqrt{5} * \sqrt{x}

\sqrt{180x^{11}} = 6x^{5} * \sqrt{5} * \sqrt{x}

From laws of indices; \sqrt{a} *\sqrt{b} = \sqrt{a*b} = \sqrt{ab}

So, we have

\sqrt{180x^{11}} = 6x^{5} * \sqrt{5*x}

\sqrt{180x^{11}} = 6x^{5} * \sqrt{5x}

\sqrt{180x^{11}} = 6x^{5}\sqrt{5x}

<em>The expression can no longer be simplified</em>

Hence, \sqrt{180x^{11}} is equivalent to 6x^{5}\sqrt{5x}

7 0
2 years ago
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56. A small square pyramid of height 6 cm was removed from the top of a large square pyramid of height 12 cm forming the solid s
icang [17]

Answer:  I think it's 15,872cm

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3 years ago
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How many eights are there in 6 1/2
Alona [7]
There are (8) eighths in 1, so multiply this by 6 1/2 to determine how many eighths there are:

8*6.5 = <u><em>52 eighths</em></u> in 6 1/2


5 0
3 years ago
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Which equation has a vertex of (-3, 4)?
babunello [35]

Answer:

Where are the equations?

Step-by-step explanation:

3 0
2 years ago
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