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3 years ago

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PLEASE HELP

1 answer:

babymother [125]3 years ago

6 0

Answer:

In mathematics, the Pythagorean theorem, or Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle.

Step-by-step explanation:

It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides. This theorem can be written as an equation relating the lengths of the sides a, b and c, often called the Pythagorean equation: a²+b²=c², where c represents the length of the hypotenuse and a and b the lengths of the triangle's other two sides.

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9% of _____ equals 4.5

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Log x √x + log √c c² = ?

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Given that

log √x (x) + log c² (c)

⇛ log x^1/2 (x) + log c² (c)

We know that

log a^m (b^n) = m/n log a (b)

⇛ 1/2 log x (x) + 2 log c (c)

We know that

log a ( a) = 1

⇛ (1/2)(1) + 2(1)

⇛ (1/2)+2

⇛ (1+4)/2

⇛ 5/2

<u>Answer</u>:- log √x (x) + log c² (c) = 5/2

[(x) ,(c) , (a) represents the bases ]

<em>Additional</em><em> comment</em><em>:</em>

(a+b)(a-b) = a²-b²
log a^m (b^n) = m/n log a (b)
log a ( a) = 1

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3 years ago

10.) Calculate the definite integral

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The indefinite integral ∫dx/x is ln(x), so your integral is

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4 years ago

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How long will it take for $2500 to double if it is invested at 6% annual interest compounded 6 times a year? Enter exact calcula

12345 [234]

Answer:

Part 1) $t=11.610\ years$

Part 2) $t=11.552\ years$

Step-by-step explanation:

Part 1) we know that

The compound interest formula is equal to

$A=P(1+\frac{r}{n})^{nt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

$A=\$5,000\\P=\$2,500\\ r=6\%=6/100=0.06\\n=6$

substitute in the formula above

$5,000=2,500(1+\frac{0.06}{6})^{6t}$

$2=(1.01)^{6t}$

Apply log both sides

$log(2)=log[(1.01)^{6t}]$

$log(2)=(6t)log(1.01)$

solve for t

$t=log(2)/[6log(1.01)]$

$t=11.610\ years$

Part 2) we know that

The formula to calculate continuously compounded interest is equal to

$A=P(e)^{rt}$

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

e is the mathematical constant number

we have

$A=\$5,000\\P=\$2,500\\ r=6\%=6/100=0.06$

substitute in the formula above

$5,000=2,500(e)^{0.06t}$

$2=(e)^{0.06t}$

Apply ln both sides

$ln(2)=ln[(e)^{0.06t}]$

$ln(2)=(0.06t)ln(e)$

$ln(2)=(0.06t)$

$t=ln(2)/(0.06)$

$t=11.552\ years$

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3 years ago

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Assoli18 [71]

Answer:

Answer is the first choice on left.

Step-by-step explanation:

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