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3 years ago

Please solve x^2-8x=8

Mathematics

2 answers:

Naily [24]3 years ago

5 0

Someone answered the question

Varvara68 [4.7K]3 years ago

3 0

Answer:4^2-(8x1)=8

Step-by-step explanation:

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A fossil was analyzed and determined to have a carbon-14 level that is 80 % that of living organisms. the half-life of c-14 is 5

liq [111]

Answer:

The fossil is 1860 years old.

Step-by-step explanation:

The equation for the amount of fossil has the following format:

$Q(t) = Q(0)e^{rt}$

In which Q(t) is the amount after t years, Q(0) is the initial amount and r is the rate of change.

Half-life of c-14 is 5730 years.

This means that $Q(5730) = 0.5Q(0)$

$Q(t) = Q(0)e^{rt}$

$0.5Q(0) = Q(0)e^{5730r}$

$e^{5730r} = 0.5$

$\ln{e^{5730r}} = \ln{0.5}$

$5730r = \ln{0.5}$

$r = \frac{\ln{0.5}}{5730}$

$r = -0.00012$

$Q(t) = Q(0)e^{-0.00012t}$

How old is the fossil?

This is t for which

$Q(t) = 0.8Q(0)$

$Q(t) = Q(0)e^{-0.00012t}$

$0.8Q(0) = Q(0)e^{-0.00012t}$

$e^{-0.00012t} = 0.8$

$\ln{e^{-0.00012t}} = \ln{0.8}$

$-0.00012t = \ln{0.8}$

$t = -\frac{\ln{0.8}}{-0.00012}$

$t = 1860$

The fossil is 1860 years old.

4 0

2 years ago

Use the properties of exponents to simplify the expression: y^(y3)2

iren [92.7K]

because y^3 is raised to the power of two, we will have to multiply the exponents rather than adding them.

By distributing the power of 2, we will get y^2(6).

Because now the exponents are being multiplied, we can just add them to get y^8. The other y has a power of 1, so we'll just add the power of that y as well to get y^9.

summary:

multiply exponents if they are being raised to a power.

add exponents if they are being multiplied, and only add them if they have the same base (in this case, both the bases of the exponents are y, so we can add them)

8 0

3 years ago

What represents the inverse of the function f(x)=4x

Yuki888 [10]

Answer:

$\frac{x}{4}$

Step-by-step explanation:

The given function is

f(x) = 4x

As we know

f(x) = y, which implies x= $f^{-1} (y)$

Therefore,

y = 4x

x = $\frac{y}{4}$

as x= $f^{-1} (y)$

So,

$f^{-1} (y) = \frac{y}{4}$

replacing y by x in the above expression

$f^{-1} (x) = \frac{x}{4}$

So our inverse function is $\frac{x}{4}$

4 0

2 years ago

How do graphs and equations reveal information about a relationship between two quantities

fiasKO [112]

Graph and equation both shows the proportional comparison between two quantities

for example, equation y = 4x, this means, the value of 'y' will always be 4 times the value of 'x'

More complex equation such as y = 3x + 5, means that the value of 'y' equals to 5 more triples of value of 'x'

Another example is the conversion graph attached below, it shows the relationship between kilometers and miles. For example, we want to find out how many miles are in 10 kilometers, we would draw a line from the point that shows 10 km towards the graph, then across from the graph to miles, and we'd get a reading of 12 miles.

3 0

3 years ago

A boat is being pulled into a dock with a rope attached to the boat at water level. When the boat is 12 feet from the dock, the

Natali5045456 [20]

Given :

A boat is being pulled into a dock with a rope attached to the boat at water level. When the boat is 12 feet from the dock, the length of the rope form the boat to the dock is 3 feet longer than twice the height of the dock above the water.

To Find :

The height of the dock.

Solution :

This will make a right angle triangle as given in link below .

Now , applying Pythagoras theorem :

$(2h+3)^2=h^2+12^2\\\\4h^2+9h+9=h^2+144\\\\h^2+4h-45=0\\\\(h-5)(h+9)=0$

Now , h = 5 or h = -9 .

Now , height cannot be negative .

So , height of the dock is 5 ft .

Hence , this is the required solution .

8 0

3 years ago