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3 years ago

Find the missing length on the triangle. Round your answer to the nearest tenth if

Mathematics

1 answer:

Ierofanga [76]3 years ago

4 0

Answer:

D. 10.6

Step-by-step explanation:

Using Pythagoras' theorem

hyp² = side ² + side²

hyp² = 7² + 8²

hyp² = 49 + 64

hyp² = 113

hyp = sqrt of 113

hyp = 10.6

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A storage tank contains a liquid radioactive element with a half-life of 96 years. It will be relatively safe for the contents t

PolarNik [594]

Answer:

The tank must remain intact for 1183 years.

Step-by-step explanation:

Exponential equation for decay:

The amount of a substance after t years is given by:

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

In which A(0) is the initial amount and r is the decay rate.

A storage tank contains a liquid radioactive element with a half-life of 96 years.

This means that $A(96) = 0.5A(0)$ , and we use this to find r.

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

$0.5A(0) = A(0)e^{96r}$

$e^{96r} = 0.5$

$\ln{e^{96r}} = \ln{0.5}$

$96r = \ln{0.5}$

$r = \frac{\ln{0.5}}{96}$

$r = -0.0072$

$A(t) = A(0)e^{-0.0072t}$

It will be relatively safe for the contents to leak from the tank when 0.02% of the radioactive element remains. How long must the tank remain intact for this storage procedure to be safe?

This is t for which $A(t) = 0.0002A(0)$ . So

$A(t) = A(0)e^{-0.0072t}$

$0.0002A(0) = A(0)e^{-0.0072t}$

$e^{-0.0072t} = 0.0002$

$\ln{e^{-0.0072t}} = \ln{0.0002}$

$-0.0072t = \ln{0.0002}$

$t = -\frac{\ln{0.0002}}{0.0072}$

$t = 1183$

The tank must remain intact for 1183 years.

5 0

3 years ago

152 + (-20) + 84 = The answers are 216, 48, -48, -126

andrey2020 [161]

Answer:

216

Step-by-step explanation:

hope this was helpful.

3 0

3 years ago

Read 2 more answers

Which equation represents a line that is parallel to the line whose equation is 2y=3x+7 ?

Sav [38]

2 and 4. In equations where the line is parallel, the slope is the same. By eyeing this number 2 is right but number four is right as well because when you put y by itself and divide the 2 from the whole equation, it is ultimately the same and still parallel from the original equation.

3 0

2 years ago

Write the equation using function notation f(x). then find f(0) 2x^2 - 3y = 6

Grace [21]

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