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3 years ago

Please help, and show work if you can :))

Mathematics

1 answer:

brilliants [131]3 years ago

5 0

Answer:

Detailed explanation down below

Step-by-step explanation:

A bisector divides an angle in half, so we can say that:

7x - 27 = x + 57

7x = x + 84

6x = 84

x= 14

So now lets input this information

7 x 14 - 27 = m∠ LMO = 98 - 27 = 71°

14° + 57° = 71°

(Actually we didnt have to do this second equation because both angles should be equal.)

71° + 71° = 142°

So the answer is C : x=14° . m∠LMN = 142°

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The use of mathematical methods to study the spread of contagious diseases goes back at least to some work by Daniel Bernoulli i

harina [27]

Answer:

$y(t) = y_o e^{\beta t}$

$x(t) = x_o e^{\frac{-\alpha y_o }{\beta }[e^{-\beta t} - 1] }$

$\lim_{t \to \infty} x(t) = x_oe^{\frac{-\alpha y_o}{\beta } }$

Step-by-step explanation:

From the question we are told that

$\frac{dy}{y} = -\beta dt$

Now integrating both sides

$ln y = \beta t + c$

Now taking the exponent of both sides

$y(t) = e^{\beta t + c}$

=> $y(t) = e^{\beta t} e^c$

Let $e^c = C$

$y(t) = C e^{\beta t}$

Now from the question we are told that

$y(0) = y_o$

Hence

$y(0) = y_o = Ce^{\beta * 0}$

=> $y_o = C$

$y(t) = y_o e^{\beta t}$

From the question we are told that

$\frac{dx}{dt} = -\alpha xy$

substituting for y

$\frac{dx}{dt} = - \alpha x(y_o e^{-\beta t })$

=> $\frac{dx}{x} = -\alpha y_oe^{-\beta t} dt$

Now integrating both sides

$lnx = \alpha \frac{y_o}{\beta } e^{-\beta t} + c$

Now taking the exponent of both sides

$x(t) = e^{\alpha \frac{y_o}{\beta } e^{-\beta t} + c}$

=> $x(t) = e^{\alpha \frac{y_o}{\beta } e^{-\beta t} } e^c$

Let $e^c = A$

=> $x(t) =K e^{\alpha \frac{y_o}{\beta } e^{-\beta t} }$

Now from the question we are told that

$x(0) = x_o$

$x(0)=x_o =K e^{\alpha \frac{y_o}{\beta } e^{-\beta * 0} }$

=> $x_o = K e^{\frac {\alpha y_o }{\beta } }$

divide both side by $(K * x_o)$

=> $K = x_o e^{\frac {\alpha y_o }{\beta } }$

$x(t) =x_o e^{\frac {-\alpha y_o }{\beta } } * e^{\alpha \frac{y_o}{\beta } e^{-\beta t} }$

=> $x(t)= x_o e^{\frac{-\alpha * y_o }{\beta} + \frac{\alpha y_o}{\beta } e^{-\beta t} }$

=> $x(t) = x_o e^{\frac{\alpha y_o }{\beta }[e^{-\beta t} - 1] }$

Generally as t tends to infinity , $e^{- \beta t}$ tends to zero

$\lim_{t \to \infty} x(t) = x_oe^{\frac{-\alpha y_o}{\beta } }$

5 0

3 years ago

Nolan rides his bike 63 miles in 270 minutes. What is his average speed in miles per hour?

s2008m [1.1K]

63 miles in 270 minutes will mean that nolan rides his bike at a distance of 63/270 miles in one minute.
there are 60 minutes in an hour. So to find out the distance he covers in 1 hour, 63/270 × 60 will give you 14 miles.
Since the question is asking for the average speed, nolan rides his bike at 14 miles per hour i think.

4 0

3 years ago

Twice the sum of four and x is three less than x.

aliya0001 [1]

Answer:

-11

Step-by-step explanation

Condition:

2(4+x)=x-3

8+2x=x-3

Combining similar terms

8+3=x-2x

11=-x

x=-11

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2 years ago

In 1999, there were 9860 Great Danes registered with the American Kennel Club. The number of

dybincka [34]

Answer:

154,897

Step-by-step explanation:

Labradors were

6997 MORE than 15 TIME Danes

So, first, what is 15 times Danes??

Given 9860 Danes, fifteen times Danes would be:

9860 * 15 = 147,900

Now, 6997 MORE to that, it would be:

147,900 + 6997 = 154,897

Thus,

There were 154,897 registered Labrador Retrievers

8 0

2 years ago

How many zeros in the standard form of 10/3

Slav-nsk [51]

If you meant, "how many zeros are there in the standard form of 'ten divided by 3,' the answer would be, "none."

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7 0

3 years ago