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2 years ago

Where on a number line are the numbers x for which |x|>1

Mathematics

1 answer:

Andrews [41]2 years ago

6 0

Answer:

Step-by-step explanation:

Given the inequality

|x|> 1

The modulus of x shows that x can be both positive and negative value.

If x is positive:

x>1

1<x

If x is negative:

-x>1

Multiplying both sides of the inequality by minus will change the inequality sign

x < -1

Combining both inequalities:

1<x<-1

Find the position on the number line in the attachment

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Newton's law of cooling is:

Mnenie [13.5K]

Answer:

$t = \frac{ln(\frac{21}{59})}{-0.15}=6.887 hr$

So it would takes approximately 6.9 hours to reach 32 F.

Step-by-step explanation:

For this case we have the following differential equationÑ

$\frac{du}{dt}= -k (u-T)$

We can reorder the expression like this:

$\frac{du}{u-T} = -k dt$

We can use the substitution $w = u-T$ and $dw =du$ so then we have:

$\frac{dw}{w} =-k dt$

IF we integrate both sides we got:

$ln |w| = -kt +C$

If we apply exponential in both sides we got:

$w = e^{-kt} *e^c$

And if we replace w = u-T we got:

$u(t)= T + C_1 e^{-kt}$

We can also express the solution in the following terms:

$u(t) = (T_i -T_{amb}) e^{kt} +T_{amb}$

For this case we know that $k =-0.15 hr$ since w ehave a cooloing, $T_{i}= 70 F, T_{amb}=11F$ , we have this model:

$u(t) = (70-11) e^{-0.15t} +11$

And if we want that the temperature would be 32F we can solve for t like this:

$32 = 59 e^{-0.15 t} +11$

$21=59 e^{-0.15 t}$

$\frac{21}{59} = e^{-0.15 t}$

If we apply natural logs on both sides we got:

$ln (\frac{21}{59}) =-0.15 t$

$t = \frac{ln(\frac{21}{59})}{-0.15}=6.887 hr$

So it would takes approximately 6.9 hours to reach 32 F.

7 0

3 years ago

Solve for x. 13(x-3) = 39 X=1 X=4 x=6 x=10

Valentin [98]

13 factored out is 13x - 39 add 39 to both sides it equals 13x=78 and 78 divided by 13 is 6 the anwser is x=6

7 0

2 years ago

OLEASE DO THIS ITS EASY PKEAS EI NEED TO FINISH IT NOW PKEASE

KATRIN_1 [288]

For x y chart 19.36.2.27.13

8 0

2 years ago

How do i make a table of values for each function rule and then graph the function for these examples:

Sholpan [36]

$\bf \begin{array}{ccllll}
y=1.5x-3\\
\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash\\

x&y\\
\textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash\\
-3&1.5(-3)-3\\
-2&1.5(-2)-3\\
-1&1.5(-1)-3\\
0&1.5(0)-3\\
1&1.5(1)-3\\
...&...
\end{array}$ $\bf \begin{array}{ccllll}
y=-x^2+4\\
\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash\\

x&y\\
\textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash\\
-3&-(-3)^2+4\\
-2&-(-2)^2+4\\
-1&-(-1)^2+4\\
0&-(0)^2+4\\
1&-(1)^2+4\\
...&...
\end{array}$

and so on, and then, you graph those x,y coordinates

5 0

2 years ago

Polygon ABCDEF is translated 12 units to the left to create polygon A′B′C′D′E′F′. If DE = 7 units, what is D′E′ ?

gizmo_the_mogwai [7]

A translation is a rigid transformation, which means angle measures and distances from two points do not change.
Polygon ABCDEF is congruent to polygon A'B'C'D'E'F'

DE = D'E' = 7

8 0

3 years ago

Read 2 more answers