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3 years ago

Solve to three significant digits 123= 500e ^ -0.12x

1 answer:

8 0

$500{ e }^{ -0.12x }=123\\ \\ { e }^{ -\frac { 12 }{ 100 } x }=\frac { 123 }{ 500 } \\ \\ { e }^{ -\frac { 3 }{ 25 } x }=\frac { 123 }{ 500 }$

$\\ \\ { \left( { e }^{ x } \right) }^{ -\frac { 3 }{ 25 } }=\frac { 123 }{ 500 } \\ \\ { e }^{ x }={ \left( \frac { 123 }{ 500 } \right) }^{ \frac { 1 }{ -\frac { 3 }{ 25 } } }$

$\\ \\ { e }^{ x }={ \left( \frac { 123 }{ 500 } \right) }^{ -\frac { 25 }{ 3 } }\\ \\ \ln { \left( { \left( \frac { 123 }{ 500 } \right) }^{ -\frac { 25 }{ 3 } } \right) } =x$

$\\ \\ x=-\frac { 25 }{ 3 } \ln { \left( \frac { 123 }{ 500 } \right) }$

$\therefore \quad x\approx 11.7$

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Find the length of AB?

vampirchik [111]

Given:

The figure of a right triangle.

To find:

The length of AB.

Solution:

In a right angle triangle,

$\cos \theta=\dfrac{Base}{Hypotenuse}$

Using this trigonometric ratio for the given triangle, we get

$\cos A=\dfrac{AB}{AC}$

$\cos (60^\circ)=\dfrac{AB}{10}$

$\dfrac{1}{2}=\dfrac{AB}{10}$

$\dfrac{1}{2}\times 10=AB$

$5=AB$

Therefore, the length of AB is 5 units.

7 0

3 years ago

Geometry math question no Guessing and Please show work thank you

ahrayia [7]

To find the angle of vertex E,we need to first find the sum of interior polygons to determine x:
$(number \: of \: sides - 2) \times 180$
In this case,the equation would be:
(7-2)×180°
=5×180°
=900°

We can then find the value of x:
(4)6x+(2)2x+8x=900°
24x+4x+8x=900°
36x=900°
x=25°

The interior angle of vertex E:

6x=6(25)=150°

Therefore,the interior angle of vertex E is 150°.

Hope it helps!

6 0

3 years ago

9-2(7-8)<br><br> Help please

yuradex [85]

9 - 2(7 - 8)
9 - 2(-1)
9 - (-2)
11

6 0

3 years ago

Read 2 more answers

Let T: Mmxn(R)Mmxn(R) be the function defined

alexandr402 [8]

Answer:

True. See the explanation and proof below.

Step-by-step explanation:

For this case we need to remeber the definition of linear transformation.

Let A and B be vector spaces with same scalars. A map defined as T: A >B is called a linear transformation from A to B if satisfy these two conditions:

1) T(x+y) = T(x) + T(y)

2) T(cv) = cT(v)

For all vectors $x,y \in V$ and for all scalars $c \in R$ . And A is called the domain and B the codomain of T.

Proof

For this case the tranformation proposed is t: $M_{mxn} (R) > M_{nxm} (R)$

Where $T(A) = A^T$

For this case we have the following assumption:

1) The transpose of an nxm matrix is an nxm matrix

And the following conditions:

2) $T(A+B) = (A+B)^T = A^T + B^T = T(A) + T(B)$

And we can express like this $T(A+B) =T(A) + T(B)$

3) If $A \in M_{mxn}(R)$ and $c \in R$ then we have this:

$T(cA) = (cA)^T = cA^T = cT(A)$

And since we have all the conditions satisfied, we can conclude that T is a linear transformation on this case.

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2 years ago

Consider the following linear equation.y = -1-Step 1 of 2: Determine the slope and the y-intercept (entered as an ordered pair)

Dmitriy789 [7]

Recall that a slope-intercept form of a linear equation is

$\begin{gathered} y=mx+b \\ \text{where} \\ m\text{ is the slope} \\ b\text{ is the y-intercept} \end{gathered}$

Rearrange the given so that it follows that slope intercept form

$\begin{gathered} y=-1-\frac{2}{5}x\Longrightarrow y=-\frac{2}{5}x-1 \\ \\ \text{Now that it is in the slope intercept form} \\ y=-\frac{2}{5}x-1 \\ \text{we can determine that the slope is } \\ m=-\frac{2}{5} \\ \text{and the y-intercept is} \\ b=-1 \end{gathered}$

The y-intercept is the value for which the linear function crosses the y-axis, this is when the value of x is equal to zero. The ordered pair therefore of the y-intercept is (0,-1).

8 0

1 year ago