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katen-ka-za [31]
3 years ago
5

WILL GIVE BRAINLIESTWhat is the value of x in the figure? 1042 (3x – 19)​

Mathematics
1 answer:
Anna11 [10]3 years ago
5 0

Answer:

x = 41

Step-by-step explanation:

We know these angles will be equal to each other (they are across from each other, I honestly forget the term ) so we can set up an equation

Our equation from given: 104 = 3x - 19

Adding 19 to both sides 123 = 3x

Dividing both sides by 3: 41 = x

Answer: x = 41

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A 50-gal tank initially contains 10 gal of fresh water. At t = 0, a brine solution
scZoUnD [109]

\huge \mathbb{SOLUTION:}

\begin{array}{l} \textsf{Let }A(t)\textsf{ be the function which gives the amount} \\ \textsf{of the salt dissolved in the liquid in the tank at} \\ \textsf{any time }t. \textsf{ We want to develop a differential} \\ \textsf{equation that, when solved, will give us an} \\ \textsf{expression for }A(t). \\ \\ \textsf{The basic principle determining the differential} \\ \textsf{equation is} \\ \\ \end{array}

\boxed{ \footnotesize \begin{array}{l} \qquad\quad \quad\Large{\dfrac{dA}{dt} = R_{in} - R_{out}} \\ \\ \textsf{where:} \\ \\ \begin{aligned} \bullet\: R_{in} &= \textsf{rate of the salt entering} \\ &= \left({\footnotesize \begin{array}{c}\textsf{Concentration of} \\\textsf{salt inflow}\end{array}}\right) \times \small(\textsf{Input of brine}) \\ \\ \bullet\: R_{out} &= \textsf{rate of the salt leaving} \\ &= \left({\footnotesize \begin{array}{c}\textsf{Concentration of} \\\textsf{salt outflow}\end{array}}\right) \times \small(\textsf{Output of brine}) \end{aligned} \end{array}} \\ \\

\begin{array}{l} \textsf{On the problem, the amount of salt in the tank,} \\ A(t), \textsf{changes overtime is given by the differential} \\ \textsf{equation}  \\ \\ \footnotesize A'(t) = \left(\dfrac{4\ \textsf{gal}}{1\ \textsf{min}}\right)\!\!\left(\dfrac{1\ \textsf{lb}}{1\ \textsf{gal}}\right) - \left(\dfrac{2\ \textsf{gal}}{1\ \textsf{min}}\right)\!\!\left(\dfrac{A(t)\ \textsf{lb}}{10 + (4 - 2)t\ \textsf{gal}}\right) \\ \\ \textsf{There's no salt in the tank (fresh water) at the} \\ \textsf{start, so }A(0) = 0. \textsf{ The amount of solution in the} \\ \textsf{tank is given by }10 + (4 -2)t, \textsf{so the tank will} \\ \textsf{overflow once this expression is equal to the total} \\ \textsf{volume or capacity of the tank.} \\ \\ 10 + (4 - 2)t = 50 \\ \\ \textsf{Solving for }t,\textsf{ we get} \\ \\ \implies \boxed{t = 20\textsf{ mins}} \\ \\ A'(t) = 4 - \dfrac{2A(t)}{10 + 2t} \\ \\ A'(t) = 4 - \dfrac{1}{5 + t} A(t) \\ \\ A'(t) + \dfrac{1}{5 + t} A(t) = 4 \\ \\ \textsf{This is a linear ODE with integrating factor} \\ \mu (t) = e^{\int \frac{1}{5 + t}\ dt} = e^{\ln |5 + t|} = 5 + t \\ \\ \textsf{Multiplying this to the ODE, we get} \\ \\ (5 + t)A'(t) + A(t) = 4(5 + t) \\ \\ [(5 + t)A(t)]' = 20 + 4t \\ \\ (5 + t)A(t) = 20t + 2t^2 + C \\ \\ \textsf{Since }A(0) = 0, \textsf{ we get } C = 0. \\ \\ A(t) = \dfrac{2t^2 + 20t}{t + 5} \\ \\ A(t) = 2t + 10 - \dfrac{50}{t + 5} \\ \\ \textsf{So the function that gives the amount of salt at} \\ \textsf{any given time }t,\textsf{ is given by} \\ \\ \implies A(t) = 2t + 10 - \dfrac{50}{t + 5} \\ \\ \textsf{The amount of salt in the tank at the moment} \\ \textsf{of overflow or at }t = 20\textsf{ mins is equal to} \\ \\ A(20) = 2(20) + 10 - \dfrac{50}{20 + 5} \\ \\ \implies \boxed{A = 48\ \textsf{gallons}} \end{array}

\Large \mathbb{ANSWER:}

\qquad\red{\boxed{\begin{array}{l} \textsf{a. }20\textsf{ mins} \\ \\ \textsf{b. }48\textsf{ gallons}\end{array}}}

#CarryOnLearning

#BrainlyMathKnower

#5-MinutesAnswer

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2 years ago
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The slope is 1/2

It moves right 2 and goes up 1.
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The measure of an angle is 89. Find the measure of its supplement
prohojiy [21]

Step-by-step explanation:

Supplementary angles are equal to 180°. To determine the supplement of any angle, subtract the given angle from 180°.

\text{Supplement \: of \: 89  \: \degree = 180 \degree - 89\degree =  \boxed{ \bold{ \text{91\degree}}}}

Hope I helped ! ツ

Have a wonderful day / night ! ♡

# { \underbrace{ \text{Carry \: On \: Learning}}} !! ✎

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁

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3 years ago
4x2 + y2 = 36<br> Obtener dominio
Veronika [31]

<em>Answer:</em>

<em>[-3,3]</em>

<em>Step-by-step explanation:</em>

<em>Write the problem as a mathematical expression.</em>

<em>4x^2+y^2=36</em>

<em>Subtract 4x^2 from both sides of the equation.</em>

<em>y^2=36-4x^2</em>

<em>Take the square root of both sides of the equation to eliminate the exponent on the left side.</em>

<em>y= + and - </em>\sqrt{36-4x^2}<em />

<em>The complete solution is the result of both the positive and negative portions of the solution.</em>

<em>y= </em>2\sqrt{(3+x)(3-x)<em />

<em />y= -2\sqrt{(3+x)(3-x)}<em />

<em>Set the radicand in </em>\sqrt{(3+x)(3-x)} \geq 0<em> greater than or equal to 0 to find where the expression is defined.</em>

<em />(3+x)(3-x)\geq 0<em />

<em>So your answer would be [-3,3]</em>

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prohojiy [21]
Jim = 40 messages
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Lucy = 20 messages
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