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Stells [14]
3 years ago
6

Please help me thank you

Mathematics
1 answer:
velikii [3]3 years ago
3 0

Answer:

The answer in radical form is 4√2

Step-by-step explanation:

Side a = 5.65685 -----> 4√2

Side b = 4

Side c = 4

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Solve the proportion
mario62 [17]

Answer:

\boxed{\sf x = 5}

Step-by-step explanation:

\sf Solve  \: for  \: x  \: over  \: the  \: real \:  numbers:  \\ \sf \implies  \frac{2}{x - 3}   =  \frac{5}{x}  \\  \\  \sf Take  \: the \:  reciprocal  \: of  \: both \:  sides:  \\ \sf \implies  \frac{x - 3}{2}  =  \frac{x}{5}  \\  \\  \sf Expand  \: out \:  terms \:  of \:  the \:  left  \: hand \:  side:  \\  \\ \sf \implies \frac{x}{2}  -  \frac{3}{2}  =  \frac{x}{5}  \\  \\  \sf Subtract \:  \frac{x}{5}   -  \frac{3}{2}  \: from  \: both  \: sides: \\  \sf \implies \frac{x}{2}  -  \frac{3}{2} - ( \frac{x}{5}   -  \frac{3}{2} ) =  \frac{x}{5} - ( \frac{x}{5}  -  \frac{3}{2} ) \\  \\  \sf \implies \frac{x}{2}  -  \frac{3}{2} -  \frac{x}{5}    +   \frac{3}{2} =  \frac{x}{5} -  \frac{x}{5}  +  \frac{3}{2}  \\  \\  \sf \frac{x}{5}  -  \frac{x}{5}  = 0 :  \\  \sf \implies \frac{x}{2}  -  \frac{x}{5}  -  \frac{3}{2}  +  \frac{3}{2}  =  \frac{3}{2}  \\  \\  \sf  \frac{3}{2}   -   \frac{3}{2}   = 0:  \\  \sf \implies \frac{x}{2}  -  \frac{x}{5}  =  \frac{3}{2}   \\  \\ \sf \frac{x}{2}  -  \frac{x}{5} =  \frac{5x - 2x}{10}  =  \frac{3x}{10} :  \\   \sf \implies \frac{3x}{10}  =  \frac{3}{2}   \\  \\ \sf Multiply \:  both  \: sides \:  by \:  \frac{10}{3}  : \\   \sf \implies \frac{3x}{10}  \times  \frac{10}{3}  =  \frac{3}{2 }  \times  \frac{10}{3}   \\  \\ \sf \frac{3x}{10}  \times  \frac{10}{3}  =   \cancel{\frac{3}{10} } \times( x) \times  \cancel{ \frac{10}{3} } = x :  \\  \sf \implies x =  \frac{3}{2}  \times  \frac{10}{3} \\  \\   \sf  \frac{3}{2}  \times  \frac{10}{3}  = \cancel{ \frac{3}{2} }  \times \cancel{ \frac{3}{2} }  \times 5 :   \\ \sf \implies x = 5

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What is the result when 12x} + 17x² + 18x + 9 is divided by 4x + 3?
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Answer:

17x^2+31x+3

Step-by-step explanation:

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If 13cos theta -5=0 find sin theta +cos theta / sin theta -cos theta​
Ivahew [28]

Step-by-step explanation:

<h3>Need to FinD :</h3>

  • We have to find the value of (sinθ + cosθ)/(sinθ - cosθ), when 13 cosθ - 5 = 0.

\red{\frak{Given}} \begin{cases} & \sf {13\ cos \theta\ -\ 5\ =\ 0\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \big\lgroup Can\ also\ be\ written\ as \big\rgroup} \\ & \sf {cos \theta\ =\ {\footnotesize{\dfrac{5}{13}}}} \end{cases}

Here, we're asked to find out the value of (sinθ + cosθ)/(sinθ - cosθ), when 13 cosθ - 5 = 0. In order to find the solution we're gonna use trigonometric ratios to find the value of sinθ and cosθ. Let us consider, a right angled triangle, say PQR.

Where,

  • PQ = Opposite side
  • QR = Adjacent side
  • RP = Hypotenuse
  • ∠Q = 90°
  • ∠C = θ

As we know that, 13 cosθ - 5 = 0 which is stated in the question. So, it can also be written as cosθ = 5/13. As per the cosine ratio, we know that,

\rightarrow {\underline{\boxed{\red{\sf{cos \theta\ =\ \dfrac{Adjacent\ side}{Hypotenuse}}}}}}

Since, we know that,

  • cosθ = 5/13
  • QR (Adjacent side) = 5
  • RP (Hypotenuse) = 13

So, we will find the PQ (Opposite side) in order to estimate the value of sinθ. So, by using the Pythagoras Theorem, we will find the PQ.

Therefore,

\red \bigstar {\underline{\underline{\pmb{\sf{According\ to\ Question:-}}}}}

\rule{200}{3}

\sf \dashrightarrow {(PQ)^2\ +\ (QR)^2\ =\ (RP)^2} \\ \\ \\ \sf \dashrightarrow {(PQ)^2\ +\ (5)^2\ =\ (13)^2} \\ \\ \\ \sf \dashrightarrow {(PQ)^2\ +\ 25\ =\ 169} \\ \\ \\ \sf \dashrightarrow {(PQ)^2\ =\ 169\ -\ 25} \\ \\ \\ \sf \dashrightarrow {(PQ)^2\ =\ 144} \\ \\ \\ \sf \dashrightarrow {PQ\ =\ \sqrt{144}} \\ \\ \\ \dashrightarrow {\underbrace{\boxed{\pink{\frak{PQ\ (Opposite\ side)\ =\ 12}}}}_{\sf \blue{\tiny{Required\ value}}}}

∴ Hence, the value of PQ (Opposite side) is 12. Now, in order to determine it's value, we will use the sine ratio.

\rightarrow {\underline{\boxed{\red{\sf{sin \theta\ =\ \dfrac{Opposite\ side}{Hypotenuse}}}}}}

Where,

  • Opposite side = 12
  • Hypotenuse = 13

Therefore,

\sf \rightarrow {sin \theta\ =\ \dfrac{12}{13}}

Now, we have the values of sinθ and cosθ, that are 12/13 and 5/13 respectively. Now, finally we will find out the value of the following.

\rightarrow {\underline{\boxed{\red{\sf{\dfrac{sin \theta\ +\ cos \theta}{sin \theta\ -\ cos \theta}}}}}}

  • By substituting the values, we get,

\rule{200}{3}

\sf \dashrightarrow {\dfrac{sin \theta\ +\ cos \theta}{sin \theta\ -\ cos \theta}\ =\ {\footnotesize{\dfrac{\Big( \dfrac{12}{13}\ +\ \dfrac{5}{13} \Big)}{\Big( \dfrac{12}{13}\ -\ \dfrac{5}{13} \Big)}}}} \\ \\ \\ \sf \dashrightarrow {\dfrac{sin \theta\ +\ cos \theta}{sin \theta\ -\ cos \theta}\ =\ {\footnotesize{\dfrac{\dfrac{17}{13}}{\dfrac{7}{13}}}}} \\ \\ \\ \sf \dashrightarrow {\dfrac{sin \theta\ +\ cos \theta}{sin \theta\ -\ cos \theta}\ =\ \dfrac{17}{13} \times \dfrac{13}{7}} \\ \\ \\ \sf \dashrightarrow {\dfrac{sin \theta\ +\ cos \theta}{sin \theta\ -\ cos \theta}\ =\ \dfrac{17}{\cancel{13}} \times \dfrac{\cancel{13}}{7}} \\ \\ \\ \dashrightarrow {\underbrace{\boxed{\pink{\frak{\dfrac{sin \theta\ +\ cos \theta}{sin \theta\ -\ cos \theta}\ =\ \dfrac{17}{7}}}}}_{\sf \blue{\tiny{Required\ value}}}}

∴ Hence, the required answer is 17/7.

6 0
2 years ago
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