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4 years ago

What are the solutions to the nonlinear equations below y=4x x^2 + y^2=17

Mathematics

1 answer:

wolverine [178]4 years ago

8 0

Answer:

x = 1 and x = -1

Step-by-step explanation:

Next time, please separate the equations with a comma or semicolon. Thanks.

We can substitute 4x for y in the quadratic equation x^2 + y^2=17:

x² + (4x)²=17.

Then x² + 16x² = 17, or

17x² = 17, or x² = 1. There are two solutions: x = 1 and x = -1.

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$\huge \mathbb{\green{\fbox{\pink{ANSWER}}}}$

$\\ \: \: \implies \: sin^{4} \: \theta + cos^{4} \: \theta \rightarrow \blue{ \frac{1}{2} }$

$\\ \\ \: \large \mathfrak \green{Solution} :$

$\\ \bf \: Given :$

$\\ \sf \: \: \bf sin \: \theta - cos \: \theta = 0$

$\\ \sf \rightarrow \: sin \: \theta = cos \: \theta$

$\\ \sf \rightarrow \: \frac{sin \: \theta} {cos \: \theta} = 1$

$\\ \sf \rightarrow \: tan \: \theta = 1$

$\\ \sf \rightarrow \: tan \: \theta = tan \: 45 \degree$

$\\ \sf \rightarrow \: \theta = 45 \degree$

$\\ \\ \therefore \: sin^{4} \: \theta + cos^{4} \: \theta$

$\\ \sf \rightarrow \: sin^{4} \: 45 \degree + cos^{4} \: 45 \degree$

$\\ \\\sf \rightarrow \: (\frac{1}{ \sqrt{2} } ) ^{4} +(\frac{1}{ \sqrt{2} } ) ^{4}$

$\\ \sf \rightarrow \: ( \frac{1}{ \cancel {\sqrt{2} }} )^{ \cancel{2}} ( \frac{1}{ \cancel{ \sqrt{2} }} )^{\cancel{2}} + ( \frac{1}{ \cancel {\sqrt{2} }} )^{ \cancel{2}} ( \frac{1}{ \cancel{ \sqrt{2} }} )^{\cancel{2}}$

$\\ \\\sf \rightarrow \: \frac{1}{2} × \frac{1}{2} + \frac{1}{2}× \frac{1}{2}$

$\\ \\ \sf \rightarrow \: \frac{1}{4} + \frac{1}{4}$

$\\ \\ \sf \rightarrow \: {\cancel \frac{2} {4}}$

$\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies \fbox{\pink {\frac{1}{2}}}$

3 0

3 years ago

Read 2 more answers

If a formula of a triangle is 18 = (h - 1) x 6 x .5 how would you get your answer?

V125BC [204]

Answer:

h = 7

Step-by-step explanation:

18 = (h - 1) × 6 × 0.5

simplify:

18 = 3(h - 1)

distribute the 3:

18 = 3h - 3

add 3 to both sides:

3h = 21

divide by 3:

h = 7

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4 years ago

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kirill115 [55]

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3 years ago

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Anna [14]

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