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3 years ago

Solve the simultaneous equations j-k= 2 and j2 + 2k=8. Give the answer in three decimal places.

Mathematics

2 answers:

vagabundo [1.1K]3 years ago

7 0

Answer:

j=2.606, j=-4.606 and k=0.606, k=-6.606

Step-by-step explanation:

First step is to merge the formulas so that you are left with one combined equation with only one variable. Let's go for j, so we won't have to fiddle with the quadratic term:

First we convert j-k=2 to k=j-2, then we plug in this value for k in the other equation:

j² + 2(j-2) = 8

j² +2j -4 = 8

j² + 2j -12 = 0

This we can solve using the quadratic formula:

j = (-2 ± √(2²-4·1·-12) ) / 2

= (-2 ± √52)/2

= -1 ± √13

So j ≈ 2.6056 or j≈-4.6056

k can be found by subtracting 2.

Vika [28.1K]3 years ago

4 0

Answer:

Step-by-step explanation:

hello :

here is an solution :

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2 years ago

. Given that O is the centre of the following circle, find the values of the unknowns.

alex41 [277]

Given:

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To find:

Value of 'a' and 'b'

Steps:

To find value of 'a', we will use Pythagoras theorem as the triangle is a right angle triangle,

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Now to find the value of 'b', i will use law of cosine,

$c=\sqrt{a^{2}+b^{2}-2ab(cos\beta ) }$

$12 = \sqrt{13^{2}+5^{2}-2(5)(13)(cos\beta )}\\12=\sqrt{169 + 25-130(cos\beta )}\\12=\sqrt{194-130(cos\beta )}\\144 = 194 - 130(cos\beta )\\50 = 130(cos\beta )\\cos\beta = 0.3846\\\beta = cos^{-1}(0.3846)\\\beta = 67.38$

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Happy to help :)

If u need any help feel free to ask

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