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user100 [1]
3 years ago
7

How many solutions will the following system of linear equations have? –2x + 4y = –7 y= -1/2x + 5 A. 0 B. 1 C. 2 D. infinite

Mathematics
2 answers:
FinnZ [79.3K]3 years ago
7 0

Answer:

B. 1

Step-by-step explanation:

they only cross at one point... look below

dsp733 years ago
6 0

ANSWER

B. 1

EXPLANATION

The given system of equations is;

–2x + 4y = –7

y= -1/2x + 5

We rewrite the first equation is slope intercept form:

4y = 2x–7

y =  \frac{1}{2}x  -  \frac{7}{4}

The two equations have different slopes.

This means that they will intersect at one point in the XY plane.

Hence the system has a unique solution.

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The curves r1(t) = 4t, t2, t3 and r2(t) = sin(t), sin(5t), 2t intersect at the origin. find their angle of intersection, θ, corr
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First get the tangent vectors by differentiating r1 and r2 
r_1 '(t) = (4,2t,3t^2) \\  \\  r_2'(t) = (cos (t), 5 cos(5t), 2)
Evaluate at t=0
r_1' = (4,0,0) \\  \\ r_2' = (1,5,2)

Use identity for angle between 2 vectors:
u*v = |u| |v| cos \theta

Evaluate dot product and unit vectors:
u*v = (4,0,0)*(1,5,2) = 4 \\  \\ |u| = \sqrt{4^2 +0^2+0^2} = 4 \\  \\ |v| = \sqrt{1^2 + 5^2+2^2} = \sqrt{30}

Sub into identity and solve for theta:
4 = 4 \sqrt{30} cos \theta \\  \\ cos\theta = \frac{1}{\sqrt{30}} \\  \\ \theta = 79.48

Answer:
Angle of intersection is about 79 degrees.




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