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nignag [31]
2 years ago
6

Question 3

Mathematics
1 answer:
vitfil [10]2 years ago
8 0

Answer:

Step-by-step explanation:

No there parallel

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A circle has centre (3,0) and radius 5. The line y = 2x + k intersects the circle in two points. Find the set
lara [203]

A circle with center (3,0) and radius 5 has equation

(x-3)^2+y^2=25 \iff x^2 + y^2- 6 x  = 16

If we substitute y=2x+k in this equation, we have

x^2+(2x+k)^2-6x=16 \iff 5x^2+(4k-6)x+k^2-16=0

This equation has two solutions (i.e. the line intersects the circle in two points) if and only if the determinant is greater than zero:

\Delta=b^2-4ac=(4k-6)^2-4\cdot 5\cdot (k^2-16)>0

The expression simplifies to

-4 (k^2 + 12 k - 89)>0 \iff k^2 + 12 k - 89

The solutions to the associated equation are

k^2 + 12 k - 89=0 \iff k=-6\pm 5\sqrt{5}

So, the parabola is negative between the two solutions:

-6-5\sqrt{5}

8 0
3 years ago
Solve the inequality graphically. 4x^2-13x+7<0
Feliz [49]

Answer:

Step-by-step explanation:

(\frac{13 - \sqrt{57} }{8} , \frac{13 + \sqrt{57} }{8} )

6 0
2 years ago
Which equation is equivalent to 4s= t+2
N76 [4]

Answer:

t=2-4s

Step-by-step explanation:

7 0
3 years ago
What is an equation of the line that passes through the points (-6, 2) and<br> (-4,-1)?
OLEGan [10]
<h2>Answer:  y - 2 = -³/₂ (x + 6)</h2>

Step-by-step explanation:

The slope of this line = (y₂ - y₁) ÷ (x₂ - x₁)

                                   =  (2 - (- 1 )) ÷  (-6 - (-4))

                                   =  3 ÷ (-2)

                                   =  - ³/₂

The equation of the line can be determined using the point-slope form:

y - y₁ = m(x - x₁)

⇒ y - 2 = -³/₂(x - (-6))

   y - 2 = -³/₂ (x + 6)

8 0
2 years ago
Write a one story problem about a ratio
Hatshy [7]

22 \div 4 = 5.5
a radio cost $22 Aaron Rodgers wants a radio Aaron saves $4 a week how many weeks would Aaron have to save? Now that 5.5 is 22 divided by 4 that means Aaron will have to save up 6 weeks
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3 years ago
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