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3 years ago

The line to the right goes through the point (6, y). If the angle the graph makes with the x-axis is 22°, what is

Mathematics

1 answer:

s344n2d4d5 [400]3 years ago

8 0

Answer:

The y-coordinate of the point is approximately 2.42.

Step-by-step explanation:

From the figure attached below the statement we derive the following equation to calculate the y-coordinate ( $y$ ), dimensionless, of the point in terms of the x-coordinate ( $x$ ), dimensionless, and angle of the line ( $\theta$ ), measured in sexagesimal degrees:

$y = x\cdot \tan \theta$ (1)

If we know that $x = 6$ and $\theta = 22^{\circ}$ , then the y-coordinate of the point is:

$y = 6\cdot \tan 22^{\circ}$

$y\approx 2.42$

The y-coordinate of the point is approximately 2.42.

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Option B $0.04803$

Step-by-step explanation:

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3 years ago

Type the correct answer in each box. Use numerals instead of words.

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Answer:

System A has 4 real solutions.

System B has 0 real solutions.

System C has 2 real solutions

Step-by-step explanation:

System A:

x^2 + y^2 = 17 eq(1)

y = -1/2x eq(2)

Putting value of y in eq(1)

x^2 +(-1/2x)^2 = 17

x^2 + 1/4x^2 = 17

5x^2/4 -17 =0

Using quadratic formula:

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

a = 5/4, b =0 and c = -17

$x=\frac{-(0)\pm\sqrt{(0)^2-4(5/4)(-17)}}{2(5/4)}\\x=\frac{0\pm\sqrt{85}}{5/2}\\x=\frac{\pm\sqrt{85}}{5/2}\\x=\frac{\pm2\sqrt{85}}{5}$

Finding value of y:

y = -1/2x

$y=-1/2(\frac{\pm2\sqrt{85}}{5})$

$y=\frac{\pm\sqrt{85}}{5}$

System A has 4 real solutions.

System B

y = x^2 -7x + 10 eq(1)

y = -6x + 5 eq(2)

Putting value of y of eq(2) in eq(1)

-6x + 5 = x^2 -7x + 10

=> x^2 -7x +6x +10 -5 = 0

x^2 -x +5 = 0

Using quadratic formula:

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

a= 1, b =-1 and c =5

$x=\frac{-(-1)\pm\sqrt{(-1)^2-4(1)(5)}}{2(1)}\\x=\frac{1\pm\sqrt{1-20}}{2}\\x=\frac{1\pm\sqrt{-19}}{2}\\x=\frac{1\pm\sqrt{19}i}{2}$

Finding value of y:

y = -6x + 5

y = -6(\frac{1\pm\sqrt{19}i}{2})+5

Since terms containing i are complex numbers, so System B has no real solutions.

System B has 0 real solutions.

System C

y = -2x^2 + 9 eq(1)

8x - y = -17 eq(2)

Putting value of y in eq(2)

8x - (-2x^2+9) = -17

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x =-2 and x = -2

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3 years ago

Read 2 more answers