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3 years ago

Barbie is analyzing a circle, y2 + x2 = 16, and a linear function g(x). Will they intersect?

Mathematics

1 answer:

evablogger [386]3 years ago

4 0

Answer:

Yes, at positive x-coordinates.

Step-by-step explanation:

Finding the equation for g(x):

Slope = (3-6)/ (1-0) = -3

y-intercept = y value when x = 0 = 6.

So g(x) = -3x + 6

Solve them simultaneously:

x^2 + y^2 = 16

g(x) : y = -3x + 6

Substitute for y in the first equation:

x^2 + (-3x + 6)^2 = 16

x^2 + ( 9x^2 - 36x + 36) = 16

10x^2 - 36x + 20 = 0

5x^2 - 18x + 10 = 0

x = [-(-18) +/- sqrt ( (-18)^2 - 4 * -18 * 10)] / (5*2)

= ( 18 +/- sqrt 124 )/ 10

= (1.8) +/- 1,114

These 2 roots are both positive.

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The tee for the sixth hole on a golf course is 305 yards from the tee. On that hole, Marsha hooked her ball to the left, as sket

EleoNora [17]

Answer:

Correct answer is option D. 96.4 yd.

Step-by-step explanation:

Please refer to the attached figure for labeling of the given diagram.

ABC is a triangle with the following labeling:

A is the hole, B is the Tee and C is the point where the ball is.

Sides are labeled as:

$a =255\ yd\\c = 305\ yd\\\angle B =17^\circ$

To find:

Side $b = ?$

Solution:

Here, we have one angle and two sides . Third side of the triangle is to be found opposite to the given angle.

We can use cosine formula here to find the value of the unknown side.

$cos B = \dfrac{a^{2}+c^{2}-b^{2}}{2ac}$

Putting all the values:

$cos 17 = \dfrac{255^{2}+305^{2}-b^{2}}{2\times 255\times 305}\\\Rightarrow 0.956 = \dfrac{65025+93025-b^{2}}{155550}\\\Rightarrow 148753.2= 158050-b^{2}\\\Rightarrow b^{2}= 158050-148753.2\\\Rightarrow b^{2}= 9296.795\\\Rightarrow b= 96.42\ yd$

So, the distance between the Ball and hole is 96.42 yd

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