1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
____ [38]
2 years ago
11

Recall the equation for a circle with center (h, k) and radius r. At what point in the first quadrant does the line with equatio

n y = 0.5x + 5 intersect the circle with radius 3 and center (0,5)?
X =
y =​
Mathematics
1 answer:
lina2011 [118]2 years ago
6 0

Answer:

The point of intersection is:

\displaystyle \left(\frac{6\sqrt{5}}{5}, \frac{3\sqrt{5}}{5}+5\right)\approx \left(2.68, 6.34)

Step-by-step explanation:

We want to find the point in QI at which the line with the equation:

y=0.5x+5

Intersect a circle with a radius of 3 and a center of (0, 5).

First, write the equation of a circle. The equation for a circle is given by:

(x-h)^2+(y-k)^2=r^2

Where (<em>h, k</em>) is the center and <em>r</em> is the radius.

Since our center is (0, 5), <em>h</em> = 0 and <em>k</em> = 5. The radius is 3. So, <em>r</em> = 3. Substitute:

(x-0)^2+(y-5)^2=(3)^2

Simplify:

x^2+(y-5)^2=9

At the point where the two equations intersect, its <em>x-</em>coordinate and <em>y-</em>coordinate will be the same. Therefore, we can substitute the equation of the line into the equation of the circle and solve for <em>x</em>. So:

x^2+((0.5x+5)-5)^2=9

Simplify:

x^2+(0.5x)^2=9

Square:

x^2+0.25x^2=9

Combine like terms:

\displaystyle 1.25x^2=\frac{5}{4}x^2=9

Solve for <em>x: </em>

<em />\displaystyle \begin{aligned} x^2&=\frac{36}{5} \\ x&=\pm\sqrt{\frac{36}{5}} \\ x&\Rightarrow \frac{6}{\sqrt{5}}=\frac{6\sqrt{5}}{5}\approx2.68\end{aligned}<em />

Note that since we are looking for the point of intersection in QI, <em>x</em> should be positive. So, we can ignore the negative answer.

To find the <em>y-</em>coordinate, substitute the <em>x-</em>value back into either equation. Using the linear equation:

\displaystyle y=0.5\left(\frac{6\sqrt{5}}{5}\right)+5=\frac{3\sqrt{5}}{5}+5\approx 6.34

So, the point of intersection in QI is:

\displaystyle \left(\frac{6\sqrt{5}}{5}, \frac{3\sqrt{5}}{5}+5\right)\approx \left(2.68, 6.34)

You might be interested in
Which is the rationalized form of the expression. A, B , C, or D?
grin007 [14]

Answer:

C

Step-by-step explanation:

Multiply the top and bottom, both by sqrtx-sqrt5. This is in order to rationalize the denominators.

You get answer C.

3 0
2 years ago
What is 500000 and 60000000 as a decimal
Juliette [100K]

The only way to make a decimal out of either of those numbers is to write a decimal point with some zeros after it.

500,000  =  500,000.000

60,000,000  =  60,000,000.00000

etc.

3 0
3 years ago
Please help you will feel good and u will get good deeds
KIM [24]

Answer:

5 or 6

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
Ratio Question:
netineya [11]

Answer:

i dont under stand but i will just ask for help to my father

Step-by-step explanation:

i dont wnow the answer!???

3 0
2 years ago
Read 2 more answers
200 children attended the school play. Of the total attendance, 40% were boys. How many
vesna_86 [32]

Answer:

120

Step-by-step explanation:Do you hundred times 40% equals 80. 200-80 = 120 which is the number of girls that attended.

5 0
3 years ago
Other questions:
  • Figure ABC is to be translated to Figure A'B'C' using the rule (x, y) → (x−3, y+4).
    8·2 answers
  • Calculate the next three terms of the following sequence.
    15·1 answer
  • Are the lines parallel, perpendicular, or neither? One line through the points (3, 2) and (6, 8), and another line through the p
    15·2 answers
  • In a simple linear regression study between two variables x ( the independent variable) and y (the dependent variable), a random
    11·1 answer
  • Consider the integral 8 (x2+1) dx 0 (a) Estimate the area under the curve using a left-hand sum with n = 4. Is this sum an overe
    8·1 answer
  • Will drawing an angle bisector always result in two acute angles?
    6·1 answer
  • Sam will place three of his eight model trucks on a shelf. In how many different orders can you please three model trucks on the
    14·1 answer
  • Due in 4 minutes Need help ASAP
    6·1 answer
  • Solve the formula for b2.<br><br> Area of a trapezoid: A=12h(b1+b2)
    13·2 answers
  • Find the exact value of sin 29π/6
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!