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kirill115 [55]
3 years ago
5

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

Mathematics
1 answer:
lara [203]3 years ago
8 0

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}

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Which of the following is an arithmetic sequence? <br> 0,2,4,6<br> 1,2,4,8<br> 1,4,8,13
STatiana [176]
It is probably 0,2,4,6 because other ones go "out of the sequence".

Hope this helps. :)
8 0
3 years ago
300 juniors at Central High School took the ACT last year. The scores were distributed normally with a mean of 24 and a standard
Usimov [2.4K]

Answer:

150 students

Step-by-step explanation:

According to statement we have the following information

number of juniors=n=300

mean score=24

standard deviation score=4

The number of students that score above 24 is determined by

Number of students score above 24=number of juniors* P(student score above 24)

P(student score above 24)=P(x>24)=P(x-mean/sd>24-24/4)=P(z>0)=0.5.

Students score above 24=np=300*0.5=150

Hence there are 150 students scored above 24.

4 0
3 years ago
Please please im beggin with my life help me
pychu [463]
Ok soo the answer for part A is 714 euros B idk
5 0
3 years ago
What is 8mn⁵-2m⁶+5m²n⁴-m³n³+n⁶-4m⁶+9m²n⁴-mn⁵-4m³n³ in standar form?
vovangra [49]

The expression in standard form is n⁶ + 7mn⁵ + 14m²n⁴ - 5m³n³ - 6m⁶

<h3>How to express in standard form?</h3>

The expression is given as:

8mn⁵-2m⁶+5m²n⁴-m³n³+n⁶-4m⁶+9m²n⁴-mn⁵-4m³n³

Collect the like terms

8mn⁵ -mn⁵ - 2m⁶ -4m⁶ + 5m²n⁴ +9m²n⁴+n⁶ - 4m³n³ - m³n³

Evaluate the like terms

7mn⁵ - 6m⁶ + 14m²n⁴+n⁶ - 5m³n³

Rewrite in standard form

n⁶ + 7mn⁵ + 14m²n⁴ - 5m³n³ - 6m⁶

Hence, the expression in standard form is n⁶ + 7mn⁵ + 14m²n⁴ - 5m³n³ - 6m⁶

Read more about expressions at:

brainly.com/question/723406

#SPJ1

7 0
1 year ago
There are three times as many people at the baseball park today than there were yesterday. Today’s attendance is 15,000. Define
Verizon [17]

The equation is:

3 x = 15,000 where x is the number of yesterday’s attendance

Step-by-step explanation:

There are three times as many people at the baseball park today than

there were yesterday

Assume that the number of the people at the baseball park

yesterday is x

∵ The number of the people at the baseball park yesterday = x

∵ The number of people at the baseball park today is three times

   as many as the number of the people yesterday

∴ The number of people at the baseball park today = 3 x ⇒ (1)

∵ Today’s attendance is 15,000

∴ The number of people at the baseball park today = 15,000 ⇒ (2)

- Equate (1) and (2)

∴ 3 x = 15,000

- To find the value of x solve the equation:

  3 x = 15,000

The equation is:

3 x = 15,000 where x is the number of yesterday’s attendance

Learn more:

You can learn more about equations in brainly.com/question/11229113

#LearnwithBrainly

4 0
3 years ago
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