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
Ilya [14]
2 years ago
12

Find the roots of h(t) = (139kt)^2 − 69t + 80

Mathematics
1 answer:
Sonbull [250]2 years ago
7 0

Answer:

The positive value of k will result in exactly one real root is approximately 0.028.

Step-by-step explanation:

Let h(t) = 19321\cdot k^{2}\cdot t^{2}-69\cdot t +80, roots are those values of t so that h(t) = 0. That is:

19321\cdot k^{2}\cdot t^{2}-69\cdot t + 80=0 (1)

Roots are determined analytically by the Quadratic Formula:

t = \frac{69\pm \sqrt{4761-6182720\cdot k^{2} }}{38642}

t = \frac{69}{38642} \pm \sqrt{\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321}  }

The smaller root is t = \frac{69}{38642} - \sqrt{\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321}  }, and the larger root is t = \frac{69}{38642} + \sqrt{\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321}  }.

h(t) = 19321\cdot k^{2}\cdot t^{2}-69\cdot t +80 has one real root when \frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321} = 0. Then, we solve the discriminant for k:

\frac{80\cdot k^{2}}{19321} = \frac{4761}{1493204164}

k \approx \pm 0.028

The positive value of k will result in exactly one real root is approximately 0.028.

You might be interested in
What is the value of X
Sindrei [870]
The answer is:  [C]:  " 3 " .
____________________________________
Explanation:
__________________________________
         4x - 1 = 2x + 5 ;  Solve for "x" ; 
__________________________________
 Subtract "2x" from each side of the equation; and add "1" to each side of the equation:
___________________________________________________
       4x - 1 - 2x + 1 = 2x + 5 - 2x + 1 ;
___________________________________________________
          2x = 6 ;
_________________________________
Divide EACH side of the equation by "2" ; to isolate "x" on ONE side of the equation;  and to solve for "x" ;
_________________________________
          2x / 2  =  6 / 2 ;
_________________________________
               x  =  3 .
_________________________________
The answer is:  [C]:  " 3 " .
_________________________________
4 0
3 years ago
Solve for X! Please help
WARRIOR [948]

The two given angles are vertical angles which mean they are the same:

9x + 72 = 4x + 112

Subtract 72 from bot sides:

9x = 4x + 40

Subtract 4x from both sides:

5x = 40

Divide both sides by 5:

X = 8

4 0
2 years ago
Please help me i really need help please i really need help please please really need help please or i'm not gonna pass please
Andre45 [30]
Is Oya a functional character or a real-life one? What is the story?
8 0
3 years ago
Pls help me answer this question and plsss do not send link
Sever21 [200]

Answer:

x=124.75

Step-by-step explanation:

Sum of angles of a triangle=180°

(x-40)+(x-20)+(1/2- 10)=180°

(x-40)+(x-20)+(−9.5)=180°

x-40+x-20−9.5=180°

x+x-40-20-9.5=180°

2x−69.5=180°

2x=180°+69.5

2x=249.5

2x/2=249.5/2

x=124.75

3 0
2 years ago
What is the slope of the line represented by the equation y = -2/5 -5x
vodka [1.7K]

Answer:

-5

Step-by-step explanation:

The slope is the coefficient of x in this case. That means that the answer is -5.

3 0
3 years ago
Other questions:
  • Help with homework q
    8·1 answer
  • Find the zeros of the function and 2x² + 72=0
    10·1 answer
  • Write equations for the horizontal and vertical lines passing through the point , −8−5.
    8·1 answer
  • IF TUPAC RAN 35 miles Away From BIGGIE SMALLS. IF BIGGIE ran 3 miles but didnt catch TUPAC how far away was TUPAC
    14·2 answers
  • Please answer quickly THIS IS FOR A TEST
    6·1 answer
  • Y + 5 = -x<br> Slope intercept
    10·1 answer
  • Find the circumference of a circle with a diameter of 30 inches. Use 3.14 for pi
    6·2 answers
  • The amount of time x in hours spent each week watching television by children under twelve is normally distributed with mean 24.
    13·1 answer
  • PLZ HELPP AND ANSWER FASTTTT. ANSWER BOTH PARTS PLZZ
    15·2 answers
  • (20 POINTS PLS HELP!!)
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!