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
Solve using synthetic division.<br><br> (−2x^3 + 5x^2 − x + 2) ÷ (x + 2)
Kitty [74]
-2x^2 + 8x - 16 + 32/x+2
5 0
3 years ago
Write and solve the proportion.
Nonamiya [84]

Answer: I believe it would be 15.42

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Please answer ASAP! An explanation is a MUST REQUIREMENT in order to receive points and the Brainliest answer. Thank you.
alexdok [17]
Group and factor/undistribute

(x^2y^3-2y^3)+(-2x^2+4)
(y^3)(x^2-2)+(-2)(x^2-2)
see the (x^2-2) is common term so undistribute
(x^2-2)(y^2-2)

last one
4 0
3 years ago
Please help with this question. Will give 5 stars and a thanks. Thanks!
EleoNora [17]
Answer: the height of the flagpole is 21 ft.
3 0
3 years ago
A cone with diameter 20 yd and a height of 20<br> yd.
stich3 [128]

What would you like to know? The total surface area? The lateral surface area? The volume, perhaps? The radius?

5 0
3 years ago
Other questions:
  • In the diagram, the measure of angle 3 is 89°, and the measure of angle 6 is 88°.
    11·2 answers
  • Find the difference 32.654 -0.1
    11·2 answers
  • Solve the equation -(-2-n)
    10·1 answer
  • Jonathan deposited $10,000 into a new savings account with a simple interest rate of 3.8%. If account has earned $2,470 in inter
    12·1 answer
  • Help!!! and in terms of pi!! please
    14·1 answer
  • sharon is planning a cookout for 42 people. each guest will get 1 veggie burger. sharona will put one slice of cheese on half of
    13·1 answer
  • 758% as a decimal to the thousands place is........
    12·2 answers
  • A law firm is going to designate associates and partners to a big new case. The daily rate charged to the client for each associ
    6·1 answer
  • HELPPP WILL MARK BRAINLYIST IF RIGHT
    13·1 answer
  • (2+3) Second power-16 divided by2
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!