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
Gnesinka [82]
3 years ago
7

During a manufacturing process, a metal part in a machine is exposed to varying temperature conditions. The manufacturer of the

machine recommends that the temperature of the machine part remain below 132 ° F. The temperature T in degrees Fahrenheit x minutes after the machine is put into operation is modeled by T = ­0.005x2 + 0.45x + 125. Will the temperature of the part ever reach or exceed 132 ° F? Use the discriminant of a quadratic equation to decide.
Mathematics
1 answer:
Bess [88]3 years ago
7 0
.005x^2+.45x+125=132

.005x^2+.45x-7=0

So the discriminant, the (b^2-4ac) from the quadratic equation is:

0.3425

Since the discriminant is positive, there are two real solutions, this implies that the temperature will reach 132 at two times. However....

x=(-.45±√.3425)/(.01)

x≈-103.52, 13.52

As you can see only the positive solution has any meaning as there is no negative running time for the machine.  And since the derivative and second derivative are positive for this function, the temperature keeps increasing after the machine reaches 132F.  So the temperature reaches and exceeds 132F for all times greater than or equal to 13.52 minutes.




You might be interested in
Solve x^2 + x - 12 = 0
bogdanovich [222]

Answer:

x₁ = -4

x₂ = 3

Step-by-step explanation:

x²+ x + 12 = 0

x = {-1±√((1²)-(4*1*-12))} / (2*1)

x = {-1±√(1+48)} / 2

x = {-1±√49} / 2

x = {-1±7} / 2

x₁ = {-1-7} / 2 = -8/2 = -4

x₂ = {-1+7} / 2 = 6/2 = 3

Check:

x₁

-4² + (-4) - 12 = 0

16 - 4 - 12 = 0

x₂

3² + 3 - 12 = 0

9 + 3 - 12 = 0

6 0
2 years ago
Which 2 numbers have a mean average of 10 and a range of 4
Aloiza [94]
Simply the answer is 12 and 8.

Mark brainliest please

Hope this helps you
5 0
3 years ago
Does (lnk)/(k^3), where as k starts at one and continues on to infinity, converge? ...?
max2010maxim [7]
Yes. The numerator does not increase as fast as the denominator increases, causing the function's value to decrease with every subsequent increase in the value of k. This causes the function to converge at a point.
7 0
3 years ago
Which expressions are equivalent to -2y-8+4y
katrin2010 [14]

Answer:

2y-8

-Step-by-step explanation:

2y +4y = 2y

so

2y - 8

8 0
3 years ago
The monthly profit for a company that makes decorative picture frames depends on the price per frame. The company determines
Anvisha [2.4K]

the price is= £21.50

hope it helps

4 0
3 years ago
Other questions:
  • Misha deposited $3,725 into a savings account 22 years ago. The account has an interest rate of 2.2% and the balance is currentl
    9·1 answer
  • Which statements about the Extreme Value theorem are true?
    11·1 answer
  • PLSSSSSHELPMEWITHTHISONEQUESTIONPLEASE
    15·1 answer
  • Round 38,496 to nearest thousand
    10·1 answer
  • You decide to take advantage of the current online dating craze and start your own Web site. You know that you have 600 people w
    10·1 answer
  • The weight of eggs from a local farm are Normally
    14·1 answer
  • Random samples of people in Canada and people in Sweden are used to estimate the difference between the two countries in the pro
    7·1 answer
  • Macy has 8 quarters for every 9 pennies in her change purse. How many pennies would she have if she has 40 quarters?
    11·2 answers
  • Worksheet<br><br> 1. −3|2x + 6| = −12<br><br> 2. |x − 2| + 10 = 12
    13·1 answer
  • Monthly payment of 1,000 where interest is 6% compounded monthly​
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!