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
Neporo4naja [7]
3 years ago
12

Barbara drives between Miami, Florida and West Palm Beach, Florida. she drives 45 miles in clear weather and then encounters a t

hunderstorm for the last 57 miles. she drives 22 mph slower in the thunderstorm than she does in clear whether. If the total time for the trip is 2.25 hours determiner her speed driving in nice weather and her Speed driving in the thunderstorm
Mathematics
1 answer:
WINSTONCH [101]3 years ago
4 0

Answer:

Barbara's speed in clear weather is 60mph and in the thunderstorm is 38mph.

Step-by-step explanation:

Let v_1 be the speed and  t_1 be the time Barbara drives in clear weather, and let v_2 be the speed and t_2 be the time she drives in the thunderstorm.

Barbara drives 22 mph lower in the thunderstorm than in the clear weather; therefore,

(1). v_2 = v_1 -22

Also,

(2). v_1t_1 = 45miles

(3). v_2 t_2 = 57,

and

(4). t_1+t_2 = 2.25hr

From equations (2) and (3) we get:

t_1 = \dfrac{45}{v_1}

t_2 =\dfrac{57}{v_2}

putting these in equation (4) we get:

\dfrac{45}{v_1}+\dfrac{57}{v_2}=2.25

and substituting for v_2 from equation (1) we get:

\dfrac{45}{v_1}+\dfrac{57}{v_1-22}=2.25

This equation can be rewritten as

2.25v_1^2-151.5v_1+990=0

which has solutions

v_1 = 60

v_1 = 7.33

We take the first solution v_1 =60 because it gives a positive value for v_2:

v_2 = v_1 -22

v_2 = 60 -22\\

v_2 = 38.

Thus, Barbara's speed in clear weather is 60mph and in the thunderstorm is 38mph.

You might be interested in
Given G, the centroid of triangle IJK as pictured above. Find the sum of the lengths of the
vekshin1

30.6

I do not have an in depth explanation, but this is for the people who are having trouble finding it, gl!

8 0
3 years ago
Find the absolute maximum and absolute minimum values of f on the given interval. f(t) = 9t + 9 cot(t/2), [π/4, 7π/4]
agasfer [191]

Answer:

the absolute maximum value is 89.96 and

the absolute minimum value is 23.173

Step-by-step explanation:

Here we have cotangent given by the following relation;

cot \theta =\frac{1 }{tan \theta} so that the expression becomes

f(t) = 9t +9/tan(t/2)

Therefore, to look for the point of local extremum, we differentiate, the expression as follows;

f'(t) = \frac{\mathrm{d} \left (9t +9/tan(t/2)  \right )}{\mathrm{d} t} = \frac{9\cdot sin^{2}(t)-\left (9\cdot cos^{2}(t)-18\cdot cos(t)+9  \right )}{2\cdot cos^{2}(t)-4\cdot cos(t)+2}

Equating to 0 and solving gives

\frac{9\cdot sin^{2}(t)-\left (9\cdot cos^{2}(t)-18\cdot cos(t)+9  \right )}{2\cdot cos^{2}(t)-4\cdot cos(t)+2} = 0

t=\frac{4\pi n_1 +\pi }{2} ; t = \frac{4\pi n_2 -\pi }{2}

Where n_i is an integer hence when n₁ = 0 and n₂ = 1 we have t = π/4 and t = 3π/2 respectively

Or we have by chain rule

f'(t) = 9 -(9/2)csc²(t/2)

Equating to zero gives

9 -(9/2)csc²(t/2) = 0

csc²(t/2)  = 2

csc(t/2) = ±√2

The solutions are, in quadrant 1, t/2 = π/4 such that t = π/2 or

in quadrant 2 we have t/2 = π - π/4 so that t = 3π/2

We then evaluate between the given closed interval to find the absolute maximum and absolute minimum as follows;

f(x) for x = π/4, π/2, 3π/2, 7π/2

f(π/4) = 9·π/4 +9/tan(π/8) = 28.7965

f(π/2) = 9·π/2 +9/tan(π/4) = 23.137

f(3π/2) = 9·3π/2 +9/tan(3·π/4) = 33.412

f(7π/2) = 9·7π/2 +9/tan(7π/4) = 89.96

Therefore the absolute maximum value = 89.96 and

the absolute minimum value = 23.173.

7 0
3 years ago
In year, 2004, I put $20.00 into an account to save. This account annual interest fee is 0.002%. However, every 10th year the in
olchik [2.2K]

9514 1404 393

Answer:

  $20.01

Step-by-step explanation:

In 2004–2012, the interest rate is 0.002%. In 2013, it is 0.004%. In 2014–2021, the interest rate is 0.002%. That is, in the 18 years between 2004 and 2021 (inclusive), the interest rate is 0.002% for 17 of them. The effective account multiplier is ...

  (1.00002^17)(1.00004^1) = 1.00038006801

Then the account balance is ...

  $20 × 1.00038006801 ≈ $20.01

_____

<em>Additional comment</em>

The annual interest earned on $20.00 is $0.0004. If the account balance is rounded to the nearest cent annually, at the end of the 18 years, the balance will still be $20.00. Not enough interest is earned in one year to increase the balance above $20. At the end of the 18 years, the amount of interest earned is 0.76¢ (a fraction of a penny) <em>only if there is no rounding in intervening years</em>.

7 0
2 years ago
What is 14 1/4 - 13 5/6 =
svlad2 [7]

Answer:5/12 (Decimal: 0.416667)

Step-by-step explanation:

3 0
3 years ago
Which of these numbers has the most factors? 6:<br> 17:<br> 25:<br> 36:
vovikov84 [41]

Answer:

36

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Other questions:
  • The largest exponet in a polynominal is called its <br> (19 letters)
    10·1 answer
  • 2550 gallons in 30 days
    9·1 answer
  • the cost of having photos taken includees fee and $12 for each photo.Mrs.fong buys 6 photos for a total cost of $87.what
    8·1 answer
  • The sum of two numbers is 17 and their difference is 29 what are the two numbers
    10·1 answer
  • What does it mean if your final exam grade is modeled by the function f(x) = 100 - 3.3x?
    10·2 answers
  • In the figure below, A shows the position of a house on the shore and B shows the position of a house on an island. To find the
    14·1 answer
  • SOMEONE HELPPPPPPPP
    8·2 answers
  • The vertices of a figure are given. Find the coordinates of the figure after the transformations given. A(−5,3),B(−2,3),C(−2,1),
    10·2 answers
  • Evan took a math quiz last week. He got 8 problems correct and 72 problems incorrect. What percentage did Evan get correct?
    13·2 answers
  • Expand the brackets and simplify: 2(5x-y)-3(3x-y)​
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!