Find the interval on which the curve of y equals the integral from 0 to x of 2 divided by the quantity 1 plus 3 times t plus t squared, dt is concave up.

Answers

Answer 1
Answer: Hello,

\frac{d^2( \int\limits^x_0 { (2)/(t^2+3t+1) } \, dt )}{dx^2} = (d((2)/(x^2+3x+1)) )/(dx) \n = (-2(2x+3))/((x^2+3x+1)^2)

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if it takes juwan exactly 35 minutes by car to get to his grandmother's. the nearest parking area is a 4-minute walk from her apartment.one week, he realized that he spent 5 hours and 12 minutes traveling to her apartment, and then back Home. how many round trips did he make to visit his grandmother's?

Answers

He made 4 round trips to visit his grandmother.

Further Explanation

Step 1

Amount of time he spent to get to his grandmother’s = 35 minutes and extra 4-minute walk (and can be expressed as 35 + 4)

= 35 + 4  

= 39

Step 2

To complete a round trip, the amount of time he spent to his grandmother’s will be multiply by 2

Therefore,

= 39 x 2

= 78

Total amount of time of a round trip = 78

Step 3

Amount of time he spent on a trip to her apartment and back home = 5 hours and 12 minutes

To determine that, 5 hours will be added to 12 minutes

Therefore,

Since 1 hour = 60,

Then, (5 x 60) +12

= (5 x 60) + 12

= 300 + 12

= 312

Amount of time he spent on a trip to her apartment and back home = 312

Step 4

To determine how many round trip he made, the amount of time he spent on a trip to her apartment and back home (312) will be divided by the total amount of time of a round trip (78) i.e. 312 ÷ 78

= 312 ÷ 78

= (312)/(78)

= 4

Therefore Juwan made a total of 4 round trips to his grandmother’s place.

LEARN MORE:

KEYWORDS:

  • juwan
  • apartment
  • 4-minute walk
  • grandmother
  • parking area
  • round trips
1 Round Trip = 2(35 min + 4 min) = 78 min

Total time spent travelling:
(5 hrs * 60 min/hr) + 12 min = 312 min

Number of Round Trips:
(312 min)/(78 min) = 4 round trips

Simplify each complex fraction. Show all work please

Answers

invert an multiply

(a/b)/(c/d)=(a/b)(d/c)=(ad)/(bc)


1..
(4x/45)/(12x/25)=(4x/45)(25/12x)=(100x)/(540x)=5/27

2.
(x/9)/(3x/2)=(x/9)(2/3x)=(2x)/(27x)=2/27

3.
(7x/9)/(49/3x)=(7x/9)(3x/49)=(21x^2)/(441)=(x^2)/21

4.
(2x^2y/3yz)/(6/xz)=(2x^2y/3yz)(xz/6)=(x^3)/(9)

5. (4y-3x)/(3xy+y^2)

6. (-9x+6)/(8x+6)

7. (yx^2+y^2)/(x^2+xy^2)

8. x^-1=1/x
(x^2)/(4x+1)




Choosing a 4-letter password using only 5 letters that may each be used more than once.

Answers

Wait a password with 4 letters using only 5? And the letters can be used more than once. I’m confused
How’s that even a question?

What's the slope of A(-10,6),B(-5,8)

Answers

Answer:

(2)/( - 5)

Step-by-step explanation:

((y1 - y2)/(x1 - x2)  \n  =  (6 - 8)/( - 10 - ( - 5))  \n  =  (2)/( - 10 + 5)  \n  =  (2)/( - 5)

If IJ = 15 and JK = 8, what is IK?

Answers

l -> j = 15
j -> k = 8

i - > k = ?

lj + ik = 15 +8
= 23

What are the trigonometric ratios

Answers

The trig ratios are a set of numbers that are properties
of every angle.

When the angle is in a right triangle, they can be defined
like this:

Sine (sin) of the angle:        (opposite leg) divided by (hypotenuse)
Cosine (cos) of the angle:  (adjacent leg) divided by (hypotenuse)

Tangent (tan) of the angle:      (opposite leg) divided by (adjacent leg)
Cotangent (cot) of the angle:  (adjacent leg) divided by (opposite leg)

Secant (sec) of the angle:  (hypotenuse) divided by (adjacent leg)
Cosecant of the angle:       (hypotenuse) divided by (opposite leg).


The size of the right triangle doesn't matter, only the ratios of
pairs of sides.  That will always be the same number for the
same angle, no matter how big or small the triangle is.

There's no easy way to calculate the numbers for an angle. 
You just have to look them up, using tables in books, or online
(try 'cosine 29' on Google), or on most hand-calculators. 
The trigonometric ratios are special measurements of a right triangle (a triangle with one angle measuring 90 ° ). Remember that the two sides of a right triangle which form the right angle are called the legs, and the third side (opposite the right angle) is called the hypotenuse.