All categories

2 years ago

Intervals, extrema and behaviot

Mathematics

1 answer:

Pani-rosa [81]2 years ago

4 0

9514 1404 393

Answer:

(a) 1

Step-by-step explanation:

For large variable magnitude, the value of a rational function approaches the ratio of the highest-degree terms of the numerator and denominator*. Here, that is ...

x/x = 1

f(x) approaches 1 as x approaches infinity.

* The function approaches the line or curve defined by the quotient. (The remainder is ignored in this case.) Here, f(x) = 1 + 3/(x-3), so the quotient is the constant 1.

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A decorative window is made up of a rectangle with semicircles at either end. The ratio of AD to AB is 3:2 and AB is 30 inches.

scZoUnD [109]

Answer: The required ratio will be

$84:1034$

Step-by-step explanation:

Since we have given that

Ratio of AD to AB is 3:2

Length of AB = 30 inches

So, it becomes

$2x=30\\\\x=\frac{30}{2}=15\ inches$

So, Length of AD becomes

$3x=3\times 15=45\ inches$

Now, at either end , there is a semicircle.

Radius of semicircle along AB is given by

$\frac{30}{2}=15\ inches$

So, Area of semicircle along AB and CD is given by

$2\times \frac{\pi r^2}{2}\\\\=\frac{22}{7}\times 15\times 15\\\\=\frac{4950}{7}\ in^2$

Radius of semicircle along AD is given by

$\frac{45}{2}=22.5\ inches$

Area of semicircle along AD and BC is given by

$2\times \frac{1}{2}\pi r^2\\\\=\frac{22}{7}\times \frac{45}{2}\times \frac{45}{2}\\\\=\frac{445500}{28}\ in^2$

And the combined area of the semicircles is given by

$\frac{4950}{7}+\frac{445500}{28}\\\\=\frac{465300}{28}\ in^2$

Area of rectangle is given by

$Length\times width\\\\=AD\times AB\\\\=45\times 30\\\\=1350\ in^2$

Hence, Ratio of the area of the rectangle to the combined area of the semicircles is given by

$1350:\frac{465300}{28}\\\\=1350\times 28:465300\\\\=37800:465300\\\\=84:1034$

Hence, the required ratio will be

$84:1034$

8 0

2 years ago

Systems of linear equations iready quiz

saw5 [17]

Answer:

<h2>One solution.</h2>

Step-by-step explanation:

The given question is

<em>Does the following system have One Solution, No Solution, or Infinite Solutions. </em>

<em />

To solve this system, we just need to multiply the first equation by -1, and then sum those equations.

$-y = -4x - 8\\y = -5x + 3$

$0=-9x-5\\5=-9x\\x=-\frac{5}{9}$

Then, we use this value to find the other one

$y=4x+8\\y=4(-\frac{5}{9} )+8\\y=-\frac{20}{9}+8\\y =\frac{-20+72}{9} \\y=\frac{52}{9}$

As you can observe, the system of equations have a unique solution.

Therefore, the answer is one solution.

7 0

3 years ago

Which graph shows the solution to the inequality -3X-/ <20?

konstantin123 [22]

Answer:

wrong❌❌

question

wrong❌❌

question

6 0

2 years ago

Help with all of these please explain if u can !

sveticcg [70]

Answer:

1. 78cm^2

2. 200 ft^2

Step-by-step explanation:

1. i always cut these complex shapes into simpler ones (in this case a rectangle and a triangle)

the rectangles area is 6*8 or 48 and the triangles area is (10*6)/2 or 30 you then add the two areas to get the area for the whole shape 48+30=78

2. once again you're going to break this shape up into the individual rooms and then add them together the garage is a 4*6 room (24) the bedroom is a 8*4 room (32) the living room is a 10*10 room (100) the kitchens a 6*6 room (36) and the bathroom is a 4*2 room (8) you then add all these together

24+32+100+36+8=200

4 0

2 years ago

Read 2 more answers

Please help me with this

elena-s [515]

Answer:

9 p.m.

Step-by-step explanation:

Lowest common multiple (LCM) of 6 and 4.

LCM of 6, 4 = 2 × 2 × 3 = 12

After 12 hours 9 A.M. = 9 P.M.

After 12 hours at 9 P.M. she will take both medicines together again.

4 0

2 years ago