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jok3333 [9.3K]
3 years ago
10

Which decimal is equivalent to 7.44343434

Mathematics
1 answer:
alexandr402 [8]3 years ago
3 0
You know what its probably 7.44
You might be interested in
10. The area of a square lot is 900 square meters. What is the perimeter of the tot, in maters?
laiz [17]

Answer: 9000

Step-by-step explanation:

8 0
3 years ago
What is the greatest decimal in hundredths that can be rounded to 14.5? What is the least​
olga55 [171]

Answer:

  • 14.45 and 14.54

Step-by-step explanation:

<u>Rule for rounding:</u>

  • Round up if number is between 5 and 9
  • Round down if number is between 0 and 4

<u>What numbers in hundredths can be rounded to 14.5?</u>

  • 14.45 to 14.49

and

  • 14.50 to 14.54

<u>From above we see that:</u>

  • The greatest decimal is 14.54
  • The least decimal is 14.45
7 0
3 years ago
Find, correct to four decimal places, the length of the curve of intersection of the cylinder 16x2 + y2 = 16 and the plane x + y
Yuri [45]

Let the curve C be the intersection of the cylinder  



16x^2+y^2=16



and the plane



x+y+z=1



The projection of C on to the x-y plane is the ellipse



16x^2+y^2=16



To see clearly that this is an ellipse, le us divide through by 16, to get



\frac{x^2}{1}+ \frac{y^2}{16}=1



or  



\frac{x^2}{1^2}+ \frac{y^2}{4^2}=1,



We can write the following parametric equations,



x=cos(t), y=4sin(t)



for  



0\le t \le 2\pi



Since C lies on the plane,



x+y+z=1



it must satisfy its equation.



Let us make z the subject first,  



z=1-x-y



This implies that,



z=1-sin(t)-4cos(t)



We can now write the vector equation of C, to obtain,



r(t)=(cos(t),4sin(t),1-cos(t)-4sin(t))



The length of the curve of the intersection of the cylinder and the plane is now given by,



\int\limits^{2\pi}_0 {|r'(t)|} \, dt



But  



r'(t)=(-sin(t),4cos(t),sin(t)-4cos(t))



|r'(t)|=\sqrt{(-sin(t))^2+(4cos(t))^2+(sin(t)-4cos(t))}



\int\limits^{2\pi}_0 {\sqrt{2sin^2(t)+32cos(t)-8sin(t)cos(t)} }\, dt=24.08778184



Therefore the length of the curve of the intersection  intersection of the cylinder and the plane is 24.0878 units correct to four decimal places.

6 0
3 years ago
A motel owner observes that when a room is priced at $60 per day, all 80 rooms of the motel are occupied. For every $3 rise in t
Zinaida [17]

Answer:

a) p(x) = 300 - 3

b) P(x) = -3 x² + 285 x

c) Price of per room per day  = $ 157.5

when Number of rooms occupied , x = 47.5

Step-by-step explanation:

Given - A motel owner observes that when a room is priced at $60 per day, all 80 rooms of the motel are occupied. For every $3 rise in the charge per room per day, one more room is vacant. Each occupied room costs an additional $15 per day to maintain.

To find - a) Find the demand function, expressing p, the price charged for each room per day, as a function of x, the number of rooms occupied.

             b) Find the profit function P(x).

             c) Find the price of per room per day the motel should charge in order to maximize its profit.

Proof -

a)

Let

(x, y) be the point

where x represents number of rooms occupied

and y represents price of room per day.

Now,

Given that,

a room is priced at $60 per day, all 80 rooms of the motel are occupied.

So, point becomes (80, 60)

And  given that For every $3 rise in the charge per room per day, one more room is vacant.

So, point becomes (79, 63)

Now, we have two points (80, 60), (79, 63)

Let us assume that,

p(x) be the price charged for each room per day

Now,

By using point - slope formula , we get

p -60 = \frac{(63 - 60}{(79 - 80)} (x - 80)

⇒p -60 = (-3)(x-80)

⇒p-60 = 240 -3 x

⇒p(x) = 240 + 60 -3 x

⇒p(x) = 300 - 3 x

b)

Given that,

Each occupied room costs an additional $15 per day to maintain.

Let C(x) be the cost function,

Then C(x) =15 x

now,

Revenue function,

R(x) =x*p

      = x*(300 -3 x )

      = 300 x - 3 x²

⇒R(x) = 300 x - 3 x²

Now,

We know

Profit function = Revenue function - Cost function

⇒P(x) = R(x)-C(x)

⇒P(x) = (300 x -3 x²) -15 x

⇒P(x) = -3 x² + 285 x

c)

P'(x) = -6 x +285

For Maximize profit , Put P'(x) = 0

⇒-6 x+ 285 =0

⇒6 x= 285

⇒x = \frac{285}{6}

⇒x= 47.5

∴ we get

Maximize profit is when price, p = 300 - 3x

                                                      = 300 -3(47.5)

                                                      = $157.5

⇒Price of per room per day  = $ 157.5

when Number of rooms occupied , x = 47.5

5 0
3 years ago
What is the value of f(x) = 2/3 x + 1/4 when x = 6?
11Alexandr11 [23.1K]

Answer:

4 1/4

Step-by-step explanation:

f(x) = 2/3(6) + 1/4

f(x) = 4 + 1/4

f(x) = 4 1/4(4.25)

4 0
3 years ago
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