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postnew [5]
3 years ago
6

3 glasses and 3 mugs costs £18.

Mathematics
1 answer:
Anestetic [448]3 years ago
3 0

Step-by-step explanation:

Suppose the cost of one glass is x

The cost of one mug is y

according to question

\Rightarrow 3x+3y=18\quad \ldots(i)\\\\\Rightarrow 6x+4y=32\quad \ldots(ii)

Solving (i)\ \&\ (ii) we get

\Rightarrow x=4\ \text{and}\ y=2

So, the cost of each glass is £4

and cost of each mug is £2

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In the Midpoint Rule for triple integrals we use a triple Riemann sum to approximate a triple integral over a box B, where f(x,
Tomtit [17]

To approximate the volume with 8 boxes, we have to split up the interval of integration for each variable into 2 subintervals, [0, 1] and [1, 2]. Each box will have midpoint m_{i,j,k} that is one of all the possible 3-tuples with coordinates either 1/2 or 3/2. That is, we're sampling f(x,y,z)=\cos(xyz) at the 8 points,

(1/2, 1/2, 1/2)

(1/2, 1/2, 3/2)

(1/2, 3/2, 1/2)

(3/2, 1/2, 1/2)

(1/2, 3/2, 3/2)

(3/2, 1/2, 3/2)

(3/2, 3/2, 1/2)

(3/2, 3/2, 3/2)

which are captured by the sequence

m_{i,j,k}=\left(\dfrac{2i-1}2,\dfrac{2j-1}2,\dfrac{2k-1}2\right)

with each of i,j,k being either 1 or 2.

Then the integral of f(x,y,z) over B is approximated by the Riemann sum,

\displaystyle\iiint_B\cos(xyz)\,\mathrm dV\approx\sum_{i=1}^2\sum_{j=1}^2\sum_{k=1}^2\cos m_{i,j,k}\left(\frac{2-0}2\right)^2

=\displaystyle\sum_{i=1}^2\sum_{j=1}^2\sum_{k=1}^2\cos\frac{(2i-1)(2j-1)(2k-1)}8

=\cos\dfrac18+3\cos\dfrac38+3\cos\dfrac98+\cos\dfrac{27}8\approx\boxed{4.104}

(compare to the actual value of about 4.159)

4 0
3 years ago
A ladder 15 feet long leans against a wall and forms an angle of 45º with the ground. How far from the wall is the ladder?
bezimeni [28]
The ladder is the hypotenuse of a 45 45 90 triangle.
The legs of a 45 45 90 triangle = hypotenuse / sqroot (2)

15 / 1.414 = 10.608

(Incidentally it is the "bottom" of the ladder that is 10.608 feet from the wall.  The "top" of the ladder is touching the wall.  LOL)

7 0
3 years ago
Read 2 more answers
F(n) = 4n - 5<br><br> g(n)=n- 1 - 2n<br><br> Find (fog)(6)
devlian [24]
If fog means f, then
answer: f(n)=15
7 0
3 years ago
HELP ME PLEASE ASAP,,,,,,,
JulsSmile [24]

Answer:

a) i) The drawing of Zeno's route is attached

ii) The bearing of Zeno's return journey is 241° from point C to point A

b) Yes, Zeno returns to Port A before 5.15pm

Step-by-step explanation:

a) i) Please find attached the drawing of Zeno's route

ii) From the attached diagram of Zeno's route created with Microsoft Whiteboard, we find the bearing of his return journey as 241° from point C to point A

b) The distance from point C to point A = 10·√5 km

The speed with which Zeno sails as he returns = 10 km/h

The time it takes Zeno to return t = Distance/Speed

∴ The time it takes Zeno to return t = 10·√5 km/(10 km/h) = √5 h ≈ 2.2361 hours ≈ 2 hours 14 minutes and 9.845 seconds

The time Zeno arrives at point A from point A ≈ 3.00 pm + 2 hours 14 minutes and 9.845 seconds = 5:14.1641 p.m. ≈ 5:14 pm.

Therefore, Zeno returns to Port A before 5.15pm.

5 0
3 years ago
What's 3(2x) + 4y(5) + (4 x 2 x z)?
xxTIMURxx [149]

Answer: I dont know the answer but I made this for you and i hope it will help

Step-by-step explanation: :D

Download pdf
5 0
3 years ago
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