MATHEMATICS COLLEGE

Find the general solution of the following equation. Express the solution explicitly as a function of the independent variable. x^2 dw/dx = √ w(2x+5)

Answers

Answer 1

Answer:

Answer:

Therefore the general solution is

$2 \sqrt w = 2 ln(x) - 5 \frac1x +c$

Step-by-step explanation:

Integration Rule:

$\int x^n dx= (x^(n+1))/(n+1)+c$
$\int \frac1x dx= ln(x) +c$

Given differential equation is

$x^2 (dw)/(dx)= √(w)(2x+5)$

$\Rightarrow x^2 dw= √(w) (2x+5) dx$ [ multiplying dx both sides]

$\Rightarrow (dw)/(\sqrt w)= ((2x+5))/(x^2) dx$ [ dividing $x^2\sqrt w$ both sides]

Integrating both sides

$\int (dw)/(\sqrt w)=\int ((2x+5))/(x^2) dx$

$\Rightarrow \int w^(-\frac12) dw=\int ((2x)/(x^2)+(5)/(x^2) )dx$

$\Rightarrow \int w^(-\frac12) dw=\int (2)/(x)dx +\int(5)/(x^2) dx$

$\Rightarrow (w^(-\frac12+1))/(-\frac12+1) =2ln x+5 (x^(-2+1))/(-2+1)+c$ [ c is arbitrary constant]

$\Rightarrow 2 \sqrt w = 2 ln(x) - 5 \frac1x +c$

Therefore the general solution is

$2 \sqrt w = 2 ln(x) - 5 \frac1x +c$

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Which of these sentences is always true for a parallelogram?

Answers

Answer:

Letter D

Remember to drink water

Answer:

parallelograms are shapes that have 2 sets of parallel sides. for example, squares, rectangles, and rhombuses are all types of parallelograms

How do you do this 6-2x=10

Answers

-2x=10-6

The answer: x= -2

Answer:

x= -2

Step-by-step explanation: (remember the 6 in this equation is positive so you'll subtract it and the 2 is actually -2x. First, you'll subtract 6 from itself and 10, the two 6's cancel out and 10-6=4. Then, you'll divide -2 and 4 by -2, the two -2's cancel out and 4 divided by -2 is -2. Finally, you'll see that x = -2. This is all done by the order of operations also known as PEMDAS. )

6 - 2x =10

-6 -6

-----------------

-2x = 4

------------

-2 = -2

x = -2

Does the Associative property always,sometimes, or never hold for subtraction? explain your reasoning using examples and counterexamples

Answers

sometimes

example when it's true
-3+(4-1)=(-3+4)-1

when it's false
-3-(4-1)≠(-3-4)-1

jewelry box with a square base is to be built with silver plated sides, nickel plated bottom and top, and a volume of 44 cm3. If nickel plating costs $1 per cm2 and silver plating costs $2 per cm2, find the dimensions of the box to minimize the cost of the materials. (Round your answers to two decimal places.) The box which minimizes the cost of materials has a square base of side length cm and a height of cm.

Answers

Answer:

The box which minimizes the cost of materials has a square base of side length 4.45cm and a height of 2.22 cm.

Step-by-step explanation:

Volume of the jewellery box=44cm³

The box has a square base and is to be built with silver plated sides and nickel plated top and base.

Therefore: Volume = Square Base Area X Height = l²h

l²h=44

h=44/l²

Total Surface Area of a Cuboid =2(lb+lh+bh)

Since we have a square base

Total Surface Area =2(l²+lh+lh)

The Total Surface Area of the box =2l²+4lh

Nickel plating costs $1 per cm³

Silver Plating costs $2 per cm³

Since the sides are to be silver plated and the top and bottom nickel plated:

Therefore, Cost of the Material for the jewellery box =1(2l²)+2(4lh)

Cost, C(l,h)=$(2l²+8lh)

Recall earlier that we derived:

h=44/l²

Substituting into the formula for the Total Cost

Cost, C(l)=2l²+8l(44/l²)

C=2l²+352/l

C=(2l³+352)/l

The minimum costs for the material occurs at the point where the derivative equals zero.

C'=(4l³-352)/l²

4l³-352=0

4l³=352

Divide both sides by 4

l³=88

l=4.45cm

Recall:

h=44/l²=44/4.45²=2.22cm

The box which minimizes the cost of materials has a square base of side length 4.45cm and a height of 2.22 cm.

BRAINLEST Find the sum of the first 6 terms of the infinite series: 1 - 2 + 4 - 8+...

Answers

Answer:

-21

Step-by-step explanation:

1-2+4-8+16-32

=-21

Answer:

The sum of the first 6 terms of the infinite series will be - 21.

Step-by-step explanation:

In this case, the infinite geometric series 1 - 2 + 4 - 8 + ... is represented by the following summation,

$\sum _{{k=0}}^{{n}}(-2)^(k)$

Therefore if we continue this pattern, the first 6 terms will be 1 - 2 + 4 - 8 + 16 - 32. Adding these terms,

1 - 2 + 4 - 8 + 16 - 32

= - 1 + 4 - 8 + 16 - 32

= 3 - 8 + 16 - 32 = - 5 + 16 - 32

= 11 - 32 = Solution : - 21

In ABC, a = 16, angle A= 30, angle B = 45, find b?

Answers

b=22.62
16/sin30=b/sin45
16sin45/sin30 =22.62

Other Questions

Cho S là ngoại diên của khái niệm con người, p(x,y) = x yêu thương y. 1) Viết các phán đoán sau đây dưới dạng công thức: a) Nhiều người yêu thương A. (Thay A bằng chính tên của em). b) A yêu thương nhiều người. (Thay A bằng chính tên của em). 2) Phủ định hai phán đoán ở phần 1) (viết dưới dạng câu văn hoàn chỉnh).

(4r2 – 3r + 2) – (-r2 – 3r) =

Complete the following proof

I dont know this please any help would be nice