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AlladinOne [14]

3 years ago

15

There are two numbers. One number is twice the other number. The difference of the smaller number and half the larger number is

20

1 answer:

bixtya [17]3 years ago

3 0

Answer: No solution

Step-by-step explanation:

Let one number be x

Other no. will be 2x

x - 1/2(2x) = 20

x - x = 20

No solution

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The ratio of boys to girls is 5 to 9. If there are 120 more girls than boys, how many boys are there? Can you please show work o

poizon [28]

5*30 = 150
9*30 = 270
Since the ratio is 5:9 you have to multiply both numbers in the ratio by the same constant.
I just started multiplying by 10, then 20, then 30 until I got numbers that had a difference of 120.
There are 150 boys.
Setting up an equation
5x + 120 = 9x
Solve for x and then multiply the ratio by the x to get the same result.

4 0

3 years ago

Please help me please

ycow [4]

Answer:

Its a i just took the test

Step-by-step explanation:

6 0

4 years ago

-6/5-2/5v+4/15+1/3v please help

PtichkaEL [24]

Answer:

-14/15-1/15v

Step-by-step explanation:

First you make all of the fractions have the common denominator 15.

And then you have -18/15-6/15v+4/15+5/15v

Then you combine like terms to get -14/15-1/15v

5 0

3 years ago

A triangular prism has a base of 9 and height of 7. The length of each side of the triangular prism is 9 and the width of the en

Sergio [31]

Answer:

Therefore,

The surface area is

$\textrm{Total Surface Area of Prism}=252\ units^{2}$

Step-by-step explanation:

Shape is triangular prism,

Base = b = 9

Height = h = 7

The length of each side of the triangular prism ,

s₁ = s₂ = s₃ = 9

Width of the entire prism

Width = W = 7

To Find:

The surface area = ?

Solution:

Total Surface Area of Prism is given by,

$\textrm{Total Surface Area of Prism}=bh + (s_{1}+s_{2}+s_{3})W$

Where,

b = Base

h = Height

s₁ , s₂ , and s₃ = length of each side of the triangular prism

W = width of the prism

Substituting the values we get

$\textrm{Total Surface Area of Prism}=9\times 7 + (9 + 9 + 9)\times 7=252\ units^{2}$

Therefore,

The surface area is

$\textrm{Total Surface Area of Prism}=252\ units^{2}$

7 0

4 years ago

Compute the second partial derivatives ∂2f ∂x2 , ∂2f ∂x ∂y , ∂2f ∂y ∂x , ∂2f ∂y2 for the following function. f(x, y) = 2xy (x2 +

blsea [12.9K]

Answer with step-by-step explanation:

We are given that a function

$f(x,y)=2xy(x^2+y^2)^2$

Differentiate partially w.r.t x

Then, we get

$\frac{\delta f}{\delta x}=2y(x^2+y^2)^2+8x^2y(x^2+y^2)=(x^2+y^2)(2x^2y+2y^3+8x^2y)=2(5x^2y+y^3)(x^2+y^2)$

Differentiate again w.r.t x

$\frac{\delta^2f}{\delta x^2}=2(10xy)(x^2+y^2)+4x(5x^2y+y^3)=20x^3y+20xy^3+20x^3y+4xy^3=40x^3y+24xy^3$

Differentiate function w.r.t y

$\frac{\delta f}{\delta y}=2x(x^2+y^2)^2+2xy\times 2(x^2+y^2)\times 2y$

$\frac{\delta f}{\delta y}=(x^2+y^2)(2x^3+2xy^2+8xy^2)=2(x^2+y^2)(x^3+5xy^2)$

Again differentiate w.r.t y

$\frac{\delta^2f}{\delta x^2}=2(2y)(x^3+5xy^2)+20xy(x^2+y^2)=4x^3y+20xy^3+20x^3y+20xy^3=24x^3y+40xy^3$

Differentiate partially w.r.t y

$\frac{\delta^2f}{\delta y\delta x}=2(2y(5x^2y+y^3)+(x^2+y^2)(5x^2+3y^2))=10x^4+36x^2y^2+10y^4$

$\frac{\delta^2f}{\delta y\delta x}=10x^4+36x^2y^2+10y^4$ $\frac{\delta^2f}{\delta x\delat y}=2(2x(x^3+5xy^2)+(3x^2+5y^2)(x^2+y^2))=10x^4+36x^2y^2+10y^4$

$\frac{\delta^2f}{\delta x\delat y}=10x^4+36x^2y^2+10y^4$

Hence, if f(x,y) is of class $C^2$ (is twice continuously differentiable), then the mixed partial derivatives are equal.

i.e $\frac{\delta^2f}{\delta y\delta x}=\frac{\delta^2f}{\delta x\delta y}$

8 0

4 years ago