1. Refer to the equation 2x

ANYONE...........help

KATRIN_1 [288]

Answer:

1 cm

Step-by-step explanation:

Sides of the picture added margin:

l = 8 + 2x
w = 5 + 2x

A(margin) = 30 cm²

Solution:

A(margin) = Total area - A(picture)
(8 + 2x)(5 + 2x) - 5*8 = 30
4x² + 10x + 16x + 40 - 40 - 30 = 0
4x² + 26x - 30 = 0
2x² + 13x - 15 = 0
x = (-13 + √(13² + 2*4*15))/4
x = (-13 + 17)/4
x = 1 cm

Note. The other root is ignored as negative.

3 0

3 years ago

D^2(y)/(dx^2)-16*k*y=9.6e^(4x) + 30e^x

MA_775_DIABLO [31]

The solution depends on the value of $k$ . To make things simple, assume $k>0$ . The homogeneous part of the equation is

$\dfrac{\mathrm d^2y}{\mathrm dx^2}-16ky=0$

and has characteristic equation

$r^2-16k=0\implies r=\pm4\sqrt k$

which admits the characteristic solution $y_c=C_1e^{-4\sqrt kx}+C_2e^{4\sqrt kx}$ .

For the solution to the nonhomogeneous equation, a reasonable guess for the particular solution might be $y_p=ae^{4x}+be^x$ . Then

$\dfrac{\mathrm d^2y_p}{\mathrm dx^2}=16ae^{4x}+be^x$

So you have

$16ae^{4x}+be^x-16k(ae^{4x}+be^x)=9.6e^{4x}+30e^x$
$(16a-16ka)e^{4x}+(b-16kb)e^x=9.6e^{4x}+30e^x$

This means

$16a(1-k)=9.6\implies a=\dfrac3{5(1-k)}$
$b(1-16k)=30\implies b=\dfrac{30}{1-16k}$

and so the general solution would be

$y=C_1e^{-4\sqrt kx}+C_2e^{4\sqrt kx}+\dfrac3{5(1-k)}e^{4x}+\dfrac{30}{1-16k}e^x$

8 0

3 years ago

P L E A S E H E L P ! ! !

Step2247 [10]

Answer:

1) 6x = 21

2) x + y - 3

3) x/z = y

4) 2-x = p

Step-by-step explanation:

1. The product of a number x and 6 is 21

A product is a multiplication. A product of a and b is a * b.

We then have a product of x and 6, that x * 6, which we write usually in the format 6x.

is 21: that means it's equal to 21....

so 6x = 21.

2. The sum of the quantity x- 3 and y

The sum is an addition. The sum of a and b is a + b.

In this case, the first part is x - 3, the second part is y

So, x - 3 + y, which we usually rewrite as x + y - 3

3. The quotient of x and z is y

A quotient is a division.

So, quotient of x and z is x/z.

x/z = y

4. The difference of 2 and x is p.

A difference is a subtraction.

Difference of 2 and x is 2 - x

2 - x = p

7 0

3 years ago

2. A solar lease customer built up an excess of 6,500 kilowatt hours (kwh) during the summer using his solar

tia_tia [17]

9514 1404 393

Answer:

a) E = 6500 -50d

b) 5000 kWh

c) the excess will last only 130 days, not enough for 5 months

Step-by-step explanation:

Given:

starting excess (E): 6500 kWh

usage: 50 kWh/day (d)

Find:

a) E(d)

b) E(30)

c) E(150)

Solution:

a) The exces is linearly decreasing with the number of days, so we have ...

E(d) = 6500 -50d

__

b) After 30 days, the excess remaining is ...

E(30) = 6500 -50(30) = 5000 . . . . kWh after 30 days

__

c) After 150 days, the excess remaining would be ...

E(150) = 6500 -50(150) = 6500 -7500 = -1000 . . . . 150 days is beyond the capacity of the system

The supply is not enough to last for 5 months.

3 0

2 years ago

I also really need help with this question! g(x)=2x - 3 h(x)=2x + 4 Find (g/h)(x)

Ray Of Light [21]

(2x-3)/(2(x+2))
x cannot equal -2

3 0

3 years ago

1. Refer to the equation 2x - 4y = 12