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3 years ago

What is the greatest number of bottles Corrine can put sand in?

Mathematics

2 answers:

coldgirl [10]3 years ago

8 0

The answer is 4 because that’s the greatest number of sand that can be put in

EastWind [94]3 years ago

6 0

Answer: 4 bottles

Step-by-step explanation:

Since 2/9=1/3, and there are 4 1/3s of sand, we know the answer is 4.

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What is r in this equation? πr^2=42π

kupik [55]

R in this equation refers to the radius

${\pi r}^{2} = 42\pi \\ {r}^{2} = \frac{42\pi}{\pi} \\ r = \sqrt{42 } \\ r = 6.480740698$

4 0

3 years ago

Two slits are illuminated by a 348 nm light. The angle between the zeroth-order bright band at the center of the screen and the

Andre45 [30]

Answer:0.369 m

Step-by-step explanation:

Given

Distance between slit and screen is $D=154 cm$

Wavelength $\lambda =348 nm$

Angle between zeroth order bright fringe and Fourth-order bright fringe is $\theta =13.5^{\circ}$

let distance between the slits be d

Distance of n th bright fringe From central Fringe is given by

$y_n=\frac{nD\lambda }{d}$

Also $\tan \theta =\frac{y_4}{D}$

$y_4=\tan (13.5)\cdot 1.54$

$y_4=0.24\times 1.54$

$y_4=0.369 m$

5 0

3 years ago

Use undetermined coefficient to determine the solution of:y"-3y'+2y=2x+ex+2xex+4e3x

Kitty [74]

First check the characteristic solution: the characteristic equation for this DE is

r ² - 3r + 2 = (r - 2) (r - 1) = 0

with roots r = 2 and r = 1, so the characteristic solution is

y (char.) = C₁ exp(2x) + C₂ exp(x)

For the ansatz particular solution, we might first try

y (part.) = (ax + b) + (cx + d) exp(x) + e exp(3x)

where ax + b corresponds to the 2x term on the right side, (cx + d) exp(x) corresponds to (1 + 2x) exp(x), and e exp(3x) corresponds to 4 exp(3x).

However, exp(x) is already accounted for in the characteristic solution, we multiply the second group by x :

y (part.) = (ax + b) + (cx ² + dx) exp(x) + e exp(3x)

Now take the derivatives of y (part.), substitute them into the DE, and solve for the coefficients.

y' (part.) = a + (2cx + d) exp(x) + (cx ² + dx) exp(x) + 3e exp(3x)

… = a + (cx ² + (2c + d)x + d) exp(x) + 3e exp(3x)

y'' (part.) = (2cx + 2c + d) exp(x) + (cx ² + (2c + d)x + d) exp(x) + 9e exp(3x)

… = (cx ² + (4c + d)x + 2c + 2d) exp(x) + 9e exp(3x)

Substituting every relevant expression and simplifying reduces the equation to

(cx ² + (4c + d)x + 2c + 2d) exp(x) + 9e exp(3x)

… - 3 [a + (cx ² + (2c + d)x + d) exp(x) + 3e exp(3x)]

… +2 [(ax + b) + (cx ² + dx) exp(x) + e exp(3x)]

= 2x + (1 + 2x) exp(x) + 4 exp(3x)

… … …

2ax - 3a + 2b + (-2cx + 2c - d) exp(x) + 2e exp(3x)

= 2x + (1 + 2x) exp(x) + 4 exp(3x)

Then, equating coefficients of corresponding terms on both sides, we have the system of equations,

x : 2a = 2

1 : -3a + 2b = 0

exp(x) : 2c - d = 1

x exp(x) : -2c = 2

exp(3x) : 2e = 4

Solving the system gives

a = 1, b = 3/2, c = -1, d = -3, e = 2

Then the general solution to the DE is

y(x) = C₁ exp(2x) + C₂ exp(x) + x + 3/2 - (x ² + 3x) exp(x) + 2 exp(3x)

4 0

3 years ago

A vehicle travels 57 kilometers north and then travels 26 kilometers south. What is the current position of the vehicle? (2 poin

solniwko [45]

Answer:

C. 31 kilometers north of its starting location

Step-by-step explanation:

Please see attached a rough sketch of the situation for your reference.

Step one:

Displacement North= 57km

Displacement South= 26km

Required

The final displacement

The current position is attained by subtracting 26km from 57km

=57-26= 31km

Therefore the current position is

C. 31 kilometers north of its starting location

5 0

3 years ago

A Web music store offers two versions of a popular song. The size of the standard version is 2.9 megabytes (MB). The size of the

Lady bird [3.3K]

Write the equations: $2.9s+4.7h=6076
 \\ h= 4s$
Substitute for h: $2.9s+4.7(4s)=6076$
Solve for s: $2.9s+4.7(4s)=6076 \\ 2.9s+18.8s=6076 \\ 21.7s=6076 \\ s=280$
There were 280 downloads of the standard version. There were 1120 downloads of the high-quality version.

5 0

3 years ago