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myrzilka [38]
3 years ago
6

John has a map that shows a rectangular park 1 1/4 cm : 8 yd. on the map, the width of the park is 2 1/2 cm. What is the parks a

ctual length?
Mathematics
1 answer:
Ber [7]3 years ago
3 0

Answer:

16 yd.  This is the park's actual length.

Step-by-step explanation:

Write and solve an equation of ratios:

1 1/4 cm     8 yd

------------ = -----------

2 1/2 cm        x

Note that 2(1 1/4 cm) = 2 1/2 cm, so the above equation becomes:

 1       8 yd

----- = ---------

  2         x

Solving for x, we get x = 16 yd.  This is the park's actual length.

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What is the mathematical relationship between the atomic radius (r) and the lattice parameter (a0) in the BCC structure? a. b. c
ryzh [129]

Answer: Lattice parameter, a = (4R)/(√3)

Step-by-step explanation:

The typical arrangement of atoms in a unit cell of BCC is shown in the first attachment.

The second attachment shows how to obtain the value of the diagonal of the base of the unit cell.

If the diagonal of the base of the unit cell = x

(a^2) + (a^2) = (x^2)

x = a(√2)

Then, diagonal across the unit cell (a cube) makes a right angled triangle with one side of the unit cell & the diagonal on the base of the unit cell.

Let the diagonal across the cube be y

Pythagoras theorem,

(a^2) + ((a(√2))^2) = (y^2)

(a^2) + 2(a^2) = (y^2) = 3(a^2)

y = a√3

But the diagonal through the cube = 4R (evident from the image in the first attachment)

y = 4R = a√3

a = (4R)/(√3)

QED!!!

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2 years ago
For questions 1 and 2, use factoring to find the x-intercepts of these quadratic equations.
Marysya12 [62]
1.x^2 +6x - 4 = 6x
X^2 + 6x -4 - 6x = 0
X^2 - 4 = 0
By difference of two squares :
X^2 - 4 = 0 can be written as (x-2) (x+2) = 0
(X-2)=0 therefore x= 2

(X+2)=0 therefore x= -2

2. X^2 - 8x = -6x
X^2 -8x + 6x = 0
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6 0
2 years ago
4-58. Lisa plans to retire on her 61st birthday. On her
mojhsa [17]

Answer:

Lisa invest "$2180.81" in her bank.

Step-by-step explanation:

The given values are:

On Lisa's 62nd birthday,

she withdraw = $10,000

The annuity of $A will remain at 3 percent for 40 years. The retirement pension of $10000 lasts 23 years at rate percentage of 3 but begins 40 years later.

⇒  A\times (\frac{P}{A} ,3 \ percent,40) - 10000 (\frac{P}{A} ,3 \ percent,23)\times \frac{1}{(1.03)40} = 0

⇒  A\times 23.1148 - 10000\times 16.4436\times 0.3066 = 0

⇒  A = 10000\times 16.4436\times \frac{0.3066}{23.1148}

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4 0
3 years ago
Determine the equation of the line that goes through points (1.1) and (3.7).
ValentinkaMS [17]

Answer:

The equation of the line that goes through points (1,1) and (3,7) is \mathbf{y=3x-2}

Step-by-step explanation:

Determine the equation of the line that goes through points (1,1) and (3,7)

We can write the equation of line in slope-intercept form y=mx+b where m is slope and b is y-intercept.

We need to find slope and y-intercept.

Finding Slope

Slope can be found using formula: Slope=\frac{y_2-y_1}{x_2-x_1}

We have x_1=1, y_1=1, x_2=3, y_2=7

Putting values and finding slope

Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{7-1}{3-1}\\Slope=\frac{6}{2}\\Slope=3

We get Slope = 3

Finding y-intercept

y-intercept can be found using point (1,1) and slope m = 3

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We get y-intercept b = -2

So, equation of line having slope m=3 and y-intercept b = -2 is:

y=mx+b\\y=3x-2

The equation of the line that goes through points (1,1) and (3,7) is \mathbf{y=3x-2}

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3 years ago
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