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4 years ago

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When baking cookies, each cookie should be placed about 2 inches from one another to allow room to expand. If one cookie has a r

adius of 1 inch and a center at C(1, –1), find the center and equation of the cookie immediately to the right. (Assume that each cookie is uniform with a radius of 1 inch and that 1 inch = 1 unit on a coordinate plane.)

1 answer:

IrinaVladis [17]4 years ago

4 0

Answer:

Center: (1, 3)

Equation: (x - 1)² + (y - 3)² = 1

Explanation:

1) The initial distance between the centers of two adjacent cookies must be equal to the separation indicated (2 inches) plus the radius of each cookie, which is 2 × 1 in.

So, the separation of the centers is 2 in + 2 × 1 in = 2in + 2 in = 4 in.

2) Then the coordinates of the center the cookie to the right of the given cookie are (1, -1 + 4) = (1, 3).

3) The equation of the circle of radius r and center (a,b) is:

(x - a)² + (y - b)² = r²

So, using a = 1, b = 3, and r = 1, you get:

(x - 1)² + (y - 3)² = 1

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Use synthetic division to solve (4x^3-3x^2+5x+6)/(x+6).what is the quotient

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Answer:

The quotient= $4x^2-27x+167$ .

Step-by-step explanation:

Given

Dividened= $4x^3-3x^2+5x+6$

Divisor= $x+6$

In synthetic division : Put denomerator is equal to zero.

Put x+6=0

x=-6

Put -6 in division box as a divisor.

Coefficient of x^3=4

Coefficient of x^2=-3

Coefficient of x=5

Constant value=6

Put the coefficient of x^3,x^2,x and constant in descending order of power of x in division problem.

Now ,bring the coefficient of x^3 is 4 straight down .

Now, multiply the numbe -6 in the division box with the number 4 brought down and put the result -24 below the number - 3 of next column.

By adding we get -27 and write result in the bottom of row .

Again ,the number -6 multiply with -27 and put the result=162 below the number of next column.

By adding two number together we get 167 and put the result in the bottom of row.

Again, the number -6 in division box multiply with the number 167 and put the result=1002 below the number of next column.

Adding two number together we get 1008 and write in the bottom of row.

Last number is remainder and then write the remainder in fraction .

In quotient the power of x reduces by 1 from the numertor.

Hence, the quotient = $4x^2-27x+167$

Remainder= $\frac{1008}{x+6}$ .

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The following observations were made on fracture toughness of a base plate of 18% nickel maraging steel (in ksi √in, given in in

Grace [21]

Answer:

A 90% confidence interval for the standard deviation of the fracture toughness distribution is [4.06, 6.82].

Step-by-step explanation:

We are given the following observations that were made on fracture toughness of a base plate of 18% nickel maraging steel below;

68.6, 71.9, 72.6, 73.1, 73.3, 73.5, 75.5, 75.7, 75.8, 76.1, 76.2, 76.2, 77.0, 77.9, 78.1, 79.6, 79.8, 79.9, 80.1, 82.2, 83.7, 93.4.

Firstly, the pivotal quantity for finding the confidence interval for the standard deviation is given by;

P.Q. = $\frac{(n-1) \times s^{2} }{\sigma^{2} }$ ~ $\chi^{2} __n_-_1$

where, s = sample standard deviation = $\sqrt{\frac{\sum (X - \bar X^{2}) }{n-1} }$ = 5.063

$\sigma$ = population standard deviation

n = sample of observations = 22

Here for constructing a 90% confidence interval we have used One-sample chi-square test statistics.

<u>So, 90% confidence interval for the population standard deviation, </u> $\sigma$ <u> is ;</u>

P(11.59 < $\chi^{2}__2_1$ < 32.67) = 0.90 {As the critical value of chi at 21 degrees

of freedom are 11.59 & 32.67}

P(11.59 < $\frac{(n-1) \times s^{2} }{\sigma^{2} }$ < 32.67) = 0.90

P( $\frac{ 11.59}{(n-1) \times s^{2}}$ < $\frac{1}{\sigma^{2} }$ < $\frac{ 32.67}{(n-1) \times s^{2}}$ ) = 0.90

P( $\frac{(n-1) \times s^{2} }{32.67 }$ < $\sigma^{2}$ < $\frac{(n-1) \times s^{2} }{11.59 }$ ) = 0.90

<u>90% confidence interval for</u> $\sigma^{2}$ = [ $\frac{(n-1) \times s^{2} }{32.67 }$ , $\frac{(n-1) \times s^{2} }{11.59 }$ ]

= [ $\frac{21 \times 5.063^{2} }{32.67 }$ , $\frac{21 \times 5.063^{2} }{11.59 }$ ]

= [16.48 , 46.45]

<u>90% confidence interval for</u> $\sigma$ = [ $\sqrt{16.48}$ , $\sqrt{46.45}$ ]

= [4.06 , 6.82]

Therefore, a 90% confidence interval for the standard deviation of the fracture toughness distribution is [4.06, 6.82].

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