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2 years ago

Write an equation of the circle with center (3,-2) and radius 6

Mathematics

1 answer:

Lubov Fominskaja [6]2 years ago

8 0

Answer:

$\displaystyle (x-3)^2 + (y+2)^2 = 36$

Step-by-step explanation:

We want to write the equation of a circle with a center at (3, -2) and a radius of 6 units.

Recall that the equation of a circle is given by:

$\displaystyle (x-h)^2 + (y-k)^2 = r^2$

Where (h, k) is the center and r is the radius.

Since our center is at (3, -2), h = 3 and k = -2. r = 6. Substitute:

$\displaystyle (x-(3))^2 +(y-(-2))^2 = (6)^2$

Simplify:

$\displaystyle (x-3)^2 + (y+2)^2 = 36$

In conclusion, the equation of the circle will be:

$\displaystyle (x-3)^2 + (y+2)^2 = 36$

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Simplify the expression 21z - 6z + 13

Bess [88]

Answer:

15z+13

Step-by-step explanation:

hey! all we have to do is combine like terms.

21z-6z+13

15z+13

there's your answer.

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3 years ago

Read 2 more answers

Factorize 2x^4-7x^3-13x^2+63x-45 using factor theorem.

zheka24 [161]

Find the possible rational roots and use synthetic division to find the first zero.
I chose x=1 (which represents the factor "x-1")

1║2 -7 -13 63 -45
║    2 -5 -18 45
    2 -5 -18 45 0
(x-1) is a factor, (2x³ - 5x² - 18x + 45) is the other factor.

Use synthetic division on the decomposed polynomial to find the next zero.
I chose x = 3 (which represents the factor "x-3")

3║2 -5 -18 45
║    6    3   -45
    2   1 -15    0

Using synthetic division, we discovered that (x-1), (x-3), & (2x² + x -15) are factors. Take the new decomposed polynomial (2x² + x -15) and find the last two factors using any method.

Final Answer: (x-1)(x-3)(x+3)(2x-5)

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3 years ago

Neighbor Fred built a retaining wall that was 2 feet outside his property line. What has Fred created?

yulyashka [42]

Answer:

An encroachment.

Step-by-step explanation:

In real estate,encroachment is building a structure between the boundaries of your property or land and your neighbor's property or land.

The retaining wall Fred build that was 2ft outside his property line is called encroachment

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3 years ago

Between what two integer powers of 2 does 2√7 lie?

prisoha [69]

Answer:

Between 5 and 6

Step-by-step explanation:

Integers refer to positive whole numbers.

Firstly, we need to know the value of the surd

By calculating, the value of the surd is 5.29

What this mean is that the surd is between the values of 5 and 6

It is slightly greater than 5 and not up to 6

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3 years ago

A major retail clothing store is interested in estimating the difference in mean monthly purchases by customers who use the stor

mixer [17]

Answer:

Critical value is t = 1.9901

Step-by-step explanation:

We are given the results of the sampling :

In-House Credit Card National Credit Card Sample Size : 32 50

Mean Monthly Purchases : $45.67 $39.87

Standard Deviation : $10.90 $12.47

Also, the managers wished to test whether there is a statistical difference in the mean monthly purchases by customers using the two types of credit cards, using a significance level α of 0.05.

Firstly, we will specify our null and alternate hypothesis;

Let $\mu_1$ = Mean Monthly Purchases of In-House Credit Card

$\mu_2$ = Mean Monthly purchases of National Credit Card

So, Null Hypothesis, $H_0$ : $\mu_1-\mu_2$ = 0 {means that there is no difference in the mean monthly purchases by customers using the two types of credit cards}

Alternate Hypothesis, $H_0$ : $\mu_1-\mu_2\neq$ 0 {means that there is statistical difference in the mean monthly purchases by customers using the two types of credit cards}

The test statistics that will be used here is Two-sample t-test statistics;

T.S. = $\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }$ ~ $t_n___1+n_2-_2$

where, $\bar X_1$ = Sample mean Purchases of In-House Credit Card = $45.67

$\bar X_2$ = Sample mean Purchases of National Credit Card = $39.87

$s_p$ = pooled variance

$n_1$ = In-house credit card sample = 32

$n_2$ = National credit card sample = 50

So, degree of freedom of t-value here is (32 + 50 - 2) = 80

Now, at 0.05 significance level, t table gives critical value of t = 1.9901 at 80 degree of freedom.

Therefore, the critical value assuming the population standard deviations are not known but that the populations are normally distributed with equal variances is t = 1.9901.

4 0

3 years ago