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2 years ago

What is the equation of the circle with a radius of 4 and a center at (3, 2) ?

Mathematics

1 answer:

ICE Princess25 [194]2 years ago

6 0

Answer:

(x - 3)^2 + (y + 2)^2 = 16

Step-by-step explanation:

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

r = radius

(h, k ) is center of circle.

The center of the circle is (3, 2) and r is 4.

(x - 3)^2 + (y + 2)^2

Best of luck :3

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The sides of a triangle are 1, x, and x2. what are possible values of x?

Whitepunk [10]

The sides of the triangle are given as 1, x, and x².

The principle of triangle inequality requires that the sum of the lengths of any two sides should be equal to, or greater than the third side.

Consider 3 cases
Case (a): x < 1,
Then in decreasing size, the lengths are 1, x, and x².
We require that x² + x ≥ 1
Solve x² + x - 1 =
x = 0.5[-1 +/- √(1+4)] = 0.618 or -1.618.
Reject the negative length.
Therefore, the lengths are 0.382, 0.618 and 1.

Case (b): x = 1
This creates an equilateral triangle with equal sides
The sides are 1, 1 and 1.

Case (c): x>1
In increasing order, the lengths are 1, x, and x².
We require that x + 1 ≥ x²
Solve x² - x - 1 = 0
x = 0.5[1 +/- √(1+4)] = 1.6118 or -0.618
Reject the negative answr.
The lengths are 1, 1.618 and 2.618.

Answer:
The possible lengths of the sides are
(a) 0.382, 0.618 and 1
(b) 1, 1 and 1.
(c) 2.618, 1.618 and 1.

7 0

3 years ago

Find sin theta in the given triangle

lana [24]

Sin = surd 3 / 2

get it????

7 0

2 years ago

Solve the equation v³ = 12.

AlexFokin [52]

Answer:

2.2894

Step-by-step explanation:

v3 = 12

v = ∛ 12

v = 2.2894

5 0

1 year ago

Suppose n(x)= 22 and n(y) is 13 what is the maximum number of elements X ∪Y can have ?

Nikolay [14]

The inclusion/exclusion principle states that

$|X\cup Y|=|X|+|Y|-|X\cap Y|$

That is, the union has as many members as the sum of the number of members of the individual sets, minus the number of elements contained in both sets (to avoid double-counting).

Therefore, $|X\cup Y|$ will have the most elements when the sets $X$ and $Y$ are disjoint, i.e. $X\cap Y=\emptyset$ , which would mean the most we can can in this case would be

$|X\cup Y|=|X|+|Y|=22+13=35$

(Note that $n(X)=|X|$ denotes the cardinality of the set $X$ .)

3 0

3 years ago

On a map the distance between rip and Janeiro Brazil and San Jose Costa Rica is 4 inches.the scale on the map shows that 1 inch=

Vera_Pavlovna [14]

Answer:

The way a proportion is set is as follows;

$\dfrac{1 \ inch}{200 \ miles } = \dfrac{4 \ inches}{ Distance \ from \ Rio \ de \ Janeiro \ to \ San \ Jose}$

The Distance from Rio de Janeiro and San Jose Costa Rica is then found as 800 miles

Step-by-step explanation:

The dimension of the distance between Rio de Janeiro and San Jose Costa Rica = 4 inches

The map scale = 1 inch to 200 miles

To figure out how many miles it is or the actual distance from Rio de Janeiro and San Jose Costa Rica, we have;

$\dfrac{1 \ inch}{200 \ miles } = \dfrac{4 \ inches}{ Distance \ from \ Rio \ de \ Janeiro \ to \ San \ Jose}$

Therefore, we have;

(4 inches × 200 miles)/(1 inche) = Distance from Rio de Janeiro and San Jose Costa Rica

Which gives;

Distance from Rio de Janeiro and San Jose Costa Rica = 800 miles.

4 0

2 years ago