Mathematics: What is the solution to the equation 4 plus root 3 2y =6

02.12.2021

What is the solution to the equation 4 plus root 3 2y =6

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Mathematics

Find the center (h, k), the radius r, and the intercepts, if any of each circle. x2 + y2 - 6x + 2y + 6 = 0 a (h, k) = (3, -1); r = 2; x-int: 3 ± √3 (x-intercept is three plus or minus the square root of three); y-int: none b (h, k) = (3, -1); r = 4; x-int: 3 ± √3 (x-intercept is three plus or minus the square root of three); y-int: none c (h, k) = (-3, 1); r = 4; x-int: 3 ± √3 (x-intercept is three plus or minus the square root of three); y-int: none d (h, k) = (-3, 1); r = 2; x-int: 3 ± √3 (x-intercept is three plus or minus the square root of

Step-by-step answer

P Answered by PhD

A. C(x,y) = (3,-1) , r = 2 , x-Intercepts: $x = 3\pm\sqrt{3}$ , y-Intercepts: none.

Step-by-step explanation:

Let $x^{2}+y^{2}-6\cdot x + 2\cdot y + 6 = 0$ be the general equation of the circle, we must transform the expression into standard form to determine its center, radius and intercepts. The procedure is shown below:

1) $x^{2}+y^{2}-6\cdot x + 2\cdot y + 6 = 0$ Given.

2) $(x^{2}-6\cdot x)+(y^{2}+2\cdot y) +6= 0$ Commutative and associative properties.

3) $(x^{2}-6\cdot x)+(y^{2}+2\cdot y) + 6 + 3 + 1 = 3 + 1$ Compatibility with addition.

4) $(x^{2}-6\cdot x +9)+(y^{2}+2\cdot y +1) = 4$ Definition of addition/Commutative and associative properties.

5) $(x-3)^{2} + (y+1)^{2} = 4$ Perfect square trinomial/Result.

The equation of the circle centered in (h, k) in standard form is defined as:

$(x -h)^{2} + (y-k)^{2} = r^{2}$ (Eq. 1)

Where:

, - Coordinate of the center of the circle, dimensionless.

- Radius of the circle, dimensionless.

By direct comparison we find that circle is centered in C(x, y) = (3, -1) and has a radius of 2.

Finally, we obtain the intercepts of the given function:

x-Intercepts ( y = 0 )

$(x-3)^{2} + (0+1)^{2} = 4$

$x^{2}-6\cdot x +9+1 = 4$

$x^{2}-6\cdot x +6=0$

Roots are found analitically by Quadratic Formula:

$x = 3\pm\sqrt{3}$

y-Intercepts ( x=0 )

$(0-3)^{2}+(y+1)^{2} = 4$

$9+y^{2}+2\cdot y +1 = 4$

$y^{2}+2\cdot y +6 = 0$

Roots are found analitically by Quadratic Formula:

$y = -1\pm i\,\sqrt{5}$

In a nutshell, there are no y-Intercepts.

We include a graphic including circle, center and x-Intercepts.

Finally, we came to the conclusion that correct answer is A.

Find the center (h, k), the radius r, and the intercepts, if any of each circle.

x2 + y2 - 6x + 2y

Mathematics

Neil places £2000 in a bank account that pays 1.5% simple interest per year. How much interest will he earn in 6 years?

Step-by-step answer

P Answered by PhD

SI=(P*R*T)/100

P=2000

R=1.5

T=6

SI=(2000*1.5*6)/100

=(2000*9)/100

=180

Neil will earn interest of 180

Mathematics

You can buy jars of the same jam in 2 sizes large jar:440g for £1.54 small jar:340g for £1.26 By considering the price per gram, work out which jar is the best value for money. Working must be shown

Step-by-step answer

P Answered by PhD

Answer: 440 grams for 1.54 is the better value
Explanation:
Take the price and divide by the number of grams
1.54 / 440 =0.0035 per gram
1.26 / 340 =0.003705882 per gram
0.0035 per gram < 0.003705882 per gram

Mathematics

The last time Robert filled up his car with gas, he paid $24.50 for 7 gallons. This time, he needs 15 gallons. If the price is the same, how much will he pay?

Step-by-step answer

P Answered by PhD

Cost of 7 gallons=$24.50

Cost of 1 gallon=24.50/7=3.5

Cost of 15 gallons=15*3.5=52.5

Cost of 15 gallons will be $52.5

Mathematics

An ice cream shop offers 5 different flavors of ice cream and 9 different toppings. How many choices are possible for a single serving of ice cream with one topping?

Step-by-step answer

P Answered by PhD