Answer:
83.79 cm²
Step-by-step explanation:
(please refer to attached)
recall that the volume of a cone is given by
V = (1/3) π r² h
where
r = radius = given as 4 cm
h = height = given as 5 cm
assume π = 3.142
substituting the values into the formula:
V = (1/3) π r² h
V = (1/3) (3.14) (4)² (5)
V = 83.79 cm²
Answer:
4y = 6x + 40
Step-by-step explanation:
The general equation of a straight line is y = mx + b
m is the slope and b is the y-intercept
let us write both equations in this form;
we have this as;
6y = -4x + 1
y = -4x/6 + 1/6
and;
2x + 3y = 18
3y = -2x + 18
y = -2x/3 + 6
So firstly we want to find an equation that is perpendicular to the first
When two lines are perpendicular, their slopes has a product of -1
The slope of the first line is -4/6
let the slope of the line we want be m
As per they are perpendicular;
-4/6 * m = -1
-4m/6 = -1
-4m = -6
m = 6/4
So now, we want the y-intercept greater than that of the second equation which is a y-intercept of 6
we can choose 10
and we have the equation as:
y = 6x/4 + 10
multiply through by 4
4y = 6x + 40
Answer:
(x, y) = (2, 1)
Step-by-step explanation:
given the 2 equations
2y - 3x = - 4 → (1)
6y + x = 8 → (2)
multiplying (2) by 3 allows the x terms to be eliminated
18y + 3x = 24 → (3)
add (1) and (3) term by term
(2y + 18y) + (- 3x + 3x) = (-4 + 24)
20y + 0 = 20 ( divide both sides by 20 )
y = 1
substitute y = 1 into either of the equations and solve for x
using (2), then
6 + x = 8 ( subtract 6 from both sides )
x = 2
solution (2, 1)
Answer:
see the attachment for the graph
Step-by-step explanation:
Since all you want is the graph, it is convenient to use a graphing program to produce it.
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You will notice that the point on the circle is 4 units over and 3 units up from the center.* This tells you the square of the radius is 4²+3² = 25. You only need to know this if you're using a graphing calculator to plot the equation ...
(x +4)^2 +(y -1)^2 = 25
If you're graphing this by hand, you can set your compass to the distance between the plotted points, as we have done in our graphing program.
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* Hopefully, you recognize these (4 and 3) as the legs of a 3-4-5 right triangle, so you know immediately that the radius is 5. Even if you don't, you can figure it using the Pythagorean theorem, as we have done above.
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The standard form equation of a circle with center (h, k) and radius r is ...
(x -h)^2 +(y -k)^2 = r^2