Answer:
Point slope is ( Y+4) = 1/2(x+3)
Slope intercept is Y = 1/2(x) -5/2
Step-by-step explanation:
For the point slope form.
Given the point as (-3,-4)
And the gradient m = 1/2
Point slope form is
(Y - y1) = m(x-x1)
So
X1 = -3
Y1 = -4
(Y - y1) = m(x-x1)
(Y - (-4)) = 1/2(x -(-3))
( Y+4) = 1/2(x+3)
For the slopes intercept form
Y = mx + c
We can continue from where the point slope form stopped.
( Y+4) = 1/2(x+3)
2(y+4)= x+3
2y + 8 = x+3
2y = x+3-8
2y = x-5
Y = x/2 - 5/2
Y = 1/2(x) -5/2
Where -5/2 = c
1/2 = m
Answer:
cylinder = 27π
cone = 9π
sphere = 36π
Step-by-step explanation:
volume of a cylinder = πr²h where r = radius and h = height
height of cylinder (h) = 3 and radius (r) = 3
so volume = π(3)²3
==> simplify exponent
volume = π9(3)
==> multiply 9 and 3
volume of cylinder = 27π
Volume of a cone = πr²(h/3) where r = radius and h = height
height of cone (h) = 3 and radius (r) = 3
so volume = π(3)²(3/3)
==> simplify exponent
volume = π9(3/3)
==> divide 3 by 3
volume = π9(1)
==> multiply 9 and 1
volume of cone = 9π
volume of a sphere = 4/3πr³ where r = radius
radius = 3
so volume = 4/3π(3)³
==> simplify exponent
volume = 4/3π27
==> multiply 4/3 and 27
volume of sphere = 36π
Set up proportions.
3/4 cups → 1 batch
x cups → 2 batches
x = 2(3/4) = 6/4 = 1 1/2 cups
3/4 cups → 1 batch
y cups → 9 batches
y = 9(3/4) = 6 3/4 cups
Remark
Study the triangle carefully. It may not be exactly as you have drawn it, but it will work if you just follow the givens.
Givens
AC = 2
AB = 1
BC = sqrt(3)
Step One
Find Cos C
Cos(C) = adjacent / Hypotenuse
Cos(C) = BC / AB
Cos(C) = sqrt(3)/2
Step Two
Find Sin(A)
Sin(A) = opposite / hypotenuse
Sin(A) = AB / AC
Sin(A) = 1/2
Step Three
Find Cos(C) * Sin(A)
Cos(C) * Sin(A) = sqrt(3)/2 * 1/2 = sqrt(3) / 4 <<<< Answer
