Answer:
y = - 9
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (1, - 6) and (x₂, y₂ ) = (4, 3)
m = =
= 3
y = 3x + c ← is the partial equation
To find c substitute any of the 2 points into the partial equation
Using (4, 3), then
3 = 12 + c ⇒ c = 3 - 12 = - 9, hence
y- intercept c = - 9 ⇒ (0, - 9 )
Answer: 72 grams.
Step-by-step explanation:
Let be "s" the amount of sugar in grams that must be used for 252 grams of coconut to keep the same ratio of coconut to sugar.
Knowing that in the recipe for the coconut cookies, should be 420 grams of coconut and 120 grams of sugar, and you only have 252 grams of coconut, you can set up this proportion to find "s":
Now, you need to solve for "s":
Answer:
The correct answer B) The volumes are equal.
Step-by-step explanation:
The area of a disk of revolution at any x about the x- axis is πy² where y=2x. If we integrate this area on the given range of values of x from x=0 to x=1 , we will get the volume of revolution about the x-axis, which here equals,
which when evaluated gives 4pi/3.
Now we have to calculate the volume of revolution about the y-axis. For that we have to first see by drawing the diagram that the area of the CD like disk centered about the y-axis for any y, as we rotate the triangular area given in the question would be pi - pi*x². if we integrate this area over the range of value of y that is from y=0 to y=2 , we will obtain the volume of revolution about the y-axis, which is given by,
If we just evaluate the integral as usual we will get 4pi/3 again(In the second step i have just replaced x with y/2 as given by the equation of the line), which is the same answer we got for the volume of revolution about the x-axis. Which means that the answer B) is correct.