Answer:
she should use 2 cups of peanut butter
Step-by-step explanation:
to know the answer to that
use this equation (pb is peanut butter &o is oil)
1cup of pb=1/2 cup of o
?=1 cup of o
1×1÷1/2= 1×1×2/1=2co cups of pb
A/b=c
times both sides by b
A=bc
divide both sides by c
A/c=b
b=A/c
Answer:
Step-by-step explanation:
given a point
the equation of a line with slope m that passes through the given point is
or equivalently
.
Recall that a line of the form
, the y intercept is b and the x intercept is
.
So, in our case, the y intercept is
and the x intercept is
.
In our case, we know that the line is tangent to the graph of 1/x. So consider a point over the graph
. Which means that ![y_0=\frac{1}{x_0}](https://tex.z-dn.net/?f=y_0%3D%5Cfrac%7B1%7D%7Bx_0%7D)
The slope of the tangent line is given by the derivative of the function evaluated at
. Using the properties of derivatives, we get
. So evaluated at
we get ![m = \frac{-1}{x_0^2}](https://tex.z-dn.net/?f=%20m%20%3D%20%5Cfrac%7B-1%7D%7Bx_0%5E2%7D)
Replacing the values in our previous findings we get that the y intercept is
![(y_0-mx_0) = (\frac{1}{x_0}-(\frac{-1}{x_0^2}x_0)) = \frac{2}{x_0}](https://tex.z-dn.net/?f=%28y_0-mx_0%29%20%3D%20%28%5Cfrac%7B1%7D%7Bx_0%7D-%28%5Cfrac%7B-1%7D%7Bx_0%5E2%7Dx_0%29%29%20%3D%20%5Cfrac%7B2%7D%7Bx_0%7D)
The x intercept is
![\frac{mx_0-y_0}{m} = \frac{\frac{-1}{x_0^2}x_0-\frac{1}{x_0}}{\frac{-1}{x_0^2}} = 2x_0](https://tex.z-dn.net/?f=%20%5Cfrac%7Bmx_0-y_0%7D%7Bm%7D%20%3D%20%5Cfrac%7B%5Cfrac%7B-1%7D%7Bx_0%5E2%7Dx_0-%5Cfrac%7B1%7D%7Bx_0%7D%7D%7B%5Cfrac%7B-1%7D%7Bx_0%5E2%7D%7D%20%3D%202x_0)
The triangle in consideration has height
and base
. So the area is
![\frac{1}{2}\frac{2}{x_0}\cdot 2x_0=2](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B2%7D%5Cfrac%7B2%7D%7Bx_0%7D%5Ccdot%202x_0%3D2)
So regardless of the point we take on the graph, the area of the triangle is always 2.
"Alaina’s sugar cookie recipe calls for 2 1/4
cups of flour per batch. If she wants to make 2/3
a batch of cookies, how much flour should she use?"
1 1/2 Cups, if she wants to make less than the original recipe, she would need less flour, you have to divide.