Answer:
16
Step-by-step explanation:
x=76
y=4
I think that answer should be right. Since it is isosceles the base angles will be the same and the top angle is an angle bisector which means that the angle split on top has even splits. Since no other side lengths- or any lengths at that matter- are give, it is safe to assume that y=4.
Answer:
remember the chain rule:
h(x) = f(g(x))
h'(x) = f'(g(x))*g'(x)
or:
dh/dx = (df/dg)*(dg/dx)
we know that:
z = 4*e^x*ln(y)
where:
y = u*sin(v)
x = ln(u*cos(v))
We want to find:
dz/du
because y and x are functions of u, we can write this as:
dz/du = (dz/dx)*(dx/du) + (dz/dy)*(dy/du)
where:
(dz/dx) = 4*e^x*ln(y)
(dz/dy) = 4*e^x*(1/y)
(dx/du) = 1/(u*cos(v))*cos(v) = 1/u
(dy/du) = sin(v)
Replacing all of these we get:
dz/du = (4*e^x*ln(y))*( 1/u) + 4*e^x*(1/y)*sin(v)
= 4*e^x*( ln(y)/u + sin(v)/y)
replacing x and y we get:
dz/du = 4*e^(ln (u cos v))*( ln(u sin v)/u + sin(v)/(u*sin(v))
dz/du = 4*(u*cos(v))*(ln(u*sin(v))/u + 1/u)
Now let's do the same for dz/dv
dz/dv = (dz/dx)*(dx/dv) + (dz/dy)*(dy/dv)
where:
(dz/dx) = 4*e^x*ln(y)
(dz/dy) = 4*e^x*(1/y)
(dx/dv) = 1/(cos(v))*-sin(v) = -tan(v)
(dy/dv) = u*cos(v)
then:
dz/dv = 4*e^x*[ -ln(y)*tan(v) + u*cos(v)/y]
replacing the values of x and y we get:
dz/dv = 4*e^(ln(u*cos(v)))*[ -ln(u*sin(v))*tan(v) + u*cos(v)/(u*sin(v))]
dz/dv = 4*(u*cos(v))*[ -ln(u*sin(v))*tan(v) + 1/tan(v)]
Answer:
(x,y,z) = (5/2, 5/2, 0)
If z = t,
(x,y,z) = ((5-3t)/2, (5-t)/2, t)
Step-by-step explanation:
-x + y - z = 0
2y + z = 5
(1/5)z = 0
From eqn 3, z = 0
2y + z = 5
Substitute for z in eqn 2
2y + 0 = 5
y = 5/2
substituting for y and z in eq 1
-x + (5/2) - 0 = 0
x = (5/2)
(x,y,z) = (5/2, 5/2, 0)
In terms of t, if z = t,
eqn 2 becomes 2y + t = 5
2y = 5 - t
y = (5 - t)/2
Eqn1 becomes
-x + (5-t)/2 - t = 0
-x + (5/2) - (t/2) - t = 0
-x + (5/2) - (3t/2) = 0
x = (5-3t)/2
(x,y,z) = ((5-3t)/2, (5-t)/2, t)
f(x) + n - shift the graph n units up
f(x) - n - shift the graph n units down
f(x + n) - shift the graph n units left
f(x - n) - shift the graph n units right
-----------------------------------------------------------------
g(x) = 4x² - 16
Shift 9 units right and 1 unit down. Therfore:
g(x - 9) - 1 = 4(x - 9)² - 16 - 1 = 4(x - 9)² - 17
<h3>Answer: A. h(x) = 4(x - 9)² - 17</h3>
