9514 1404 393
Answer:
Step-by-step explanation:
The marked angles form a linear pair, so have a sum of 180°.
(4a +10) +(6a) = 180
10a = 170 . . . . . . . . . . subtract 10
a = 17 . . . . . . . . . . . . . divide by 10
__
Then the measure of angle ABC is ...
∠ABC = 4a +10 = 4(17) +10 = 68 +10 . . . . . substitute 17 for 'a'
∠ABC = 78°
Let the curve C be the intersection of the cylinder
and the plane
The projection of C on to the x-y plane is the ellipse
To see clearly that this is an ellipse, le us divide through by 16, to get
or
,
We can write the following parametric equations,
for
Since C lies on the plane,
it must satisfy its equation.
Let us make z the subject first,
This implies that,
We can now write the vector equation of C, to obtain,
The length of the curve of the intersection of the cylinder and the plane is now given by,
But
Therefore the length of the curve of the intersection intersection of the cylinder and the plane is 24.0878 units correct to four decimal places.
Answer:
450
Step-by-step explanation:
60 x 7.5=450
Answer:
n<2
Step-by-step explanation:
6.2n<2n+8.4
Move variable to the left hand side and change its sign
6.2n - 2n < 8.4
Combine like terms
4.2n < 8.4
divide both side by 4.2
n < 2
Answer:
This would be shifted down 8 and made 3 times less steep.
Step-by-step explanation:
In order to determine these transformations, we first need to compare the constants at the end. This will determine the up or downward shift. Since the f(x) is 5 and the g(x) is -3, we know that it went down 8.
Next we compare the coefficients of x. Since the f(x) is 6 and the g(x) is 2, we know that it is 3 times less steep.