Answer:
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This is a weird one. I'm going to work it, but I also want you to look back at the
book or the worksheet and make sure that you copied it correctly.
Because it's weird, I tell you.
| y + 9 | > 4
Subtract 9 from each side of the inequality:
<em> | y | > -5</em>
OK. Now, here we go:
'Absolute value' means just the size of the number, no matter whether it's
negative or positive. <em>So the absolute value of every number is positive</em>.
Got that ? <em>The absolute value of every number is positive</em>.
So <u>EVERY</u> number is a solution to this inequality. It doesn't matter what number
' y ' is, its absolute value is always positive. And if the absolute value is always
positive, then it's definitely always greater than -5 .
Weird ? I told you so.
Answer:
.
Step-by-step explanation:
The equation of a circle of radius centered at is:
.
.
Differentiate implicitly with respect to to find the slope of tangents to this circle.
.
Apply the power rule and the chain rule. Treat as a function of , .
.
.
That is:
.
Solve this equation for :
.
The slope of the tangent to this circle at point will thus equal
.
Apply the slope-point of a line in a cartesian plane:
, where
- is the gradient of this line, and
- are the coordinates of a point on that line.
For the tangent line in this question:
- ,
- .
The equation of this tangent line will thus be:
.
That simplifies to
.
Answer:
A = 32°, a = 19, b = 14, B=22.98°, C = 125.02°, c = 29.36
Step-by-step explanation:
We have two sides of the triangle and we have an angle.
A = 32 °, a = 19, b = 14
We use the sine theorem to find the angle B.
We know that according to the sine theorem it is true that:
We know that the sum of the internal angles of a triangle is always equal to 180.
So:
Finally we find the c side