Answer:
-1 < x < 4.
Step-by-step explanation:
- 6 < 2x - 4 <4
2x - 4 < 4
2x < 8
x < 4. Also we have:
2x - 4 > -6
2x > -2
x > -1.
Answer:
"the sum of the cube of 6x and 2"
Step-by-step explanation:
We see that only the expression of 6x is being cubed, not the entire expression of (6x)³ + 2.
The first blank must apply to both these terms 6x and 2, so the word can't be cubed. Instead, because we're finding the sum of these two, the word should be "sum".
The second blank should apply to only the 6x because we've already described the relationship of 6x and 2. So, since we are cubing 6x, the word here should be "cube".
The final sentence should read:
"the sum of the cube of 6x and 2"
Answer:
10 and 40 I think maybe?
Step-by-step explanation:
I hope this is correct if not I am so so so so so so sorry
The complete question in the attached figure
Part a)
we know that
ABC is a right triangle
∠ACB=45°
AC=hypotenuse------> 6√2 cm
sin 45=AB/AC-----> AB=AC*sin 45----> AB=6√2*√2/2----> AB=6 cm
the answer part a) isAB=6 cmPart b)
we know that
volume of the pyramid=(1/3)*Area of the base*height
area of the base=50 cm²
height=6 cm
so
volume of the pyramid=(1/3)*50*6----> 100 cm³
the answer part b) is 100 cm³
The tangent line to <em>y</em> = <em>f(x)</em> at a point (<em>a</em>, <em>f(a)</em> ) has slope d<em>y</em>/d<em>x</em> at <em>x</em> = <em>a</em>. So first compute the derivative:
<em>y</em> = <em>x</em>² - 9<em>x</em> → d<em>y</em>/d<em>x</em> = 2<em>x</em> - 9
When <em>x</em> = 4, the function takes on a value of
<em>y</em> = 4² - 9•4 = -20
and the derivative is
d<em>y</em>/d<em>x</em> (4) = 2•4 - 9 = -1
Then use the point-slope formula to get the equation of the tangent line:
<em>y</em> - (-20) = -1 (<em>x</em> - 4)
<em>y</em> + 20 = -<em>x</em> + 4
<em>y</em> = -<em>x</em> - 24
The normal line is perpendicular to the tangent, so its slope is -1/(-1) = 1. It passes through the same point, so its equation is
<em>y</em> - (-20) = 1 (<em>x</em> - 4)
<em>y</em> + 20 = <em>x</em> - 4
<em>y</em> = <em>x</em> - 24
