Answer:
x = 18 degrees
Step-by-step explanation:
because lines n and m are parallel, 3x and 126 are same side interior angles. This means that when added up they equal 180, so make an equation as so:
3x + 126 = 180
Solve for it and x will equal 18.
Answer:
394.9 cm
Step-by-step explanation:
The formula for a cone's surface area is A = π r ( r + √r^2 + h^2 ).
r = radius
h = height
The Pythagorean theorem, a^2 + b^2 = c^2, will be needed to find the height.
Plug in the values.
a(unknown)^2 + 6^2 = 15^2
A + 36 = 255
255 - 36 = 189
√189 ≈ 13.7
Surface area formula, plug in the values.
A = 3.14 × 6 ( 6 + √6^2 + 13.7^2 )
*PEMDAS*
A = 3.14 × 6 ( 6 + √36 + 187.69 )
A = 3.14 × 6 ( 6 + √223.69 )
A = 3.14 × 6 ( 6 + 14.95 )
A = 3.14 × 6 ( 20.96 )
A = 3.14 × 125.76
A = 394.8864
*round to nearest tenth*
A = 394.9 cm
Hope this helps! :)
(a) The "average value" of a function over an interval [a,b] is defined to be
(1/(b-a)) times the integral of f from the limits x= a to x = b.
Now S = 200(5 - 9/(2+t))
The average value of S during the first year (from t = 0 months to t = 12 months) is then:
(1/12) times the integral of 200(5 - 9/(2+t)) from t = 0 to t = 12
or 200/12 times the integral of (5 - 9/(2+t)) from t= 0 to t = 12
This equals 200/12 * (5t -9ln(2+t))
Evaluating this with the limits t= 0 to t = 12 gives:
708.113 units., which is the average value of S(t) during the first year.
(b). We need to find S'(t), and then equate this with the average value.
Now S'(t) = 1800/(t+2)^2
So you're left with solving 1800/(t+2)^2 = 708.113
<span>I'll leave that to you</span>
Answer:
1 3/8
Step-by-step explanation:
3 2/3 = 11/3
2 2/3 = 8/3
11/3 / 8/3 = 11/3*3/8 = 11/8 = 1 3/8
