168cm2
Let r cm be the radius of the balloon, then
<span>2pi(r)=23=>r=23/(2pi) </span>
<span>The surface area= </span>
<span>4pi(r^2)= </span>
<span>4pi[23/2pi)]^2= </span>
<span>(23^2)/pi=168.386 cm^2 </span>
<span>approximately.</span>
An= mth term.
an=a₁+(n-1)*d
a₁₂=41
a₁₅=140
a₁₂=41
41=a₁+(12-1)*d
41=a₁+11d
a₁+11d=41 (1)
a₁₅=140
140=a₁+(15-1)*d
140=a₁+14d
a₁+14d=140 (2)
With the equiations (1) and (2) build a system of equations
a₁+11d=41
a₁+14d=140
we solve it.
-(a₁+11d=41)
a₁+14d=140
--------------------
3d=99 ⇒d=99/3=33
a₁+11d=41
a₁+(11*33)=41
a₁+363=41
a₁=41-363=-322
an=a₁+(n-1)*d
an=-322+(n-1)*33
an=-322+33n-33
an=-355+33n
an=-355+33n
To check:
a₁₂=-355+33*12=-355+396=41
a₁₅=-355+33*15=-355+495=140.
Answer:
angle 2
Step-by-step explanation:
adds up to 180 degrees
Answer:
Step-by-step explanation:
f(x) = 3x² -5x - 1
f'(x) =2*3x - 5*1 +0
= 6x - 5
f'(4) = 6*4 - 5
= 24 - 5
= 19
Answer:
See attached
Step-by-step explanation:
When there is a lot of repetitive calculation to do, I like to let a spreadsheet or graphing calculator do it. The attached shows a spreadsheet that computes all the values you're asked to find.
For a linear equation in standard form, ax +by = c
- the x-intercept is: c/a
- the y-intercept is: c/b
- the slope is: m = -a/b
Of course, the slope-intercept form of the equation is ...
y = (slope)·x + (y-intercept)
and the values of the various points on the graph can be computed from that equation.
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You will note that the last two equations describe the same line.
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<em>Note on spreadsheet formulas</em>
When you put the formulas into the spreadsheet, make sure to fix the column number or row number of the values you're computing, as appropriate. For example, the y-values in the different columns always use the slope from the slope column (fixed), the y-intercept from that column (fixed), and the x-value from the top row (fixed). If you make the cell references relative instead of fixed, you will get wrong answers.