(1)
Here, s is a slant height and a is the altitude.
We can find s with the Pythagorean theorem.
s2 + 162 = 652
s2 = 652 - 162
s2 = 3969
s = 63
Now we can find a with the Pythagorean theorem.
a2 + 332 = s2
a2 + 332 = 632
a2 = 632 - 332
a2 = 2880
a = √[ 2880 ]
a = 24√5
*****edit*****
My original answer for lateral area wasn't right because I didn't take into account that the faces aren't all the same.
The same way we found s , we can find the length of the other slant height.
other slant height = √[ 652 - 332 ] = 56
lateral area = 2 * (1/2) * 32 * 63 + 2 * (1/2) * 66 * 56 = 32 * 63 + 66 * 56 = 5712 square units
And we can check this answer with this handy dandy calculator: here
**************
volume = (1/3) * area of base * altitude
volume = (1/3) * (32 * 66) * a
volume = (1/3) * (32 * 66) * 24√5
volume = 16896√5 cubic units
If you have a question about where any of these numbers came from please ask
In the sequence
1, 2, 2, 4, 8, 32, 256,...,
each term starting from the third term) is the product of the two terms before it. For example, the seventh term is 256, which is the product of the fifth term (8) and the sixth term (32).
This sequence can be continued forever, though the numbers very quickly grow enormous!
(For example, the 14th term is close to some estimates of the number of particles in the observable universe.)
What is the last digit of the 35th term of the sequence?
see: https://web2.0calc.com/questions/help-please_92099#r8
We're given a point and a slope so we can easily write the equation of the line in point-slope form.
The equation of the line in point-slope form is....
y - -4 = -\(\frac38\)(x - 5)
Now we just need to get this equation into standard form.
The standard form of a line is Ax + By = C where A is a positive integer, and B and C are integers.
y - -4 = -\(\frac38\)(x - 5)
y + 4 = -\(\frac38\)(x - 5)
Multiply both sides of the equation by 8 .
8(y + 4) = -3(x - 5)
Distribute the 8 and the -3
8y + 32 = -3x + 15
Add 3x to both sides of the equation.
3x + 8y + 32 = 15
Subtract 32 from both sides.
3x + 8y = -17
Now the equation is in standard form. Here's a graph: https://www.desmos.com/calculator/momem4spgv
___ | 9x2 - 6x - 24 | ____ | |
| Split -6x into two terms such that the product of their coefficients = (-24)(9) = -216 What two numbers add to -6 and multiply to -216 ?→ +12 and -18 | ||
= | 9x2 - 18x + 12x - 24 |
| Notice here that if we combine like terms we get back the previous expression. |
| Factor 9x out of the first two terms. | ||
= | 9x(x - 2) + 12x - 24 |
| Notice here that if we distribute 9x we get back the previous expression. |
| Factor 12 out of the last two terms. | ||
= | 9x(x - 2) + 12(x - 2) |
| Notice here that if we distribute 12 we get back the previous expression. |
| Factor (x - 2) out of both remaining terms. | ||
= | (x - 2)(9x + 12) | ||
We can factor 3 out of both terms in the second factor. We could have done this in the beginning which would have made the numbers smaller. | |||
= | (3)(x - 2)(3x+4) |