Answer:
37 units
Step-by-step explanation:
The two points form a right triangle so
a²+b²=c² so
(8-20)²(x values)+(40-5)²(y values)=c² (distance) so
12²+35²=c² so
144+1225=c²
1369=c²
c=37 units
(a) converges; consider the function <em>f(x)</em> = <em>a</em> ˣ, which converges to 0 as <em>x</em> gets large for |<em>a</em> | < 1. Then the limit is 2.
(b) converges; we have
4ⁿ / (1 + 9ⁿ) = (4ⁿ/9ⁿ) / (1/9ⁿ + 9ⁿ/9ⁿ) = (4/9)ⁿ × 1/(1/9ⁿ + 1)
As <em>n</em> gets large, the exponential terms vanish; both (4/9)ⁿ → 0 and 1/9ⁿ → 0, so the limit is 1.
(c) converges; we know ln(<em>n</em> ) → ∞ and arctan(<em>n</em> ) → <em>π</em>/2 as <em>n</em> → ∞. So the limit is <em>π</em>/2.
Answer and Step-by-step explanation:
Section the figure into two 3D shapes.
We get both figures to be a rectangular prism.
The Volume of a rectangular prism is length times width times height.
V (of top Rectangular Prism) = 2 × 2 × 4 = 16
V (of bottom Rectangular Prism) = 6 × 4 × 2 = 48
Now, we add those two volumes together to get the volume of the irregular figure.
16 + 48 = 64.
<u><em>The volume of the irregular figure is 64 </em></u>
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<u><em>#teamtrees #PAW (Plant And Water)</em></u>
Answer:
The translation for the above map points is 8 units up and 5 units left.
Step-by-step explanation:

The translation for the above map points is 8 units up and 5 units left.
Step 1: 8 units up
(Add 8 to y co-ordinate) 
Step 2: 5 units left
(subtract 5 from x-co-ordinate) 