Answer:
7.07 (3 significant figures)
Step-by-step explanation:
the distance between the two points on the x axis is 5 and the distance between the two point son the y axis is 5. thus by using pythagerous theorem you are able to get the hypotenuse which is the distance between the two points which in this case is 7.07 when rounded to 3 significant figures. not sure if im correct but i hope it helps
Answer:
14
Step-by-step explanation:
We solve this by using 2 to open the bracket
(3+4)2 is the same as 2(3+4)
2(3)+2(4)
=6+8
=14
OR
(3+4)2 is the same as 2(3+4)
So we can solve the one inside the bracket first
=2(7)=14
Answer:
262 and 263 are consecutive natural numbers whose sum is 525.
Step-by-step explanation:
Natural number are a subset of real numbers consisting in positive integers (i.e. 1, 2, 3, 525) and two natural numbers are consecutive when distance between each other is equal to 1. (
, 
) We can interpret the statement mathematically by means of the following expression:
Where 
, 
, 
.
This system is reduced to a single equation and solved afterwards:
Now we evaluate and to obtain the natural numbers:
262 and 263 are consecutive natural numbers whose sum is 525.
Sandwich cost $7.70 and the soda costs $2.20.
We can find this using the formula: L= ∫√1+ (y')² dx
First we want to solve for y by taking the 1/2 power of both sides:
y=(4(x+1)³)^1/2
y=2(x+1)^3/2
Now, we can take the derivative using the chain rule:
y'=3(x+1)^1/2
We can then square this, so it can be plugged directly into the formula:
(y')²=(3√x+1)²
<span>(y')²=9(x+1)
</span>(y')²=9x+9
We can then plug this into the formula:
L= ∫√1+9x+9 dx *I can't type in the bounds directly on the integral, but the upper bound is 1 and the lower bound is 0
L= ∫(9x+10)^1/2 dx *use u-substitution to solve
L= ∫u^1/2 (du/9)
L= 1/9 ∫u^1/2 du
L= 1/9[(2/3)u^3/2]
L= 2/27 [(9x+10)^3/2] *upper bound is 1 and lower bound is 0
L= 2/27 [19^3/2-10^3/2]
L= 2/27 [√6859 - √1000]
L=3.792318765
The length of the curve is 2/27 [√6859 - √1000] or <span>3.792318765 </span>units.
