Answer:
8 girls
Step-by-step explanation:
We want write a ratio to solve
3 boys 12 boys
------------ = -------------------
2 girls x girls
Using cross products
3x = 2*12
3x = 24
Divide by 3
3x/3 = 24/3
x = 8
There are 8 girls
Answer:
-5/3
Step-by-step explanation:
To solve for slope we use the slope formula which is y2-y1/x2-x1.
For this problem I chose the points: (-5,10) and (-2,5)
-5 is x1, 10 is y1, -2 is x2 and 5 is y2
We now plug in the points into the slope formula:
5-10/-2-(-5)= -5/3
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.
Answer:
all work is shown and pictured