<span><span>220<span> cm2</span>/s </span>
EXPLINATION</span>
L length of rectangel (cm)
W width of rectangel(cm)
A area of rectangel (cm²)
T time (s)
we are told that:
d1\dt=8cm\s(const),and dw\dt =3cm\s(const)
the area of the rectangel is
A=LW
Differentiating wrt t (using the product rule) we get;
<span><span><span>dA</span><span>dt</span></span>=<span>(l)</span><span>(<span><span>dw</span><span>dt</span></span>)</span>+<span>(<span><span>dl</span><span>dt</span></span>)</span><span>(w)</span></span>
∴<span><span>dA</span><span>dt</span></span>=3l+8w
So when <span>l=20</span><span> and </span><span>w=10⇒</span>
<span> <span><span>dA</span><span>dt</span></span>=3⋅20+8⋅20</span>
<span>∴<span><span>dA</span><span>dt</span></span>=60+160</span>
<span>∴<span><span>dA</span><span>dt</span></span>=220<span> cm2</span>/<span>s</span></span>
Step-by-step explanation:
I cant show a number line so i'll do my best to explain how its graphed.
15) x - 1 < 15
add 1 to both sides:
x < 16
Because it is less than, rather than less than or equal to, it's graphed with an open circle (not filled in) on 16, and everything less than 16 highlighted
---------------------------------------------------------
16) 2(y + 1) - 2 ≥ 12
distribute the 2:
2y + 2 - 2 ≥ 12
combine like terms
2y ≥ 12
isolate y:
y ≥ 6
This one is greater than or equal to, so it's graphed with a closed circle (filled in) and everything above 6 highlighted
In part A, we need to solve for the total length of sides 1, 2 and 3.
Since all three sides measurements are given, we have the solution below:
Sides123 = Side 1 + Side 2 + Side 3
Sides123 = (3y² + 2y - 6) + (4y² + 3y -7) + (5y² + 4y -8)
Sides123 = 12y² + 9y - 21
This is the total length of sides 1,2 and 3 "12y² + 9y - 21"
In part B, we need to solve for the length of the fourth side and the solution is shown below:
Side 4 = Perimeter / Sides123
Side 4 = (4y³ + 18y² + 16y -26) / 12y² + 9y -21
Surface area of a sphere = <span>4π<span>r2</span></span>
the volume of a sphere= <span><span>43</span>π<span>r3</span></span>
so <span>5000π=<span>4/3</span><span>πr3
</span></span><span>> r^3 = 5000 x 3 / 4
=>
r^3 = 3750
</span>taking cube root on both sides
r=15.53616
hope it helps
To find the rate of change, you look at how much the y value increases with a change of 1 x. We see that as x increases from 1 to 2, y increases from 120 to 144. Then we subtract 144-120 to find the rate of change, which is just 24 (also note that x changes by 1 here).
Then for the initial value:
We see that y increases by 24 for 1 x, so subtracting the value at x=1 by 24 we get 120-24 = 96, which is the initial value.
Hope this helps
