Answer:;4.4
Step-by-step explanation: Since it varies inversely we know G times H squared is equal to some constant, k. So we have G*H*H=k. We are told that when H=4, G=.25. Plugging this in, we have .25*4*4=k. This simplifies to 4=k. Our new equation is G*H*H=4. Now, we want to solve for G when H=.3. We plug it in. G*.3*.3=4 => G*.09=4. G=4/.09. This means G is approximately 44.4.
Answer:
s(2) = 7.75
Step-by-step explanation:
given the velocity v(t) = t^3
we can find the position s(t) by simply integrating v(t) and using the boundary conditions s(1)=2

we know throught s(1) = 2, that at t=1, s =2. we can use this to find the value of the constant c.

Now we can use this value of t to formulate the position function s(t):

this is the position at time t.
to find the position at t=2



the position of the particle at time, t =2 is s(2) = 7.75
1-9 are all numbers that are less than 10, and 1 is included because the number can be greater than or equal to 1.
Hope this helped!
Answer:
a= 22.5
b= 37.5
Step-by-step explanation:
<u>In</u><u> </u><u>△</u><u>BCD</u><u>:</u>
Applying Pythagoras' Theorem,
a² +30²= b²
a² +900= b² -----(1)
<u>In</u><u> </u><u>△</u><u>ABC</u><u>:</u>
Applying Pythagoras' Theorem,
b² +50²= (40 +a)² -----(2)
Substitute (1) into (2):
a² +900 +50²= 40² +2(40)(a) +a²<em> </em><em> </em><em> </em><em> </em><em> </em><em>(</em><em>expand</em><em> </em><em>bracket</em><em>)</em>
a² +900 +2500= 1600 +80a +a²
a² +3400= a² +80a +1600 <em>(</em><em>simplify</em><em>)</em>
a² +3400 -a² -80a -1600= 0 <em>(</em><em>bring</em><em> </em><em>everything</em><em> </em><em>to</em><em> </em><em>1</em><em> </em><em>side</em><em>)</em>
-80a +1800= 0
80a= 1800 <em>(</em><em>+</em><em>8</em><em>0</em><em> </em><em>on</em><em> </em><em>both</em><em> </em><em>sides</em><em>)</em>
a= 1800 ÷80
a= 22.5
Subst. a= 22.5 into (1):
22.5² +900= b²
b²= 506.25 +900
b²= 1406.25
b= √1406.25 <em>(</em><em>square</em><em> </em><em>root</em><em> </em><em>both</em><em> </em><em>sides</em><em>)</em>
b= 37.5 <em>(</em><em>reject</em><em> </em><em>negative</em><em> </em><em>value</em><em> </em><em>since</em><em> </em><em>b</em><em> </em><em>is</em><em> </em><em>a</em><em> </em><em>length</em><em>)</em>
☆(a +b)²= a² +2ab +b²
The first step is to subtract 6 from both sides to cancel it out. You will be left with -3x= -1.