(a) It looks like the ODE is
<em>y'</em> = 4<em>x</em> √(1 - <em>y </em>^2)
which is separable:
d<em>y</em>/d<em>x</em> = 4<em>x</em> √(1 - <em>y</em> ^2) => d<em>y</em>/√(1 - <em>y</em> ^2) = 4<em>x</em> d<em>x</em>
Integrate both sides. On the left, substitute <em>y</em> = sin(<em>t </em>) and d<em>y</em> = cos(<em>t</em> ) d<em>t</em> :
∫ d<em>y</em>/√(1 - <em>y</em> ^2) = ∫ 4<em>x</em> d<em>x</em>
∫ cos(<em>t</em> ) / √(1 - sin^2(<em>t</em> )) d<em>t</em> = ∫ 4<em>x</em> d<em>x</em>
∫ cos(<em>t</em> ) / √(cos^2(<em>t</em> )) d<em>t</em> = ∫ 4<em>x</em> d<em>x</em>
∫ cos(<em>t</em> ) / |cos(<em>t</em> )| d<em>t</em> = ∫ 4<em>x</em> d<em>x</em>
Since we want the substitutiong to be reversible, we implicitly assume that -<em>π</em>/2 ≤ <em>t</em> ≤ <em>π</em>/2, for which cos(<em>t</em> ) > 0, and in turn |cos(<em>t</em> )| = cos(<em>t</em> ). So the left side reduces completely and we get
∫ d<em>t</em> = ∫ 4<em>x</em> d<em>x</em>
<em>t</em> = 2<em>x</em> ^2 + <em>C</em>
arcsin(<em>y</em>) = 2<em>x</em> ^2 + <em>C</em>
<em>y</em> = sin(2<em>x</em> ^2 + <em>C </em>)
(b) There is no solution for the initial value <em>y</em> (0) = 4 because sin is bounded between -1 and 1.
Answer:
The deer population decreased. The producers increased. So the number of different species increased.
Step-by-step explanation:
wolves are reintroduced ---> deer population decreases --> producer population begins to increase --> other species numbers increase as well
Answer:
In the procedure
Step-by-step explanation:
we have
<em>System 1</em>
Ax+By=C -----> equation A
Lx+My=N -----> equation B
<em>step 1</em>
Multiply equation B by -1 both sides
(-1)*(Lx+My=)N*(-1)
-Lx-My=-N ------> equation C
<em>step 2</em>
Adds equation A and equation C
Ax+By=C
-Lx-My=-N
----------------
Ax-Lx+By-My=C-N
(A-L)x+(B-M)y=C-N -----> equation D
step 3
An equivalent system (System 2) is formed with
Ax+By=C -----> equation A
(A-L)x+(B-M)y=C-N -----> equation D
Answer:
H0: σ1=σ2
Ha : σ1 >σ2
B. Upper H 0H0:
sigma Subscript 1 Superscript 2σ21equals=sigma Subscript 2 Superscript 2σ22
Upper H 1H1:
sigma Subscript 1 Superscript 2σ21greater than>sigma Subscript 2 Superscript 2σ22
Step-by-step explanation:
The claim is that the treatment group has errors that <em><u>vary significantly</u></em> more than the errors of the placebo group.
The claim is the alternative hypothesis and the opposite of claim is the null hypothesis.
Vary significantly means that it is greater than so we choose the alternate hypothesis of greater than and the null hypothesis will be equal to errors of the placebo group.
So the correct choice is B.
B. Upper H 0H0:
sigma Subscript 1 Superscript 2σ21equals=sigma Subscript 2 Superscript 2σ22
Upper H 1H1:
sigma Subscript 1 Superscript 2σ21greater than>sigma Subscript 2 Superscript 2σ22
Choice A,C and D all are incorrect.
This can be written as
H0: σ1=σ2
Ha : σ1 >σ2
Answer:
18 days
Step-by-step explanation:
brailiest please!
