Answer:
i have the same question
Step-by-step explanation:
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Decuct 30 minutes from 10:08 = 09:38
Answer:
![x \geq -\frac{7}{2}](https://tex.z-dn.net/?f=x%20%5Cgeq%20-%5Cfrac%7B7%7D%7B2%7D)
Step-by-step explanation:
we have
![y=4\sqrt{2x+7}](https://tex.z-dn.net/?f=y%3D4%5Csqrt%7B2x%2B7%7D)
we know that
The radicand must be greater than or equal to zero
so
![2x+7 \geq 0](https://tex.z-dn.net/?f=2x%2B7%20%5Cgeq%200)
Solve for x
Subtract 7 both sides
![2x+7-7 \geq 0-7](https://tex.z-dn.net/?f=2x%2B7-7%20%5Cgeq%200-7)
![2x \geq -7](https://tex.z-dn.net/?f=2x%20%5Cgeq%20-7)
Divide by 2 both sides
![x \geq -\frac{7}{2}](https://tex.z-dn.net/?f=x%20%5Cgeq%20-%5Cfrac%7B7%7D%7B2%7D)
The domain is the interval --------> [-7/2,∞)
Answer:
y=x/2-1/4
Step-by-step explanation:
From exercise we have
C=0.
dy/dx+2y=x
Use the formula:
∫xe^(2x)dx=e^(2x)(x/2−1/4).
We know that a linear differential equation is written in the standard form:
y' + a(x)y = f(x)
we get that: a(x)=2 and f(x)=x.
We know that the integrating factor is defined by the formula:
u(x)=e^{∫ a(x) dx}
⇒ u(x)=e^{∫ 2 dx} = e^{2x}
The general solution of the differential equation is in the form:
y=\frac{ ∫ u(x) f(x) dx +C}{u(x)}
⇒ y=\frac{ ∫ e^{2x}· x dx + 0}{e^{2x}}
y=\frac{e^{2x} (x/2-1/4)}{e^{2x}
y=x/2-1/4
Step-by-step explanation:
![\underline{\underline{\sf{➤ \:\: Solution }}}](https://tex.z-dn.net/?f=%5Cunderline%7B%5Cunderline%7B%5Csf%7B%E2%9E%A4%20%5C%3A%5C%3A%20Solution%20%7D%7D%7D)
![\sf\: \: \: \dfrac{1}{ \sqrt{3} - \sqrt{2} }](https://tex.z-dn.net/?f=%20%5Csf%5C%3A%20%5C%3A%20%20%5C%3A%20%20%5Cdfrac%7B1%7D%7B%20%5Csqrt%7B3%7D%20-%20%20%5Csqrt%7B2%7D%20%20%7D%20)
On rationalising,
![\sf \implies \dfrac{1}{ \sqrt{3} - \sqrt{2} } \times \dfrac{\sqrt{3} + \sqrt{2} }{\sqrt{3} + \sqrt{2} }](https://tex.z-dn.net/?f=%20%5Csf%20%5Cimplies%20%20%5Cdfrac%7B1%7D%7B%20%5Csqrt%7B3%7D%20-%20%20%5Csqrt%7B2%7D%20%20%7D%20%20%20%5Ctimes%20%20%5Cdfrac%7B%5Csqrt%7B3%7D%20%20%2B%20%20%5Csqrt%7B2%7D%20%7D%7B%5Csqrt%7B3%7D%20%20%2B%20%20%5Csqrt%7B2%7D%20%7D%20)
Combine the fractions,
![\sf \implies \dfrac{1(\sqrt{3} + \sqrt{2}) }{(\sqrt{3} - \sqrt{2})(\sqrt{3} + \sqrt{2}) }](https://tex.z-dn.net/?f=%20%5Csf%20%5Cimplies%20%20%20%5Cdfrac%7B1%28%5Csqrt%7B3%7D%20%20%2B%20%20%5Csqrt%7B2%7D%29%20%7D%7B%28%5Csqrt%7B3%7D%20-%20%20%5Csqrt%7B2%7D%29%28%5Csqrt%7B3%7D%20%20%2B%20%20%5Csqrt%7B2%7D%29%20%7D%20)
We know that,
![\sf \implies (a - b)(a + b) = (a)^{2} - (b)^{2}](https://tex.z-dn.net/?f=%20%5Csf%20%5Cimplies%20%20%20%28a%20-%20b%29%28a%20%2B%20b%29%20%3D%20%28a%29%5E%7B2%7D%20%20-%20%28b%29%5E%7B2%7D%20)
So,
![\sf \implies \dfrac{1(\sqrt{3} + \sqrt{2}) }{(\sqrt{3})^{2} - (\sqrt{2}) ^{2} }](https://tex.z-dn.net/?f=%20%5Csf%20%5Cimplies%20%20%20%5Cdfrac%7B1%28%5Csqrt%7B3%7D%20%20%2B%20%20%5Csqrt%7B2%7D%29%20%7D%7B%28%5Csqrt%7B3%7D%29%5E%7B2%7D%20%20-%20%20%28%5Csqrt%7B2%7D%29%20%5E%7B2%7D%20%7D)
![\sf \implies \dfrac{1(\sqrt{3} + \sqrt{2}) }{3 - 2 }](https://tex.z-dn.net/?f=%20%5Csf%20%5Cimplies%20%20%20%5Cdfrac%7B1%28%5Csqrt%7B3%7D%20%20%2B%20%20%5Csqrt%7B2%7D%29%20%7D%7B3%20-%20%202%20%7D)
![\sf \implies \dfrac{1(\sqrt{3} + \sqrt{2}) }{1 }](https://tex.z-dn.net/?f=%20%5Csf%20%5Cimplies%20%20%20%5Cdfrac%7B1%28%5Csqrt%7B3%7D%20%20%2B%20%20%5Csqrt%7B2%7D%29%20%7D%7B1%20%7D)
![\sf \implies ( \sqrt{3} + \sqrt{2})](https://tex.z-dn.net/?f=%20%5Csf%20%5Cimplies%20%20%28%20%5Csqrt%7B3%7D%20%20%2B%20%20%5Csqrt%7B2%7D%29%20)
Hence,
On rationalising we got,
![\implies \bf (\sqrt{3} + \sqrt{2})](https://tex.z-dn.net/?f=%5Cimplies%20%20%5Cbf%20%28%5Csqrt%7B3%7D%20%20%2B%20%20%5Csqrt%7B2%7D%29%20)