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2 years ago

Evaluate the expression for the given value of the variable 5 ×(h+3) for h=7

Mathematics

1 answer:

Bad White [126]2 years ago

5 0

Answer:

Step-by-step explanation:

Put h = 7 to the expression 5 · (h + 3):

$5\cdot(7+3)=5\cdot10=50$

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What is the discriminant of the quadratic equation 3 – 4x = –6x2?

kogti [31]

3-4x=-6x^2
+6x^2=+6x^2
_____________
6x^2+3-4x=0
6x^2-4x+3=0

(-4)^2-4(6)(3)
16-72
Final Answer: -56

5 0

3 years ago

Read 2 more answers

Consider the differential equation:

Wewaii [24]

(a) Take the Laplace transform of both sides:

$2y''(t)+ty'(t)-2y(t)=14$

$\implies 2(s^2Y(s)-sy(0)-y'(0))-(Y(s)+sY'(s))-2Y(s)=\dfrac{14}s$

where the transform of $ty'(t)$ comes from

$L[ty'(t)]=-(L[y'(t)])'=-(sY(s)-y(0))'=-Y(s)-sY'(s)$

This yields the linear ODE,

$-sY'(s)+(2s^2-3)Y(s)=\dfrac{14}s$

Divides both sides by $-s$ :

$Y'(s)+\dfrac{3-2s^2}sY(s)=-\dfrac{14}{s^2}$

Find the integrating factor:

$\displaystyle\int\frac{3-2s^2}s\,\mathrm ds=3\ln|s|-s^2+C$

Multiply both sides of the ODE by $e^{3\ln|s|-s^2}=s^3e^{-s^2}$ :

$s^3e^{-s^2}Y'(s)+(3s^2-2s^4)e^{-s^2}Y(s)=-14se^{-s^2}$

The left side condenses into the derivative of a product:

$\left(s^3e^{-s^2}Y(s)\right)'=-14se^{-s^2}$

Integrate both sides and solve for $Y(s)$ :

$s^3e^{-s^2}Y(s)=7e^{-s^2}+C$

$Y(s)=\dfrac{7+Ce^{s^2}}{s^3}$

(b) Taking the inverse transform of both sides gives

$y(t)=\dfrac{7t^2}2+C\,L^{-1}\left[\dfrac{e^{s^2}}{s^3}\right]$

I don't know whether the remaining inverse transform can be resolved, but using the principle of superposition, we know that $\frac{7t^2}2$ is one solution to the original ODE.

$y(t)=\dfrac{7t^2}2\implies y'(t)=7t\implies y''(t)=7$

Substitute these into the ODE to see everything checks out:

$2\cdot7+t\cdot7t-2\cdot\dfrac{7t^2}2=14$

5 0

3 years ago

What adds to 17 but multiplies to -200

ollegr [7]

-8 + 25= 17
-8 • 25 =-200

4 0

3 years ago

Help

jenyasd209 [6]

Step-by-step explanation:

1) when x= 1/5

y = 1/5 + 1/2

y = 7/10

2) when x= 1/4

y = 1/4 + 1/2

y= 3/4

3) when x= 1/3

y = 1/3 + 1/2

y = 5 /6

3 0

3 years ago

What is the quotient of 35.86 divided by 2.123

madam [21]

Answer:

Its just 16.

Step-by-step explanation:

6 0

2 years ago