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3 years ago

Find the area of the trapezoid below. 4 cm 3 cm 8 cm

Mathematics

2 answers:

bixtya [17]3 years ago

8 0

Answer:

13 it is very easy

Step-by-step explanation:

kkurt [141]3 years ago

4 0

Which numbers are the bases?

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What is the inverse of y=-x-4

Nimfa-mama [501]

Answer:

$f^-1 -1(x)=x+4$

Step-by-step explanation:

i hope this helps

8 0

3 years ago

Consider the initial value problem y′+5y=⎧⎩⎨⎪⎪0110 if 0≤t<3 if 3≤t<5 if 5≤t<[infinity],y(0)=4. y′+5y={0 if 0≤t<311 i

rosijanka [135]

It looks like the ODE is

$y'+5y=\begin{cases}0&\text{for }0\le t$

with the initial condition of $y(0)=4$ .

Rewrite the right side in terms of the unit step function,

$u(t-c)=\begin{cases}1&\text{for }t\ge c\\0&\text{for }t$

In this case, we have

$\begin{cases}0&\text{for }0\le t$

The Laplace transform of the step function is easy to compute:

$\displaystyle\int_0^\infty u(t-c)e^{-st}\,\mathrm dt=\int_c^\infty e^{-st}\,\mathrm dt=\frac{e^{-cs}}s$

So, taking the Laplace transform of both sides of the ODE, we get

$sY(s)-y(0)+5Y(s)=\dfrac{e^{-3s}-e^{-5s}}s$

Solve for $Y(s)$ :

$(s+5)Y(s)-4=\dfrac{e^{-3s}-e^{-5s}}s\implies Y(s)=\dfrac{e^{-3s}-e^{-5s}}{s(s+5)}+\dfrac4{s+5}$

We can split the first term into partial fractions:

$\dfrac1{s(s+5)}=\dfrac as+\dfrac b{s+5}\implies1=a(s+5)+bs$

If $s=0$ , then $1=5a\implies a=\frac15$ .

If $s=-5$ , then $1=-5b\implies b=-\frac15$ .

$\implies Y(s)=\dfrac{e^{-3s}-e^{-5s}}5\left(\frac1s-\frac1{s+5}\right)+\dfrac4{s+5}$

$\implies Y(s)=\dfrac15\left(\dfrac{e^{-3s}}s-\dfrac{e^{-3s}}{s+5}-\dfrac{e^{-5s}}s+\dfrac{e^{-5s}}{s+5}\right)+\dfrac4{s+5}$

Take the inverse transform of both sides, recalling that

$Y(s)=e^{-cs}F(s)\implies y(t)=u(t-c)f(t-c)$

where $F(s)$ is the Laplace transform of the function $f(t)$ . We have

$F(s)=\dfrac1s\implies f(t)=1$

$F(s)=\dfrac1{s+5}\implies f(t)=e^{-5t}$

We then end up with

$y(t)=\dfrac{u(t-3)(1-e^{-5t})-u(t-5)(1-e^{-5t})}5+5e^{-5t}$

3 0

4 years ago

The sides of a triangle have measures of 2x, 8, 12. If the measure of the longest side is 2x. What value of x makes the triangle

Strike441 [17]

Answer:

8+12= 2x

multiply all of them by power of 2

Step-by-step explanation:

so,

64+144 = 4x

208=4x

x = 52 what is the root of 52 the answer is

x = 7.188 or 3/16

4 0

3 years ago

A. Find y in terms of x if ????y????x=x6y−7 and y(0)=4. y(x)= (8/7x^7+4^8)^(1/8) . B. For what x-interval is the solution define

topjm [15]

Answer:

Step-by-step explanation:

part A)

given

$x=x6y-7$

so y in terms of x would be

$y=(x+7)/x6$

part b)

in order to find intervals of function, we determine the intervals where the function has a positive first derivative . To find intervals, first we find the critical values, or points at which the first derivative of the function is equal to zero. For the given function the intervals would be

put zero in equation

$y=(x+7)/6x$