Given:
The function is:
![h(x)=x^2-3x+5](https://tex.z-dn.net/?f=h%28x%29%3Dx%5E2-3x%2B5)
To find:
The value of
.
Solution:
We have,
![h(x)=x^2-3x+5](https://tex.z-dn.net/?f=h%28x%29%3Dx%5E2-3x%2B5)
Putting
, we get
![h(2x+1)=(2x+1)^2-3(2x+1)+5](https://tex.z-dn.net/?f=h%282x%2B1%29%3D%282x%2B1%29%5E2-3%282x%2B1%29%2B5)
![h(2x+1)=(2x)^2+2(2x)(1)+(1)^2-3(2x)-3(1)+5](https://tex.z-dn.net/?f=h%282x%2B1%29%3D%282x%29%5E2%2B2%282x%29%281%29%2B%281%29%5E2-3%282x%29-3%281%29%2B5)
![h(2x+1)=4x^2+4x+1-6x-3+5](https://tex.z-dn.net/?f=h%282x%2B1%29%3D4x%5E2%2B4x%2B1-6x-3%2B5)
On combining like terms, we get
![h(2x+1)=4x^2+(4x-6x)+(1-3+5)](https://tex.z-dn.net/?f=h%282x%2B1%29%3D4x%5E2%2B%284x-6x%29%2B%281-3%2B5%29)
![h(2x+1)=4x^2-2x+3](https://tex.z-dn.net/?f=h%282x%2B1%29%3D4x%5E2-2x%2B3)
Therefore, the required function is
.
Answer:
a) v(t) = 14-2t.
b) The particle is moving in a positive direction in the interval [0,7) and it's moving a negative direction in the interval ![(7,\infty)](https://tex.z-dn.net/?f=%287%2C%5Cinfty%29)
c) the particles changes direction at t=7.
Step-by-step explanation:
Recall that
. We will assume that whenever its velocity is positive, it is moving in a positive direction and that whenever the velocity is negative, it is moving in a negative direction. We know that the particle changes direction when the velocity passes from positive to negative or viceversa, as t goes by.
To calculate the velocity (t), we will derivate s(t) with respect to t. Recall that given a functio of the form
its derivative is
. Thus, using the properties of derivatives we get that
.
We can see that 14-2t>0 if 14>2t which is equivalent that 7>t. So the particle moves in a positive direction whenever
. On the same way, 14-2t<0 when t>7 (
and it changes direction at t=7 since it passes from positive to negative.
The answer is 216
Hope this helps
Answer:
584 square feet of carpet
Step-by-step explanation:
12 x 12 = 144
20 x 15 = 300
10 x 14 = 140
144 + 300 + 140 = 584
Answer:
VF= $3.281,42
Interes= 3.281,42 - 3.000= $281.42
Step-by-step explanation:
Dada la siguiente información:
Prestamo (P)= $3.000
Tasa (i)= 0,015/2= 0,0075
Cantidad de periodos (n)= 6*2= 12 semestres
<u>Para calcular el valor final del prestamos, tenemos que usar la siguiente formula:</u>
VF= P*(1 + i)^n
VF= 3.000*1,0075^12
VF= $3.281,42
Interes= 3.281,42 - 3.000= $281.42