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4 years ago

9

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1 answer:

Radda [10]4 years ago

6 0

Answer:

h = f(t) = -15cos((π/5)t) +20

Step-by-step explanation:

If you like, you can make a little table of positions:

(t, h) = (0, 5), (5, 35)

Since the wheel is at an extreme position at t=0, a cosine function is an appropriate model:

h = Acos(kt) +C

The amplitude A of the function is half the difference between the t=0 value and the t=5 value:

A = (1/2)(5 -35) = -15

The midline value C is the average of the maximum and minimum:

C = (1/2)(5 + 35) = 20

The factor k satisfies the relation ...

k = 2π/period = 2π/10 = π/5

So, the function can be written as ...

h = f(t) = -15cos((π/5)t) +20

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3 years ago

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3 years ago

Read 2 more answers

The 3rd term of a geometric sequence is -1/3 and the 8th term is 81. what is the 11th term?

shepuryov [24]

Answer: $t_{11}=-2187$

Step-by-step explanation:

$t_{3}=-1/3$

That is :

$ar^{2} = -1/3$ ................. equation 1

Also

$t_{8}=81$

that is

$ar^{7}=81$ ................. equation 2

divide equation 2 by equation 1 , that is

$\frac{ar^{7}}{ar^{2}} = 81 / -1/3$

$r^{5}=$ $81$ x $-3/1$

$r^{5}= -243$

find the fifth root of both sides

$r = -3$

substitute $r = -3$ , into equation 1 to find a , that is

$a(-3^{2})= -1/3$

$9a = -1/3$

multiply through by 3

$27a = -1$

$a =- 1/27$

To find the 11th term , the formula for the 11th term is given as :

$t_{11}=ar^{10}$

$t_{11}= -1/27(-3^{10})$

$t_{11}=-2187$

6 0

4 years ago

Terence makes $11.50 per hour selling ice cream in the summer. He worked for 6 hours on Saturday and for h hours on Sunday. Writ

Airida [17]

Answer:

t= 11.50h + 6

and

t= 11.50+6+h

Step-by-step explanation:

t= total amount of wages

11.50 x h =

11.50h + 6

t= 11.50h + 6

and

t= 11.50+6+h

6 0

4 years ago

The base and sides of a container is made of wood panels. The container does not have a lid. The base and sides are rectangular.

vfiekz [6]

Answer:

Minimum surface area = $70.77 cm^2$

Step-by-step explanation:

We are given that

Width of container=x cm

Length of container=2x cm

Volume of container= $54 cm^3$

We have to find the minimum surface areas that this container will have.

Volume of container= $l\times b\times h$

$x\times 2x\times h=54$

$2x^2h=54$

$h=\frac{54}{2x^2}=\frac{27}{x^2}$

Surface area of container= $2(b+l)h+lb$

Because the container does not have lid

Surface area of container= $S=2(2x+x)\times \frac{27}{x^2}+2x\times x$

$S=\frac{162}{x}+2x^2$

Differentiate w.r.t x

$\frac{dS}{dx}=-\frac{162}{x^2}+4x$

$\frac{dx^n}{dx}=nx^{n-1}$

Substitute $\frac{dS}{dx}=0$

$-\frac{162}{x^2}+4x=0$

$4x=\frac{162}{x^2}$

$x^3=\frac{162}{4}=40.5$

$x^3=40.5$

$x=(40.5)^{\frac{1}{3}}$

$x=3.4$

Again differentiate w.r.t x

$\frac{d^2S}{dx^2}=\frac{324}{x^3}+4$

Substitute x=3.4

$\frac{d^2S}{dx^2}=\frac{324}{(3.4)^3}+4=12.24>0$

Hence, function is minimum at x=3.4

Substitute x=3.4

Then, we get

Minimum surface area = $\frac{162}{(3.4)}+2(3.4)^2=70.77 cm^2$

8 0

3 years ago