If f(x) = 2x+1 and g(x) = 3x-2 Find f[g(1)] =

The ordered pairs (t, 36), (5, 45) represent a proportional relationship. Find the value of t.

olasank [31]

The answer for t is 4 and the proportional relationship is 9

6 0

3 years ago

The population of Weston is 4320. The town’s records show that 45 percent of the population are males, and 2 3 23 of these males

lbvjy [14]

Answer:

In Weston 1,296 males are married

Step-by-step explanation:

step 1

Find out the number of males

Multiply the total population by 45%

$45\%=45/100=0.45$

$4,320(0.45)=1,944\ males$

step 2

Find out the number of males that are married

Multiply the number of males by 2/3

$\frac{2}{3}(1,944)=1,296\ males\ married$

therefore

In Weston 1,296 males are married

7 0

3 years ago

A young sumo wrestler decided to go on a diet to gain weight rapidly. He gained weight at a rate of 5.5kg a month. After 11 mont

kondaur [170]

Answer:

$W(t)=5.5t+79.5$ .

Step-by-step explanation:

Please consider the complete question.

A young sumo wrestler decided to go on a special high-protein diet to gain weight rapidly. He gained weight at a rate of 5.5 kilograms per month. After 11 months, he weighed 140 kilograms. Let W(t) denote the sumo wrestler's weight W(measured in kilograms) as a function of time t (measured in months).

Since wrestler gained weight at a rate of 5.5 kilograms per month, so slope of line be 5.5.

Now, we will use point-slope form of equation as:

$y-y_1=m(x-x_1)$ , where,

m = Slope

$(x_1,y_1)$ = Given point on the line.

Upon substituting coordinates of point (11,140) in above formula, we will get:

$y-140=5.5(x-11)$

$y-140=5.5x-60.5$

$y-140+140=5.5x-60.5+140$

$y=5.5x+79.5$

Therefore, our required function would be $W(t)=5.5t+79.5$ .

3 0

3 years ago

an inverted conical water tank with a height of 20 ft and a radius of 8 ft is drained through a hole in the vertex (bottom) at a

viktelen [127]

Answer:

the rate of change of the water depth when the water depth is 10 ft is; $\mathbf{\dfrac{dh}{dt} = \dfrac{-25}{100 \pi} \ \ ft/s}$

Step-by-step explanation:

Given that:

the inverted conical water tank with a height of 20 ft and a radius of 8 ft is drained through a hole in the vertex (bottom) at a rate of 4 ft^3/sec.

We are meant to find the rate of change of the water depth when the water depth is 10 ft.

The diagrammatic expression below clearly interprets the question.

From the image below, assuming h = the depth of the tank at a time t and r = radius of the cone shaped at a time t

Then the similar triangles ΔOCD and ΔOAB is as follows:

$\dfrac{h}{r}= \dfrac{20}{8}$ ( similar triangle property)

$\dfrac{h}{r}= \dfrac{5}{2}$

$\dfrac{h}{r}= 2.5$

h = 2.5r

$r = \dfrac{h}{2.5}$

The volume of the water in the tank is represented by the equation:

$V = \dfrac{1}{3} \pi r^2 h$

$V = \dfrac{1}{3} \pi (\dfrac{h^2}{6.25}) h$

$V = \dfrac{1}{18.75} \pi \ h^3$

The rate of change of the water depth is :

$\dfrac{dv}{dt}= \dfrac{\pi r^2}{6.25}\ \dfrac{dh}{dt}$

Since the water is drained through a hole in the vertex (bottom) at a rate of 4 ft^3/sec

Then,

$\dfrac{dv}{dt}= - 4 \ ft^3/sec$

Therefore,

$-4 = \dfrac{\pi r^2}{6.25}\ \dfrac{dh}{dt}$

the rate of change of the water at depth h = 10 ft is:

$-4 = \dfrac{ 100 \ \pi }{6.25}\ \dfrac{dh}{dt}$

$100 \pi \dfrac{dh}{dt} = -4 \times 6.25$

$100 \pi \dfrac{dh}{dt} = -25$

$\dfrac{dh}{dt} = \dfrac{-25}{100 \pi}$

Thus, the rate of change of the water depth when the water depth is 10 ft is; $\mathtt{\dfrac{dh}{dt} = \dfrac{-25}{100 \pi} \ \ ft/s}$

4 0

4 years ago

The ratio to isabella's money to shane's money is 3:11 if isabella has $33 how much money do shane and isabella have together us

alexgriva [62]

Shane and Isabella have 154 dollars

4 0

3 years ago