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Nady [450]
2 years ago
10

Margaret makes bracelets and sells them to tourists. the function s(t) approximates how many bracelets margaret makes per hour.

the function w(h) represents how hours per week margaret spends making bracelets. what are the units of measurement for the composite function s(w(h))?
Mathematics
1 answer:
Fantom [35]2 years ago
4 0

The units for the composite function s(w(h)) is <u>bracelets over a week</u> when the function s(t) approximates how many bangles Margaret makes per hour and the function w(h) represents how many hours per week Margaret spends making the bracelets.

To define the unit of the composite function s(w(h)), we first need to find the units of the functions s(t) and w(h).

The function s(t)  represents the number of bangles per hour, so its unit will be bangles over an hour.

The function w(h) represents the hours per week spent on making the bracelets, so its unit will be hours over a week.

Now, we can define the unit of the composite function s(w(h)).

To find the unit of the composite function we follow these steps:-

s(w(h)),

= s(hours over a week) {replacing the function w(h) by its units},

= (bangles over an hour(hours over a week)) {replacing the function s(t) with its units},

= bangles over a week {Simplifying}.

Thus, the units for the composite function s(w(h)) is <u>bracelets over a week</u> when the function s(t) approximates how many bangles Margaret makes per hour and the function w(h) represents how many hours per week Margaret spends making the bracelets.

Learn more about the units of a composite function at

brainly.com/question/15056566

#SPJ4

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The gardener mows your lawn in $9 and earns $45. Write and solve an equation to find the number of hours of the gardener worked
amid [387]

Answer:

45/9=__

Step-by-step explanation:

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4 0
3 years ago
Pam has 90 m of fencing to enclose an area in a petting zoo with two dividers to separate three types of young animals. The thre
andrew-mc [135]

Answer:

The area function is

A=\frac{135}{2}x-\frac{9}{2}x^2.

The domain and range of A is (0,15m) and (0, 253.125 m^2].

Step-by-step explanation:

The given length of fencing is 90 m.

Let the length and width of each pen be x and y respectively as shown in the figure.

As there are 3 pens, so, the total area,

A= 3 xy \;\cdots (i)

From the figure the total length of fencing is 6x+4y.

Here, for a significant area for the animals, x>0 as well as y>0 as x and y are the sides of ben.

From the given value:

6x+4y=90\;\cdots (ii)

\Rightarrow  y=\frac {45}{2}-\frac{3x}{2}

Now, from equation (i)

A=3x\left(\frac {45}{2}-\frac{3x}{2}\right)

\Rightarrow A=\frac{135}{2}x-\frac{9}{2}x^2\;\cdots (iii)

This is the required area function in the terms of variable x.

For the domain of area function, from equation (ii)

x=15-\frac{2y}{3}

\Rightarrow x [as y>0]

So, the domain of area function is (0,15m).

For the range of area function:

As x \rightarrow 0 or y\rightarrow 0, then A\rightarrow 0 [from equation (i)]

\Rightarrow A>0

Now, differentiate the area function with respect to x .

\frac {dA}{dx}=\frac{135}{2}-9x

Equate \frac {dA}{dx}  to zero to get the extremum point.

\frac {dA}{dx}=0

\Rightarrow \frac{135}{2}-9x=0

\Rightarrow x=\frac{15}{2}

Check this point by double differentiation

\frac {d^2A}{dx^2}=-9

As,  \frac {d^2A}{dx^2}, so, point x=\frac{15}{2} is corresponding to maxima.

Put this value back to equation (iii) to get the maximum value of area function. We have

A=\frac{135}{2}\times \frac {15}{2}-\frac{9}{2}\times \left(\frac {15}{2}\right)^2

\Rightarrow A=253.125 m^2

Hence, the range of area function is (0, 253.125 m^2].

4 0
3 years ago
Read the ques
Dafna11 [192]

Answer:

0.25feet

Step-by-step explanation:

The equation is not well written. Let the equation of the height be modelled as;

h = -16d²+8d+4

The velocity of the ball is zero at its maximum height.

Velocity = change in displacement/time

v = dh/dd

Differentiate

v = -32d+8

Since dh/dd = v = 0

0 = -32d+8

Add 32d to both sides

0+32d = 8

32d = 8

Divide both sides by 32

32d/32 = 8/32

d = 1/4

d = 0.25feet

Hence the maximum height of the tennis ball is 0.25feet

Note that the modeled equation was assumed. You can apply the same calculation to any equation given

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