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Mila [183]
3 years ago
9

suppose you have 76 feet of fencing to enclose a rectangular dog pen. The function A=38x-x^2, where x= width, gives you the area

of the dog pen per square feet. What width gives you the maximum area? What is the maximum area? Round to the nearest tenth if necessary.
Mathematics
1 answer:
yan [13]3 years ago
3 0
If A=38x-x^2 then

dA/dx=38-2x

d2A/dx2=-2

Since the acceleration, d2A/dx2 is a constant negative, when velocity, dA/dx=0, it will be an absolute maximum for A(x)

dA/dx=0 only when 38=2x, x=19

A(19)=38(19)-19^2

A(19)=722-361

A(19)=361 ft^2

So the maximum possible area is 361 ft^2

(This will always be true as the maximum possible area enclosed by a given amount of material will always be a perfect square...)
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Roberto has $200 in spending money. He wants to buy some video games that cost $25.50 each. Write and solve an inequality to fin
Veseljchak [2.6K]

Answer:

f(x) = 25.50x      Roberto can buy 7 video games

Step-by-step explanation:

Each game is $25.50 which in math means it has an "x"

So if x=1 then 25.50x says that 1 video game is $25.50

Set up the equation:

200 = 25.50x (divide both sides by 25.50 to isolate the x)

200/25.50 = 7.84

x = 7.84

You can't have 0.84 of a video game, so Roberto can only buy 7 of them.

3 0
3 years ago
Read 2 more answers
a theater is designed with 15 seats in the first row, 19 in the second, 23 in the third, and so on. if this seating pattern cont
marusya05 [52]

Answer:

<u>131 seats</u> are in the 30th row.

Step-by-step explanation:

The theater is designed with the first row there are 15 seats, in second row 19 seats and in the third row there are 23 seats.

Now, to find the number of seats in the 30th row.

So, we get the common difference(d) from the arithmetic sequence first:

19-15=4.

Thus, d=4.

So, the first tem a(1) = 15.

The number of last row (n) = 30.

Now, to get the number of seat in the 30th row we put formula:

a(n) = a(1) + d(n-1)

a(30)=15+4(30-1)

a(30)=15+4\times 29

a(30)=15+116

a(30)=131

Therefore, 131 seats are in the 30th row.

4 0
4 years ago
What is a factor of 67
pishuonlain [190]

Answer:The factors of 67. Answer : 1,67

Step-by-step explanation:

6 0
3 years ago
In a scale drawing of an apartment 1 centimet represents 2 3/4 feet. If the length of the kitchen is 4 1/2cm on the scale drawin
weeeeeb [17]

Answer:

12 3/8 feet

Step-by-step explanation:

Because 4 1/2 times 2 3/4 equals 99/8, then 99 divided by 8 equals 12 3/8.

3 0
3 years ago
If your starting salary is $40,000 and you  receive a 4.2% raise every year, how much  TOTAL money will you make in 15 years?
Oliga [24]
The first year, the amount is 40,000

the second year is 40000 + 4.2% of 40000, or 0.042 * 4000, so 40000+(0.042*4000)
common factoring that  we get 40000(1 + 0.042), or just 40000(1.042)

in short, the starting amount is 40000, and to get the next term's value you'd use the "common ratio" of 1.042, namely the multiplier of 1.042.

for the third year it'll be 40000(1.042) + (0.042 *40000(1.042) ), again, common factoring that

40000(1.042)(1 + 0.042) or 40000(1.042)(1.042) or 40000(1.042)²

therefore,

\bf \qquad \qquad \textit{sum of a finite geometric sequence}\\\\&#10;S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad &#10;\begin{cases}&#10;n=n^{th}\ term\\&#10;a_1=\textit{first term's value}\\&#10;r=\textit{common ratio}\\&#10;----------\\&#10;a_1=40000\\&#10;r=1.042\\&#10;n=15&#10;\end{cases}&#10;\\\\\\&#10;S_{15}=40000\left( \cfrac{1-1.042^{15}}{1-1.042} \right)\implies S_{15}\approx 40000\left( \cfrac{-0.8536}{-0.042} \right)&#10;\\\\\\&#10;S_{15}\approx 812951.42
5 0
3 years ago
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