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brilliants [131]
3 years ago
10

At the local grocery store, cans of beans are arranged in rows. The number of cans in each row forms an arithmetic sequence. The

re are 93 cans in row 1, 88 cans in row 2, 83 cans in row 3, and so on. One row contains 48 cans. Which row is this?
Mathematics
1 answer:
Helen [10]3 years ago
7 0
It seems the cans are arranged in a sequence 93,88,83,78,73,68,68,58,53,48 so the row containing 48 cans is row 10
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There is 1500 ft of fencing available to make 6 identical pens. Find the maximum area for EACH pen (meaning maximum of one pen).
hjlf

Answer:

The maximum area is therefore is 93750 ft²

Step-by-step explanation:

The given parameter are;

The a]length of fencing available = 1500 ft.

The perimeter of the figure = 9·x + 4·y

Therefore, 9·x + 4·y = 1500 ft.

The area of the figure = 6 × (x × y) = 3·x × 2·y

From the equation for the perimeter, we have;

9·x + 4·y = 1500

y = 1500/4 - 9/4·x = 375 - 9/4·x

y = 375 - 9/4·x

Substituting the value of y in the equation for the area gives;

Area = 3·x × 2·y = 3·x × 2·(375 - 9/4·x) = 2250·x - 27/2·x²

Area = 2250·x - 27/2·x²

The maximum area is found by taking the derivative and equating to zero as follows;

d(2250·x - 27/2·x²)/dx = 0

2250 - 27·x = 0

x = 2250/27 = 250/3

x = 250/3

y = 375 - 9/4·x = 375 - 9/4×250/3 = 187.5

The maximum area is therefore, 3·x × 2·y = 3 × 250/3 × 2 × 187.5 = 93750 ft²

The maximum area is therefore = 93750 ft.²

4 0
3 years ago
Express the complex number in trigonometric form. <br><br> -4i
jeka57 [31]

Answer:

-4i =  4(cos 270 +i sin 270)

Step-by-step explanation:

We have a+ib = r(cosθ+isinθ)

r=\sqrt{a^2+b^2}\texttt{ and }tan\theta =\frac{b}{a}

Here a = 0  and b = -4

Substituting

       r=\sqrt{0^2+(-4)^2}\\\\r=4\\\\tan\theta =\frac{-4}{0}\\\\\theta =270^0\texttt{(Since a is zero and b is negative)}

-4i =  4(cos 270 +i sin 270)

3 0
3 years ago
PLEASE HELP!!!!!!!!!! What decimal is represented by this expanded form?
olga55 [171]
Answer=3610.201

3*1000=3,000
6*100=600
1*10=10
2*1/10=0.2
1*1/1000=0.001

3000+600+10+0.2+0.001=3610.201
3 0
4 years ago
Manny has 48 feet of wood. He wants to use all of it to create a border around a garden. The equation 2 l plus 2 w equals 48 can
Lelu [443]

Answer:

2l + 2w = 48

if garden is 15' long

2(15) + 2w = 48 \\ 30 + 2w = 48 \\ 30 - 30 + 2w = 48 - 30 \\ 2w = 18 \\  \frac{2w}{2}  =  \frac{18}{2}  \\ w = 9 \: feet \: wide

7 0
3 years ago
Find the absolute minimum and absolute maximum values of f on the given interval. f(t) = t 25 − t2 , [−1, 5]
Zina [86]

Answer: Absolute minimum: f(-1) = -2\sqrt{6}

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Step-by-step explanation: To determine minimum and maximum values in a function, take the first derivative of it and then calculate the points this new function equals 0:

f(t) = t\sqrt{25-t^{2}}

f'(t) = 1.\sqrt{25-t^{2}}+\frac{t}{2}.(25-t^{2})^{-1/2}(-2t)

f'(t) = \sqrt{25-t^{2}} -\frac{t^{2}}{\sqrt{25-t^{2}} }

f'(t) = \frac{25-2t^{2}}{\sqrt{25-t^{2}} } = 0

For this function to be zero, only denominator must be zero:

25-2t^{2} = 0

t = ±\sqrt{2.5}

\sqrt{25-t^{2}} ≠ 0

t = ± 5

Now, evaluate critical points in the given interval.

t = -\sqrt{2.5} and t = - 5 don't exist in the given interval, so their f(x) don't count.

f(t) = t\sqrt{25-t^{2}}

f(-1) = -1\sqrt{25-(-1)^{2}}

f(-1) = -\sqrt{24}

f(-1) = -2\sqrt{6}

f(\sqrt{12.5}) = \sqrt{12.5} \sqrt{25-(\sqrt{12.5} )^{2}}

f(\sqrt{12.5}) = 12.5

f(5) = 5\sqrt{25-5^{2}}

f(5) = 0

Therefore, absolute maximum is f(\sqrt{12.5}) = 12.5 and absolute minimum is

f(-1) = -2\sqrt{6}.

8 0
3 years ago
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