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alekssr [168]
3 years ago
11

The Pumpkin Patch is open every day. If it sells 2,750 pounds of pumpkins each day, about how many pounds does it sell in 7 days

?
Mathematics
2 answers:
tresset_1 [31]3 years ago
3 0

The answer to this question is 19,250 pounds of pumpkins sold in 7 days. This is true because to find the answer you just have to multiply the pumpkins that sell every day and the days it asking for. Equation 2,750 pounds*7=19,250 pounds.

I hope this helps you!

MArishka [77]3 years ago
3 0
19,250 is the answer because 2750x7=19,250
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For the function defined by f(t)=2-t, 0≤t<1, sketch 3 periods and find:
Oksi-84 [34.3K]
The half-range sine series is the expansion for f(t) with the assumption that f(t) is considered to be an odd function over its full range, -1. So for (a), you're essentially finding the full range expansion of the function

f(t)=\begin{cases}2-t&\text{for }0\le t

with period 2 so that f(t)=f(t+2n) for |t| and integers n.

Now, since f(t) is odd, there is no cosine series (you find the cosine series coefficients would vanish), leaving you with

f(t)=\displaystyle\sum_{n\ge1}b_n\sin\frac{n\pi t}L

where

b_n=\displaystyle\frac2L\int_0^Lf(t)\sin\frac{n\pi t}L\,\mathrm dt

In this case, L=1, so

b_n=\displaystyle2\int_0^1(2-t)\sin n\pi t\,\mathrm dt
b_n=\dfrac4{n\pi}-\dfrac{2\cos n\pi}{n\pi}-\dfrac{2\sin n\pi}{n^2\pi^2}
b_n=\dfrac{4-2(-1)^n}{n\pi}

The half-range sine series expansion for f(t) is then

f(t)\sim\displaystyle\sum_{n\ge1}\frac{4-2(-1)^n}{n\pi}\sin n\pi t

which can be further simplified by considering the even/odd cases of n, but there's no need for that here.

The half-range cosine series is computed similarly, this time assuming f(t) is even/symmetric across its full range. In other words, you are finding the full range series expansion for

f(t)=\begin{cases}2-t&\text{for }0\le t

Now the sine series expansion vanishes, leaving you with

f(t)\sim\dfrac{a_0}2+\displaystyle\sum_{n\ge1}a_n\cos\frac{n\pi t}L

where

a_n=\displaystyle\frac2L\int_0^Lf(t)\cos\frac{n\pi t}L\,\mathrm dt

for n\ge0. Again, L=1. You should find that

a_0=\displaystyle2\int_0^1(2-t)\,\mathrm dt=3

a_n=\displaystyle2\int_0^1(2-t)\cos n\pi t\,\mathrm dt
a_n=\dfrac2{n^2\pi^2}-\dfrac{2\cos n\pi}{n^2\pi^2}+\dfrac{2\sin n\pi}{n\pi}
a_n=\dfrac{2-2(-1)^n}{n^2\pi^2}

Here, splitting into even/odd cases actually reduces this further. Notice that when n is even, the expression above simplifies to

a_{n=2k}=\dfrac{2-2(-1)^{2k}}{(2k)^2\pi^2}=0

while for odd n, you have

a_{n=2k-1}=\dfrac{2-2(-1)^{2k-1}}{(2k-1)^2\pi^2}=\dfrac4{(2k-1)^2\pi^2}

So the half-range cosine series expansion would be

f(t)\sim\dfrac32+\displaystyle\sum_{n\ge1}a_n\cos n\pi t
f(t)\sim\dfrac32+\displaystyle\sum_{k\ge1}a_{2k-1}\cos(2k-1)\pi t
f(t)\sim\dfrac32+\displaystyle\sum_{k\ge1}\frac4{(2k-1)^2\pi^2}\cos(2k-1)\pi t

Attached are plots of the first few terms of each series overlaid onto plots of f(t). In the half-range sine series (right), I use n=10 terms, and in the half-range cosine series (left), I use k=2 or n=2(2)-1=3 terms. (It's a bit more difficult to distinguish f(t) from the latter because the cosine series converges so much faster.)

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Natali5045456 [20]

Answer:

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Step-by-step explanation:

5 0
3 years ago
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Shtirlitz [24]

Answer:

The equation in the slope-intercept form is

y = -5x - 41

Step-by-step explanation:

The given equation in the question is;

y = -5x + 2

The equation of a straight line graph can be written in the form;

y = mx + c

where m is the slope and c is the intercept

From here, we can see that the slope m is -5

Since the line is parallel to the new line we are trying to write its equation, it means that they have the same value of intercept.

Hence, the slope of the new line is also -5

Now, we can write the equation of the new line as;

y = -5x + c

we need to get the value of c here however

To get the value of c, we need to input the value of x and y

From the graph, x = -7 and y = -6

Substituting these values, we have;

-6 = -5(-7) + c

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c = -6 -35

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y = -5x - 41

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3 years ago
Whats the area of this tile
Alenkasestr [34]

Answer:

9

Step-by-step explanation:

3 times 3 is 9

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2 years ago
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if eight times a number is increased by 3 the result is 19 more than six times this digit. find the number
Verdich [7]

Answer:

8

Step-by-step explanation:

Even though we don't know the number yet, let's name this number "n".

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8n + 3 - 6n = 6n + 19 - 6n

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2n = 16

n = 16/2

n = 8

Our number is 8.

Note: This answer is 100% correct.  

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2 years ago
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