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WARRIOR [948]
3 years ago
5

Help! Giving brainliest.

Mathematics
2 answers:
VMariaS [17]3 years ago
6 0

<u>Answer:</u>

a) Steven is incorrect.

b) Steven is incorrect, because he claims that, in other words, 15 units squared = 18 units squared. 18 > 15, so the statement that 15 = 18 is false. 15 does not equal 18.

<u>Step-by-step explanation:</u> Steven claims that the area of rectangle A is double the area of square B. The area of rectangle A is 15 units squared, because you get a product of 15 when you multiply the side lengths 5 and 3. The area of square B is 9 units squared, because you get a product of 9 when you multiply the side lengths 3 and 3. In other words, Steven is claiming that the area of rectangle A is not 15 units squared, but 18 units squared (this is double the area of square B, as 18 is the product of 9 and 2), and that statement is false, because we know that 18 > 15. Therefore, 18 cannot equal 15; the figure that is made from the value of double the area of square B (18 units squared) is larger than rectangle A (15 units squared) - this reinforces the fact that 18 > 15, and hence cannot be equal to 15.

Daniel [21]3 years ago
4 0

Answer:

The area of rectangle A is length x breadth

= 3x5

= 15 units^2

The area of square B is side x side

= 3x3

= 9 units^2

Therefore,

The area of the rectangle is not double of the area of the square because 9x2 is not equal to 15. Steven isn't correct.

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If g(x)= 4, then g(5x) = ?
Neporo4naja [7]

Answer:

g(5x)= 20

Step-by-step explanation:

g(x)=4 is basically saying that 1 x is equal to 4.

g(5x) wants to know what 5 times 1 x is equal to (5 times 4 (4 is equal to 1 x)

g(5x)= 5(x=4)

g(5x)= 20

4 0
3 years ago
For the function defined by f(t)=2-t, 0≤t&lt;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.)

5 0
3 years ago
PLZZZZZZZZZZZZZZ HELP ME
ANTONII [103]

Answer:

316.41

Step-by-step explanation:

Because if you mutiply to find both volumes then add the volumes together you would get 316.41

3 0
3 years ago
Nolan watched a beetle on the sidewalk. It crawled 7/12 of a yard, then rested for a bit, and then crawled 1/4 of a yard farther
liberstina [14]
D, because 1/4 is equivalent to 4/12 and 7/12+4/12=11/12 which is equivalent to 5/6
5 0
3 years ago
85% expressed as a fraction in simplest form is
Marizza181 [45]

Hello There!

85% = 85/100

85/100 = 0.85

0.85/1 * 100/100

85/100

SIMPLIFIED IS 17/20

8 0
3 years ago
Read 2 more answers
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