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2 years ago

Find the sum (-14.2b - 97.35) + (6.76d - 118.7 – 3.4d)

Mathematics

1 answer:

s344n2d4d5 [400]2 years ago

5 0

Answer:

−14.2b+3.36d−216.05

Step-by-step explanation:

collect terms:(−14.2b−97.35)+((6.76d−3.4d)−118.7)

simplify: −14.2b−97.35+3.36d−118.7

terms: −14.2b+3.36d+(−97.35−118.7)

simplify: −14.2b+3.36d−216.05

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So what's the answer for 35% of 22

kondor19780726 [428]

You divide 22 by 10 (2.2) and then multiply that by 3 to get 30%, which is 6.6. Then, you divide 2.2 by 2 to get 1.1, which is 5%. After this you just add them up to get the answer as 7.7.
Also, if you have q calculator, you can do it the short way and do 22 × 0.35 = 7.7

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2 years ago

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Find the Fourier series of f on the given interval. f(x) = 1, ?7 < x < 0 1 + x, 0 ? x < 7

Zolol [24]

$f(x)=\begin{cases}1&\text{for }-7$

The Fourier series expansion of $f(x)$ is given by

$\dfrac{a_0}2+\displaystyle\sum_{n\ge1}a_n\cos\frac{n\pi x}7+\sum_{n\ge1}b_n\sin\frac{n\pi x}7$

where we have

$a_0=\displaystyle\frac17\int_{-7}^7f(x)\,\mathrm dx$
$a_0=\displaystyle\frac17\left(\int_{-7}^0\mathrm dx+\int_0^7(1+x)\,\mathrm dx\right)$
$a_0=\dfrac{7+\frac{63}2}7=\dfrac{11}2$

The coefficients of the cosine series are

$a_n=\displaystyle\frac17\int_{-7}^7f(x)\cos\dfrac{n\pi x}7\,\mathrm dx$
$a_n=\displaystyle\frac17\left(\int_{-7}^0\cos\frac{n\pi x}7\,\mathrm dx+\int_0^7(1+x)\cos\frac{n\pi x}7\,\mathrm dx\right)$
$a_n=\dfrac{9\sin n\pi}{n\pi}+\dfrac{7\cos n\pi-7}{n^2\pi^2}$
$a_n=\dfrac{7(-1)^n-7}{n^2\pi^2}$

When $n$ is even, the numerator vanishes, so we consider odd $n$ , i.e. $n=2k-1$ for $k\in\mathbb N$ , leaving us with

$a_n=a_{2k-1}=\dfrac{7(-1)-7}{(2k-1)^2\pi^2}=-\dfrac{14}{(2k-1)^2\pi^2}$

Meanwhile, the coefficients of the sine series are given by

$b_n=\displaystyle\frac17\int_{-7}^7f(x)\sin\dfrac{n\pi x}7\,\mathrm dx$
$b_n=\displaystyle\frac17\left(\int_{-7}^0\sin\dfrac{n\pi x}7\,\mathrm dx+\int_0^7(1+x)\sin\dfrac{n\pi x}7\,\mathrm dx\right)$
$b_n=-\dfrac{7\cos n\pi}{n\pi}+\dfrac{7\sin n\pi}{n^2\pi^2}$
$b_n=\dfrac{7(-1)^{n+1}}{n\pi}$

So the Fourier series expansion for $f(x)$ is

$f(x)\sim\dfrac{11}4-\dfrac{14}{\pi^2}\displaystyle\sum_{n\ge1}\frac1{(2n-1)^2}\cos\frac{(2n-1)\pi x}7+\frac7\pi\sum_{n\ge1}\frac{(-1)^{n+1}}n\sin\frac{n\pi x}7$

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2 years ago

Lexie began making posters for the school awards banquet. She can make 6 posters per minute. Zach joined her 10 minutes after sh

Snowcat [4.5K]

10 * 6 = 60 by the time Zach joins so 125-60 = 65
Now 6 (lexie) +7 (zach) = 13 (together) and 65/13 = 5.
6*5 = 30 and 7*5 = 35. 35+30 = 65
Your answer is 5.

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3 years ago

The flag of a country contains an isosceles triangle. (Recall that an isosceles triangle contains two angles with the same mea

weeeeeb [17]

31 degrees, 31 degrees, 118 degrees

Step-by-step explanation:

Step 1 :

Let x be the measure of 2 angles of the given isosceles triangle with same measure

Let y be the measure of 3rd angle

So we have x + x + y = 180

Step 2 :

Given that the measure of 3rd angle of triangle is 25° more than three times the measure of either of the other two angles

So we have , y = 3 x + 25

Step 3:

Substituting for y in the first equation we have,

x + x + 3 x + 25 = 180

=> 5 x + 25 = 180

=> 5 x = 180-25 = 155

=> x = 155/5 = 31

Hence the 2 angles of the triangle are 31 degrees.

Step 4:

we have y = 3 x + 25

=> y = 3 * 31 + 25 = 118

Hence the 3rd angle of given triangle is 118 degrees

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2 years ago

I will mark you brainliest! How much money did Nikki orginally invest?

Deffense [45]

Answer:D

Step-by-step explanation:

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