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3 years ago

I bed help with these two

Mathematics

2 answers:

Veseljchak [2.6K]3 years ago

8 0

21.5 is the first ine

frozen [14]3 years ago

5 0

Well if each band needs 15.5 inches and she needs to make 12 headbands she needs 15.5 inches 12 times. Now you can add 15.5 + 15.5 +15.5 (so on) 12 times or you can do it the easier way and do 15.5 times 12. this comes out to 186 inches of ribbon. She estimated 160 inches of ribbon, this is unreasonable because it is significantly less that 186.

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For the function given below, find a formula for the Riemann sum obtained by dividing the interval [0,5] into n equal subinterva

sergij07 [2.7K]

Given

we are given a function

$f(x)=x^2+5$

over the interval [0,5].

Required

we need to find formula for Riemann sum and calculate area under the curve over [0,5].

Explanation

If we divide interval [a,b] into n equal intervals, then each subinterval has width

$\Delta x=\frac{b-a}{n}$

and the endpoints are given by

$a+k.\Delta x,\text{ for }0\leq k\leq n$

For k=0 and k=n, we get

$\begin{gathered} x_0=a+0(\frac{b-a}{n})=a \\ x_n=a+n(\frac{b-a}{n})=b \end{gathered}$

Each rectangle has width and height as

$\Delta x\text{ and }f(x_k)\text{ respectively.}$

we sum the areas of all rectangles then take the limit n tends to infinity to get area under the curve:

$Area=\lim_{n\to\infty}\sum_{k\mathop{=}1}^n\Delta x.f(x_k)$

Here

$f(x)=x^2+5\text{ over the interval \lbrack0,5\rbrack}$ $\Delta x=\frac{5-0}{n}=\frac{5}{n}$ $x_k=0+k.\Delta x=\frac{5k}{n}$ $f(x_k)=f(\frac{5k}{n})=(\frac{5k}{n})^2+5=\frac{25k^2}{n^2}+5$

Now Area=

$\begin{gathered} \lim_{n\to\infty}\sum_{k\mathop{=}1}^n\Delta x.f(x_k)=\lim_{n\to\infty}\sum_{k\mathop{=}1}^n\frac{5}{n}(\frac{25k^2}{n^2}+5) \\ =\lim_{n\to\infty}\sum_{k\mathop{=}1}^n\frac{125k^2}{n^3}+\frac{25}{n} \\ =\lim_{n\to\infty}(\frac{125}{n^3}\sum_{k\mathop{=}1}^nk^2+\frac{25}{n}\sum_{k\mathop{=}1}^n1) \\ =\lim_{n\to\infty}(\frac{125}{n^3}.\frac{1}{6}n(n+1)(2n+1)+\frac{25}{n}n) \\ =\lim_{n\to\infty}(\frac{125(n+1)(2n+1)}{6n^2}+25) \\ =\lim_{n\to\infty}(\frac{125}{6}(1+\frac{1}{n})(2+\frac{1}{n})+25) \\ =\frac{125}{6}\times2+25=66.6 \end{gathered}$

So the required area is 66.6 sq units.

3 0

1 year ago

4+5(6t+1) and 9+30t equivalent or not equivalent

andrezito [222]

Answer:

No, 4+5(6t+1) EQUALS 9+30t

And 9+30t Equals 3(3+10t)

Step-by-step explanation:

GCF=3

3(9/3 + 30t/ 3) =

3(3+10t)

And

4+5(6t+1)

4+30t+5

30t+ (4+5)

Simplifying =

30t+9

4 0

3 years ago

Please help Please thank you

Marina CMI [18]

Answer: C) The student made an error in step 3.

Step-by-step explanation:

When dividing by a negative while working with inequalities, you must "flip the sign." Thus, there is an error in step 3.

N.B. The answer could very well be interpreted as B), but I believe C) is the best and most defensible answer.

Hope it helps :) and let me know if you want me to elaborate.

8 0

3 years ago

Read 2 more answers

Help me find the surface area

Brut [27]

Answer:

Step-by-step explanation:

area of triangular face = ½·3·4 = 6 cm²

area of 3 by 7 face = 3×7 = 21 cm²

area of 5 by 7 face = 5×7 = 35 cm²

area of 4 by 7 face = 4×7 = 28 cm²

total surface area = 2×6 + 21 + 35 + 28 = 96 cm²

6 0

3 years ago

HELP DUE NOW PLEse help this is it.

tekilochka [14]

The answer will be -1.7

4 0

3 years ago

Read 2 more answers