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3 years ago

Calculate the following using long division show all working 896 divided by 7

Mathematics

1 answer:

MrRissso [65]3 years ago

8 0

Answer:

128

Step-by-step explanation:

896

7 goes into 8 once

Subtract 7 from 8 and bring the one down.

8 goes into 19 twice

Subtract 14 from 19 and bring the five down.

7 goes into 56 eight times.

So your answer is 128.

Hope this helps

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3 years ago

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PLEASE HELP I've tried putting all my working out into the box but it said wrong to..

Inessa05 [86]

Answer:

£59.25

Step-by-step explanation:

It appears you can measure the height of the trapezoid [trapezium :-) ??]. If you can't, you can use the Pythagorean Theorem (image attached). Draw a line from the upper right-hand corner down to the baseline--the 20m side. You'll form a right triangle with one leg h , hypotenuse 17m and the other leg 8m (the difference between 20m and 12m).

(leg)^2 + (leg)^2 = (hypotenuse)^2

h^2 + 8^2 = 17^2

h^2 + 64 = 289

h^2 = 225

h = 15m

The area of the trapezium is $A=\frac{1}{2}h\left(b_1+b_2\right)$ where the b's are the lengths of the two bases (upper and lower sides).

$A=\frac{1}{2}(15)(12+20)=\frac{1}{2}(480) = 240$ m^2

One can of weedkiller covers 100 m^2 of area. You'll need 3 cans (2 cans isn't enough, and you can't buy a fraction of a can). Tricky question!

Three cans will cost 3 x 19.75 pounds = £59.25

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2 years ago

The region in the first quadrant bounded by the x-axis, the line x = ln(π), and the curve y = sin(e^x) is rotated about the x-ax

charle [14.2K]

First, it would be good to know that the area bounded by the curve and the x-axis is convergent to begin with.

$\displaystyle\int_{-\infty}^{\ln\pi}\sin(e^x)\,\mathrm dx$

Let $u=e^x$ , so that $\mathrm dx=\dfrac{\mathrm du}u$ , and the integral is equivalent to

$\displaystyle\int_{u=0}^{u=\pi}\frac{\sin u}u\,\mathrm du$

The integrand is continuous everywhere except $u=0$ , but that's okay because we have $\lim\limits_{u\to0^+}\frac{\sin u}u=1$ . This means the integral is convergent - great! (Moreover, there's a special function designed to handle this sort of integral, aptly named the "sine integral function".)

Now, to compute the volume. Via the disk method, we have a volume given by the integral

$\displaystyle\pi\int_{-\infty}^{\ln\pi}\sin^2(e^x)\,\mathrm dx$

By the same substitution as before, we can write this as

$\displaystyle\pi\int_0^\pi\frac{\sin^2u}u\,\mathrm du$

The half-angle identity for sine allows us to rewrite as

$\displaystyle\pi\int_0^\pi\frac{1-\cos2u}{2u}\,\mathrm du$

and replacing $v=2u$ , $\dfrac{\mathrm dv}2=\mathrm du$ , we have

$\displaystyle\frac\pi2\int_0^{2\pi}\frac{1-\cos v}v\,\mathrm dv$

Like the previous, this require a special function in order to express it in a closed form. You would find that its value is

$\dfrac\pi2(\gamma-\mbox{Ci}(2\pi)+\ln(2\pi))$

where $\gamma$ is the Euler-Mascheroni constant and $\mbox{Ci}$ denotes the cosine integral function.