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3 years ago

When 1480 is divided into 12 equal parts, the remainder is 4. What is a correct way to write the quotient? (3 points)

Mathematics

1 answer:

In-s [12.5K]3 years ago

3 0

Answer:

Depending on what type of math class you are in, or how your teacher taught it, it could be either 12 R:4 or 12 + 1/370.

Step-by-step explanation:

Remainders can be written in two ways, R: [remainder] or the whole number quotient + [remainder number]/[dividend]. For this problem you would have to simplify 4/1480 to 1/370 because 1480/4 equals 370. So, your final answer would be 12 + 1/370 or 12 R:4.

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Lauren bought 20 ounces of sliced ham. She used 3/4 of the ham to make sandwiches for her friends and 1/5 of the ham in an omele

NeX [460]

4 ounces are left because 3/4 of 20 is 5. And 1/5 of 5 is 4. I hope this helps

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3 years ago

What is the diameter of a circle with a circumference of 11.27 pi ft

KatRina [158]

Circumference of circle = 11.27π ft
so,
C = 2πr
or, 11.27π = 2πr
or, 11.27π/2π = r
so, r = 5.635 ft
now,
diameter = 2r
= 2 x 5.635
= 11.27 ft

7 0

3 years ago

Imagine that you need to compute e^0.4 but you have no calculator or other aid to enable you to compute it exactly, only paper a

labwork [276]

Answer:

0.0032

Step-by-step explanation:

We need to compute $e^{0.4}$ by the help of third-degree Taylor polynomial that is expanded around at x = 0.

Given :

$e^{0.4}$ < e < 3

Therefore, the Taylor's Error Bound formula is given by :

$|\text{Error}| \leq \frac{M}{(N+1)!} |x-a|^{N+1}$ , where $M=|F^{N+1}(x)|$

$\leq \frac{3}{(3+1)!} |-0.4|^4$

$\leq \frac{3}{24} \times (0.4)^4$

$\leq 0.0032$

Therefore, |Error| ≤ 0.0032

4 0

3 years ago

Find e^cos(2+3i) as a complex number expressed in Cartesian form.

ozzi

Answer:

The complex number $e^{\cos(2+31)} = \exp(\cos(2+3i))$ has Cartesian form

$\exp\left(\cosh 3\cos 2\right)\cos(\sinh 3\sin 2)-i\exp\left(\cosh 3\cos 2\right)\sin(\sinh 3\sin 2)$ .

Step-by-step explanation:

First, we need to recall the definition of $\cos z$ when $z$ is a complex number:

$\cos z = \cos(x+iy) = \frac{e^{iz}+e^{-iz}}{2}$ .

Then,

$\cos(2+3i) = \frac{e^{i(2+31)} + e^{-i(2+31)}}{2} = \frac{e^{2i-3}+e^{-2i+3}}{2}$ . (I)

Now, recall the definition of the complex exponential:

$e^{z}=e^{x+iy} = e^x(\cos y +i\sin y)$ .

So,

$e^{2i-3} = e^{-3}(\cos 2+i\sin 2)$

$e^{-2i+3} = e^{3}(\cos 2-i\sin 2)$ (we use that $\sin(-y)=-\sin y)$ .

Thus,

$e^{2i-3}+e^{-2i+3} = e^{-3}\cos 2+ie^{-3}\sin 2 + e^{3}\cos 2-ie^{3}\sin 2)$

Now we group conveniently in the above expression:

$e^{2i-3}+e^{-2i+3} = (e^{-3}+e^{3})\cos 2 + i(e^{-3}-e^{3})\sin 2$ .

Now, substituting this equality in (I) we get

$\cos(2+3i) = \frac{e^{-3}+e^{3}}{2}\cos 2 -i\frac{e^{3}-e^{-3}}{2}\sin 2 = \cosh 3\cos 2-i\sinh 3\sin 2$ .

Thus,

$\exp\left(\cos(2+3i)\right) = \exp\left(\cosh 3\cos 2-i\sinh 3\sin 2\right)$

$\exp\left(\cos(2+3i)\right) = \exp\left(\cosh 3\cos 2\right)\left[ \cos(\sinh 3\sin 2)-i\sin(\sinh 3\sin 2)\right]$ .

5 0

3 years ago

What is the slope of the line that passes through these two points? (6,4) 10 pa

kati45 [8]

Answer:

Step-by-step explanation:

(7-4)/(-2-6)= 3/-8 = -3/8 is the slope

5 0

3 years ago