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2 years ago

Solve for y.

Mathematics

1 answer:

inysia [295]2 years ago

5 0

Answer:

18) y = (24-4x)/7

19) y = 5/7x

20) y = a/b

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An 8-sided die is formed when two square pyramids are attached by their bases. The perimeter of the base shape is 6 centimeters.

bogdanovich [222]

1. Check the picture attached. Consider the half of the 8-sided die, that is the pyramid ABCDE:

2. The perimeter of the base is 6, so each side of the base is 6/4=3/2

3. The distance between the tallest points is 2 cm, si the height of Pyramid ABCDE is 1 cm.

4. Consider the right triangle EOM in the figure:

EO=1, OM= 3/4 (it is half of AB=3/2) and EM is the hypothenuse, so by the pythagorean theorem length of EM is $\sqrt{1+ ( \frac{3}{4} )^{2} }= \sqrt{1+ \frac{9}{16} }= \sqrt{ \frac{25}{16} }= \frac{5}{4}$ (cm)

5. So side EBC has area
$\frac{1}{2}BC*EM= \frac{1}{2}* \frac{3}{2}* \frac{5}{4}= \frac{15}{16}$

6. The total area is 8*Area(EBC)= $8* \frac{15}{16}= \frac{15}{2}=7.5 ( cm^{2} )$

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3 years ago

Read 2 more answers

Which of the following is true when probability answer is written in the form of a fraction

____ [38]

The subject area of probability is actually expressed as a fraction or percentage because it represents a part of a whole. In lay man's term, probability is the scientific study of chance, likeliness and odds of an event happening. For example, you want to find the odds of getting a heads in a toss of the coin. You know that there are 2 possible results: head and tails. So, the probability of getting a head is 1/2 or 50%. Since it is a part of a whole, the probability in fraction should never be an improper fraction. This is the type of fraction in which the numerator is greater than the denominator. This is impossible as a probability because it will never exceed 1.

7 0

2 years ago

Simplify. Show your work. 5-1/3 + (-3-9/18)

Ipatiy [6.2K]

You have to use PEMDAS, it stands for parenthesis, exponents, multiplication, division, addition, and subtraction. So first you have to subtract the numbers in the parenthesis which is -3.5 (9/18=1/2). Since there are no exponents or multiplying or dividing, we skip those. Now, we do 5-1/3 and we get 4 2/3. Lastly, add 4 2/3 and -3.5(which is equal to -3 1/2). We get 2 1/6=13/6=1.166666667

I hope this helps!

4 0

2 years ago

What is The volume of right rectangular prism 3 cm 3 cm 12 cm

Cloud [144]

Answer:

Step-by-step explanation:

4 0

3 years ago

Question on laplace transform... number 7

irinina [24]

Recall a few known results involving the Laplace transform. Given a function $f(t)$ , if the transform exists, then denote it by $F(s)$ . We have

$\mathcal L_s\left\{e^{ct}f(t)\right\}=\mathcal L_{s-c}\left\{f(t)\right\}=F(s-c)$

$\mathcal L_s\left\{\displaystyle\int_0^t f(u)\,\mathrm du\right\}=\dfrac{F(s)}s$

$\mathcal L_s\left\{f'(t)\right\}=sF(s)-f(0)$

Let's put all this together by taking the transform of both sides of the ODE:

$y'(t)+2e^{-2t}\displaystyle\int_0^te^{2u}y(u)\,\mathrm du=e^{-t}\sin t$

$\implies \bigg(sY(s)-y(0)\bigg)+2\mathcal L_s\left\{e^{-2t}\displaystyle\int_0^te^{2u}y(u)\,\mathrm du\right\}=\dfrac1{(s+1)^2+1}$

Here we use the third fact and immediately compute the transform of the right hand side (I'll leave that up to you).

Now we invoke the first listed fact:

$\mathcal L_s\left\{e^{-2t}\displaystyle\int_0^te^{2u}y(u)\,\mathrm du\right\}=\mathcal L_{s+2}\left\{\displaystyle\int_0^te^{2u}y(u)\,\mathrm du\right\}$

Let $g(u)=e^{2u}y(u)$ . From the second fact, we get

$\mathcal L_s\left\{\displaystyle\int_0^tg(u)\,\mathrm du\right\}=\dfrac{G(s)}s\implies\mathcal L_{s+2}\left\{\displaystyle\int_0^tg(u)\,\mathrm du\right\}=\dfrac{G(s+2)}{s+2}$

From the first fact, we get

$G(s)=\mathcal L_s\left\{e^{2u}y(u)\right\}=Y(s-2)$

so we're left with

$\dfrac{G(s+2)}{s+2}=\dfrac{Y((s+2)-2)}{s+2}=\dfrac{Y(s)}{s+2}$

To summarize, taking the Laplace transform of both sides of the ODE yields

$sY(s)+\dfrac{2Y(s)}{s+2}=\dfrac1{(s+1)^2+1}$

Isolating $Y(s)$ gives

$Y(s)=\dfrac1{\left(s+\frac2{s+2}\right)\left((s+1)^2+1\right)}$
$Y(s)=\dfrac{s+2}{\left((s+1)^2+1\right)^2}$

All that's left is to take the inverse transform. I'll leave that to you as well. You should end up with something resembling

$y(t)=\dfrac12(t\cos t-(t+1)\sin t)(\sinh t-\cosh t)$

4 0

3 years ago