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Papessa [141]
3 years ago
13

Samantha is making soup. to make the broth, she combines 2/5 cup of vegetable stock and 2/3 cup of chicken soup stock. Boiling

the broth causes 1/4 cup of the liquid to evaporate. How much broth is left after it is boiled?
Mathematics
2 answers:
klasskru [66]3 years ago
8 0
Add 2/5 + 2/3, but first change the fractions so that they have an equal denominator. Since 3 and 5 (the denominators) both have 15 in common lets multiply 2/5 by 3/3 which gets you 6/15. 2/3 x 5/5 equals 10/15. 6/15 + 10/15= 16/15. Don't change 16/15 into a mixed number yet we still have to subtract 1/4 cup of liquid (after it's boiled) from the total amount of liquid (before it's boiled): 16/15. 16/15 and 1/4 don't have the same denominator, we're going to have to change that. 15 and 4 both have 60 in common. So now let's multiply 1/4 by 15/15 which equals 15/60. Now we're going to change 16/15 by multiplying it by 4/4 which equals 64/60. Finally, we're going to subtract 64/60 - 15/60=49/60.49/60 cups of broth is left after its boiled.
storchak [24]3 years ago
6 0
First,you do,2/5+2/3,but since you will need a common denominator,you will find the least common denominator for 5 and 3.The LCD(Least Common Denominator) will be 15 since both 5 and 3 could go in 15.Now,the equation looks like this: 2/15+2/15 since whatever you do to the bottom numbers,you NEED to do to the top numbers:2 and 2.Now you will need to do,2x3,since 5x3=15 and the answer to 2x3=6 then you do 2x5,since 3x5=15 the answer is 10 now the equation looks like this:6/15+10/15 now you add them together,and the answer will be 16/15 and if you want the answer to be a mixed number,it would look like this: 1 1/15. Hope this helps!
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hram777 [196]

Given

\frac{88}{90}

So,

\frac{88}{90}=\frac{2\cdot44}{2\cdot45}=\frac{44}{45}

So, the simplest form of 88/90 is 44/45

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Double angle identity. Just 5 questions. Really need help as my teacher has been frustrated with me
BartSMP [9]

The double angle identities are

\sin(2x)=2\sin x\cos x

\cos(2x)=\cos^2x-\sin^2x

Then

2\sin\dfrac\pi6\cos\dfrac\pi6=\sin\left(\dfrac{2\pi}6\right)=\sin\dfrac\pi3

\cos^2\dfrac\pi{10}-\sin^2\dfrac\pi{10}=\cos\left(\dfrac{2\pi}{10}\right)=\cos\dfrac\pi5

The second identity together with the Pythagorean identity, \sin^2x+\cos^2x=1, gives us another equivalent expression:

\cos^2x-\sin^2x=\cos^2x-(1-\cos^2x)=2\cos^2x-1

so

2\cos^2(0.5)-1=\cos(2\cdot0.5)=\cos1

4 0
3 years ago
Read 2 more answers
Mark has already run 33.4 miles this week. He can run 2.5 miles in one hour. Construct an equation that represents the total num
DanielleElmas [232]

Answer:

y = 2.5x + 33.4, y = 75.9 miles

Step-by-step explanation:

Equation is y = 2.5x + 33.4

17 = 2.5 x + 33.4

y = 2.5 (17) + 33.4

y = 42.5 + 33.4

y = 75.9 miles

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2 years ago
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Dimas [21]
3 x 12 = 36
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Compute the differential of surface area for the surface S described by the given parametrization.
AysviL [449]

With S parameterized by

\vec r(u,v)=\langle e^u\cos v,e^u\sin v,uv\rangle

the surface element \mathrm dS is

\mathrm dS=\left\|\dfrac{\partial\vec r}{\partial u}\times\dfrac{\partial\vec r}{\partial v}\right\|\,\mathrm du\,\mathrm dv

We have

\dfrac{\partial\vec r}{\partial u}=\langle e^u\cos v,e^u\sin v,v\rangle

\dfrac{\partial\vec r}{\partial v}=\langle -e^u\sin v,e^u\cos v,u\rangle

with cross product

\dfrac{\partial\vec r}{\partial u}\times\dfrac{\partial\vec r}{\partial v}=\langle ue^u\sin v-ve^u\cos v,-ve^u\sin v-ue^u\cos v,e^{2u}\cos^2v+e^{2u}\sin^2v\rangle

\dfrac{\partial\vec r}{\partial u}\times\dfrac{\partial\vec r}{\partial v}=\langle e^u(u\sin v-v\cos v),-e^u(v\sin v+u\cos v),e^{2u}\rangle

with magnitude

\left\|\dfrac{\partial\vec r}{\partial u}\times\dfrac{\partial\vec r}{\partial v}\right\|=\sqrt{e^{2u}(u\sin v-v\cos v)^2+e^{2u}(v\sin v+u\cos v)^2+e^{4u}}

\left\|\dfrac{\partial\vec r}{\partial u}\times\dfrac{\partial\vec r}{\partial v}\right\|=e^u\sqrt{u^2+v^2+e^{2u}}

So we have

\mathrm dS=\boxed{e^u\sqrt{u^2+v^2+e^{2u}}\,\mathrm du\,\mathrm dv}

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