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3 years ago

10

Jen has 2 meters of taffy. She wants to give each of her 3 best friends an equal amount of taffy. How many centimeters of taffy

will each friend get? Write your answer as a fraction.

2 answers:

timurjin [86]3 years ago

7 0

Each friend will get 2/3 of a meter. This is so because if you divide the 2 meters of taffy by her 3 friends, then you get 2/3 of a meter.

Natali [406]3 years ago

7 0

1 meter = 100 cm.....so 2 meters = (100 * 2) = 200 cm

and u want to split it 3 ways....
200/3 cm. or 66 2/3 cm. <== ur answer

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Lorico [155]

Answer:

Step-by-step explanation:

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3 years ago

Evaluate the expression 3x² + 2x - 4 for x =-2.

marin [14]

Answer:

4

Step-by-step explanation:

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3 years ago

For 0 ≤ ϴ < 2π, how many solutions are there to tan(StartFraction theta Over 2 EndFraction) = sin(ϴ)? Note: Do not include va

Black_prince [1.1K]

Answer:

3 solutions:

$\theta={0, \frac{\pi}{2}, \frac{3\pi}{2}}$

Step-by-step explanation:

So, first of all, we need to figure the angles that cannot be included in our answers out. The only function in the equation that isn't defined for some angles is $tan(\frac{\theta}{2})$ so let's focus on that part of the equation first.

We know that:

$tan(\frac{\theta}{2})=\frac{sin(\frac{\theta}{2})}{cos(\frac{\theta}{2})}$

therefore:

$cos(\frac{\theta}{2})\neq0$

so we need to find the angles that will make the cos function equal to zero. So we get:

$cos(\frac{\theta}{2})=0$

$\frac{\theta}{2}=cos^{-1}(0)$

$\frac{\theta}{2}=\frac{\pi}{2}+\pi n$

or

$\theta=\pi+2\pi n$

we can now start plugging values in for n:

$\theta=\pi+2\pi (0)=\pi$

if we plugged any value greater than 0, we would end up with an angle that is greater than $2\pi$ so, that's the only angle we cannot include in our answer set, so:

$\theta\neq \pi$

having said this, we can now start solving the equation:

$tan(\frac{\theta}{2})=sin(\theta)$

we can start solving this equation by using the half angle formula, such a formula tells us the following:

$tan(\frac{\theta}{2})=\frac{1-cos(\theta)}{sin(\theta)}$

so we can substitute it into our equation:

$\frac{1-cos(\theta)}{sin(\theta)}=sin(\theta)$

we can now multiply both sides of the equation by $sin(\theta)$

so we get:

$1-cos(\theta)=sin^{2}(\theta)$

we can use the pythagorean identity to rewrite $sin^{2}(\theta)$ in terms of cos:

$sin^{2}(\theta)=1-cos^{2}(\theta)$

so we get:

$1-cos(\theta)=1-cos^{2}(\theta)$

we can subtract a 1 from both sides of the equation so we end up with:

$-cos(\theta)=-cos^{2}(\theta)$

and we can now add $cos^{2}(\theta)$

to both sides of the equation so we get:

$cos^{2}(\theta)-cos(\theta)=0$

and we can solve this equation by factoring. We can factor $cos(\theta)$ to get:

$cos(\theta)(cos(\theta)-1)=0$

and we can use the zero product property to solve this, so we get two equations:

Equation 1:

$cos(\theta)=0$

$\theta=cos^{-1}(0)$

$\theta={\frac{\pi}{2}, \frac{3\pi}{2}}$

Equation 2:

$cos(\theta)-1=0$

we add a 1 to both sides of the equation so we get:

$cos(\theta)=1$

$\theta=cos^{-1}(1)$

$\theta=0$

so we end up with three answers to this equation:

$\theta={0, \frac{\pi}{2}, \frac{3\pi}{2}}$

7 0

3 years ago

2. Sally is eating a bag of M&M's. 12 were green, 16 were brown, 8 were

MariettaO [177]

Answer:

60%

Step-by-step explanation: 12+16+8+4 is equal to 40. 40 minus the number of brown m&ms is 24 .24/40 as a percentage is 60%. Hope this helps!!!

3 0

3 years ago

Im a little confused on this on can someone help me with this thanks!

Arlecino [84]

This is a bit confusing, double check if you typed everything correctly.

6 0

2 years ago

Read 2 more answers