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2 years ago

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Suppose Monica Walks 1 kilometer every 15 minutes. How many meters further can she walk in 1 hour at this new rate? EXPLAIN how

you found your answer

1 answer:

skelet666 [1.2K]2 years ago

4 0

Well every 15 minutes he walks 1 step. So divide an hour which is 60minutes by 15 minutes. Then the answer to that you multiply by 1. So the equation would be (60/15)x1= and you will find the answer.

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Paint sells in metal cans one gallon each. How many gallons of paint must be purchased to paint a room containing 840 square fee

Kisachek [45]

Answer:

5 Gallons of paint

Step-by-step explanation:

840 square ft one Gallons covers 190 square ft

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3 years ago

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ivolga24 [154]

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3 years ago

Read 2 more answers

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

2 years ago

Hey i need help this assignment is like 3 pages long

slavikrds [6]

Answer:

c=1.96

Step-by-step explanation:

2.1/c=1.5/1.4

2.1*1.4=1.5*c

2.94/1.5=1.5c/1.5

c=1.96

7 0

2 years ago

A 12 ounce bottle of cleaner cost $3.74 a 16 ounce bottle of cleaner cost $5.34 which bottle would be the best spot which cost l

Valentin [98]

Answer:

12 ounce bottle

Step-by-step explanation:

12 x 3 = 36

16 x 5 = 80

So, that means the 12 ounce bottle is cheaper. :)

5 0

3 years ago