Unit rate per orange

What is the unit rate for 500.48 meters in 27.2 hours?

Daniel [21]

27.2h÷1h=27.2
500.48m in 27.2h
(÷27.2)
18.4 in 1h

Ans: 18.4m/h

4 0

3 years ago

the annual interest rate for jacks savings account increased from 2.8% to 4.1%. Describe the change as a relative change in term

densk [106]

Answer:

The additional 1.3% of increase in the annual interest rate that Jack is receiving in his savings account, from 2.8% to 4.1%, represent an increase of 46.42%.

Step-by-step explanation:

Jacks's savings account annual interest rate before = 2.8%

Jacks's savings account annual interest rate after the increase = 4.1%

Difference of the two rates = 4.1% - 2.8% = 1.3%

How much percentage is that additional 1.3% from the rate before the increase?

(1.3 * 100)/ 2.8 = 130/2.8 = 46.42%

The annual interest rate increased by 46.42% from the previous annual interest rate.

3 0

3 years ago

I dont get this so cant help daughter

sergey [27]

1.

We are told that the coordinates of the image are of the formula:

P'(x-2 , y-3) where x and y are the actual points and x-2 and y-3 are the reflections

Finding the coordinates of point A:

We are given that the coordinates of reflection of A are: A'(-4 , 3)

we also know that reflected point follow the formula: P'(x-2 , y-3)

So, the points of A'(-4 , 3) follow the formula P'(x-2 , y-3)

So, their respective x and y coordinates will be equal

Hence,

x - 2 = -4

x = -2 [adding 2 on both sides]

Also,

y - 3 = 3

y = 6 [adding 3 on both sides]

Therefore, the coordinates of A are A(-2,6)

Finding the coordinates of B:

We are given the coordinates of B' are B'(-4 , 2)

So,

x - 2 = -4

x = -2 [adding 2 on both sides]

also,

y-3 = 2

y = 5 [adding 5 on both sides]

Therefore, the coordinates of B are: B(-2,5)

Finding the coordinates of C:

We are given that the coordinates of reflection of C are: C'(-2,3)

Using the general formula given in the question:

x - 2 = -2

x = 0 [adding 2 on both sides]

y - 3 = 3

y = 6 [adding 3 on both sides]

Therefore, the coordinates of C are: C(0,6)

Finally, the coordinates of A, B and C are:

A(-2,6) , B(-2,5) , C(0,6)

__________________________________________________________

2.

Reflecting the pre-image along the x-axis

To reflect along x-axis, we multiply the y-coordinate by -1

Coordinates of the pre-image:

A(-2,6) , B(-2,5) , C(0,6)

Coordinates of points reflected along the x-axis:

A(-2,-6) , B(-2,-5) , C(0,-6)

5 0

3 years ago

A particle moves on the hyperbola xy=18 for time t≥0 seconds. At a certain instant, y=6 and dydt=8. What is x that this instant?

professor190 [17]

Answer:

The value of x at this instant is 3.

Step-by-step explanation:

Let $x\cdot y = 18$ , we get an additional equation by implicit differentiation:

$x\cdot \frac{dy}{dt}+y\cdot \frac{dx}{dt} = 0$ (1)

From the first equation we find that:

$x = \frac{18}{y}$ (2)

By applying (2) in (1), we get the resulting expression:

$\frac{18}{y}\cdot \frac{dy}{dt}+y\cdot \frac{dx}{dt} = 0$ (3)

$y\cdot \frac{dx}{dt}=-\frac{18}{y}\cdot \frac{dy}{dt}$

$\frac{dx}{dt} = -\frac{18}{y^{2}} \cdot \frac{dy}{dt}$

If we know that $y = 6$ and $\frac{dy}{dt} = 8$ , then the first derivative of x in time is:

$\frac{dx}{dt} = -\frac{18}{6^{2}} \cdot (8)$

$\frac{dx}{dt} = -4$

From (1) we determine the value of x at this instant:

$x\cdot \frac{dy}{dt} = -y\cdot \frac{dx}{dt}$

$x = -y\cdot \left(\frac{\frac{dx}{dt} }{\frac{dy}{dt} } \right)$

$x = -6\cdot \left(\frac{-4}{8} \right)$

$x = 3$

The value of x at this instant is 3.

4 0

3 years ago

Suppose the sound wave has the form y=7cos(3x-pi/6) for x in the interval [pi/6 , 7pi/18]. Express x as a function of y, and sta

Vesnalui [34]

Answer:

x = ⅓ acos(y/7) + π/18, [-7, 7/2]

Step-by-step explanation:

y = 7 cos(3x − π/6)

Solving for x:

y/7 = cos(3x − π/6)

acos(y/7) = 3x − π/6

acos(y/7) + π/6 = 3x

x = ⅓ acos(y/7) + π/18

The domain of x is the same as the range of y.

When x = π/6:

y = 7 cos(3π/6 − π/6)

y = 7 cos(π/3)

y = 7/2

When x = 7π/18:

y = 7 cos(21π/18 − π/6)

y = 7 cos(π)

y = -7

So the domain of x as a function of y is [-7, 7/2].

5 0

4 years ago