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3 years ago

Write a rate that represents the situation

Mathematics

2 answers:

Anna35 [415]3 years ago

5 0

Answer:

$r=\frac{10}{3}$

Step-by-step explanation:

A rate in this context refers to the ratio of change of one variable with respect to the other one.

So, as you can observe, the variable liters is increasing 10 units, and the variable of time expressed in minutes is increasing 3 units. The ratio would be the fraction of these two increase numbers. Therefore the ratio for this situation would be:

$r=\frac{10}{3}$

Alika [10]3 years ago

3 0

Pretty sure it's 10 liters to every 3 min. (10:3 or 10 over 3)
i got u fam

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3 years ago

The endpoints of RS are R: (9,-4) and S: (2, -8).

Vladimir79 [104]

Answer:

B, (11/2,-6)

Step-by-step explanation:

to get the midpoint of two endpoints, simply take the average of each corresponding coordinate

midpoint: ((Rx+Sx)/2,(Ry+Sy/2)).

((9+2/2),(-4+-8/2)) = (11/2,-12/2) = (11/2,-6)

the midpoint formula in general is : ((x+x1)/2),(y+y1)/2))

where x1 is the initial or first x coordinate, y1 is the initial or first y coordinate, x is the second, last, or final x coordinate. and y is the second, last, or final y coordinate.

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2 years ago

Cathy uses 3/4 teaspoon of vanilla in a batch of cookies. How many teaspoons are needed for 8 batches of cookies

34kurt

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8 0

2 years ago

Let v = (v1, v2) be a vector in R2. Show that (v2, −v1) is orthogonal to v, and use this fact to find two unit vectors orthogona

andrey2020 [161]

Answer:

a. v.v' = v₁v₂ - v₁v₂ = 0 b. (20, -21)/29 and (-20,21)/29

Step-by-step explanation:

a. For two vectors a, b to be orthogonal, their dot product is zero. That is a.b = 0.

Given v = (v₁, v₂) = v₁i + v₂j and v' = (v₂, -v₁) = v₂i - v₁j, we need to show that v.v' = 0

So, v.v' = (v₁i + v₂j).(v₂i - v₁j)

= v₁i.v₂i + v₁i.(- v₁j) + v₂j.v₂i + v₂j.(- v₁j)

= v₁v₂i.i - v₁v₁i.j + v₂v₂j.i - v₂v₁j.j

i.i = 1, i.j = 0, j.i = 0 and j.j = 1

So, v.v' = v₁v₂i.i - v₁v₁i.j + v₂v₂j.i - v₂v₁j.j

= v₁v₂ × 1 - v₁v₁ × 0 + v₂v₂ × 0 - v₂v₁ × 1

= v₁v₂ - v₂v₁

= v₁v₂ - v₁v₂ = 0

So, v.v' = 0

b. Now a vector orthogonal to the vector v = (21,20) is v' = (20,-21).

So the first unit vector is thus a = v'/║v'║ = (20, -21)/√[20² + (-21)²] = (20, -21)/√[400 + 441] = (20, -21)/√841 = (20, -21)/29.

A unit vector perpendicular to a and parallel to v is b = (-21, -20)/29. Another unit vector perpendicular to b, parallel to a and perpendicular to v is thus a' = (-20,-(-21))/29 = (-20,21)/29

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