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Allushta [10]
3 years ago
6

Use the grid to draw three different rectangles so that each has an area of 12 square units and they all have different widths.

What are the dimensions of the rectangles?

Mathematics
2 answers:
Ymorist [56]3 years ago
6 0
What numbers multiply to 12?
1 and 12
2 and 6
3 and 4

A rectangle with each of these dimensions will have an area of 12.
mamaluj [8]3 years ago
4 0

Answer:

1,2,3,4,6,12

Step-by-step explanation:

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(1 point) A student was asked to find the equation of the tangent plane to the surface z=x2−y3 at the point (x,y)=(5,1). The stu
Nonamiya [84]

Answer:

Options a and d are the correct ones.

Step-by-step explanation:

The complete question is as follows

A student was asked to find the equation of the tangent plane to the surface z = x^2-y^3 at the point (x,y)=(5,1). The student's answer was  z = 24+2x(x-5)-3y^2(y-1). (a) At a glance, how do you know this is wrong. What mistakes did the student make? Select all that apply.

a) The answer is not a linear function

b) The (x-5) and (y-1) should be x and y

c) the 24 should not be in the answer

d) the partial derivatives were not evaluated at the point

e) all of the above.

Recall that, given a surface of the form z=f(x,y) where f is differentiable, then at a given point (x_0,y_0) we can find the equation of the tangent plane by

z=f(x_0,y_0)+\frac{df}{dx}(x_0,y_0) (x-x_0)+\frac{df}{dy}(x_0,y_0) (y-y_0)

We are given that (x_0,y_0) = (5,1) Note that f(5,1) = 24. Then, c is not true. Also, the formula says that we must have the factors (x-5) and (y-1), since we are evaluating the tangent plane in a neighborhood of that point, hence option b is not true. Since B and C are not true, then E is not true. Note that the given function by the student has a mutiplication of 2x and (x-5) which will give us the function 2x^2-10 which is of degree two. Then, the function given by the student is not a linear function, since linear functions have a degree at most 1. Finally, we must check that d is also true.

REcall that

\frac{df}{dx} = 2x, \frac{df}{dy} = -3y^2

so we see that this coincide with the the terms that multiply the factors (x-5) and (y-1) respectively, which tell us that even though the student was trying to follow the formula, he/she forgot to evaluate the partial derivatives at the given point, hence the option D is also true.

Recall that if we want the tangent plane at the point given, we must evaluate the partial derivatives at x=5 and y=1. Hence, the formula of the tangent plane is

z = 24+10(x-5)-3(y-1)

5 0
3 years ago
To rent a van, a moving company charges $50.00 plus $5.50 per mile. The table shows the total cost for the number of miles drive
LuckyWell [14K]
Y = 55/10x + 50 is the equation to represent this situation
5 0
3 years ago
Pilar is playing with a motorized toy boat. She puts the boat in a lake and it travels 400m at a constant speed. On the way back
ankoles [38]

Answer:

The trip normally takes 8 minutes

Step-by-step explanation:

The given information states that the away distance the boat traveled = 400 m

The time traveled at the same initial  speed , v₁, by the boat on the way back = 2 minutes

The increase in speed of the boat by Pilar =  10 m/min

The new speed, v₂ = v₁ + 10

The time for the return trip, t₂ = 60 seconds (1 minute) faster than time for the trip, t₁

t₂ = t₁ - 1

Therefore we have;

v₁ × t₁ = v₁×2 + v₂×(t₂-2) = 400

v₁×2 + (v₁ + 10)×(t₂-2) = 400

(v₁ + 10)×t₂ - 20 = 400

But v₁ = 400/t₁ = 400/(t₂ + 1)

Which gives;

(400/(t₂ + 1) + 10)×t₂ - 20 = 400

10×(t₂²+ 36·t₂-2)/(t₂+1) = 400

10·t₂²+ 10·t₂-420 = 0

t₂²+ t₂-42 = 0

(t₂ - 7)(t₂ + 6) = 0

t₂ = 7 minutes or -6 minutes

Given that t₂ is a natural number, we have, t₂ = 7 minutes

Whereby, t₂ = t₁ - 1, we have;

7 =  t₁ - 1

t₁ = 1 + 7 = 8 Minutes

The trip normally takes 8 minutes

3 0
3 years ago
Nigel wants to average 85% on his four tests. He got 77%, 89%, 78% on his first three tests. What does he need to get on his las
Arte-miy333 [17]

Answer:

He needs to get 96%

Step-by-step explanation:

Add 96 89 77 and 78 together and divide by 4, it should be 85

4 0
3 years ago
I need help finding values of x,y,z. I want to know if there is an answer apart from 0, since that is what I need to find. Thank
vichka [17]

Answer:

They all equal zero

Step-by-step explanation:

A number cannot equal itself times any number that isn't zero, unless it itself is zero.

3 0
2 years ago
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