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2 years ago

15

Recall that the standard basis of ℝ3 is {E1, E2, E3}. If T:ℝ3→ℝ2 is a transformation and the action of T on the vectors Ei is as

given, find a formula for T(X), where X is any vector in ℝ3.
T(E1)= 2 T(E2)= \begin{bmatrix} 0 \\ 5 \end{bmatrix} T(E3) = \begin{bmatrix} 4 \\ 0 \end{bmatrix}

T\begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} ? \\ ? \\ ? \end{bmatrix}

1 answer:

omeli [17]2 years ago

4 0

Answer:

Your question is not clear. But it seems like the answer could be like the one at the images.

Step-by-step explanation:

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Identify the 12th term of the arithmetic sequence in which a7 = 40 and a18 = 106.

Lady_Fox [76]

we are given

airthematic sequence

we can use nth term formula

$a_n=a_1+(n-1)d$

n is number of terms

an is nth term

d is common difference

a1 is first term

We are given

a7=40

we can use it

$a_7=a_1+(7-1)d$

$40=a_1+6d$

$a_1+6d=40$

a18 = 106

$a_1_8=a_1+(18-1)d$

$a_1+17d=106$

we can subtract both equations

$a_1+17d-a_1-6d=106-40$

$11d=66$

$d=6$

now, we can find a1

$a_1+6d=40$

we can plug d=6

$a_1+6*6=40$

$a_1=4$

12th term:

$a_1_2=a_1+(12-1)d$

now, we can plug values

$a_1_2=4+(12-1)*6$

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$a_1_2=70$

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2 years ago

A stereo manufacturer makes three types of stereo systems, I, II, and III, with profits of $20, $30, and $40, respectively. No m

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So,

1. Type I profits $20
2. Type II profits $30
3. Type III profits $40
4. I/day < 100
5. Type I needs 5 hrs.
6. Type II needs 10 hrs.
7. Type III needs 15 hrs.
8. Total hrs. available: 2000 hrs.

Every +5 hrs. spent yields an extra $10.
If we use 500 hrs. to make 100 Type I stereos, we will profit $2000.
If we use 500 hrs. to make 50 Type II stereos, we will profit $1500.
If we use 495 hrs. to make 33 Type III stereos, we will profit $1320.

We should use the first 500 hrs. to make Type I stereos.
We should use the last 1500 hrs. to make Type II stereos.

$2000 + $4500 = x
$6500 = x

There must be 100 Type I stereos made along with 150 Type II stereos made.

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Use differentials to estimate the amount of paint needed to apply a coat of paint 0.07 cm thick to a hemispherical dome with dia

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Answer:

10.12 $m^{3}$

Step-by-step explanation:

Given:

0.07 cm thick = 0.007m and it is dr (the change in radius)

As we know that, the volume of a hemispherical dome with diameter 48 m is:

V = $\frac{2}{3}$ π $r^{3}$

Take the derivative of V we have:

$\frac{dV}{dr}$ = 2π $r^{2}$

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Hope it will find you well.

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