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fiasKO [112]
3 years ago
8

An artist is painting the outside of the box shown below. The top and bottom will NOT be painted. What is the total surface area

that the artist will be painting?
Mathematics
1 answer:
Montano1993 [528]3 years ago
3 0

Answer:

15 square feet

Step-by-step explanation:

Multiply 1.5 by 3 which equals 4.5

Multiply 1.5 by 2 which equals 3

Add the above answers (4.5 plus 3)

Then multiply by 2 (7.5 times 2)

It equals 15

I hope this helps and that this is the right problem. There is no picture shown but I just did this problem for someone else so I thought I would take a shot at it :)

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EXAMPLE 1 (a) Find the derivative of r(t) = (2 + t3)i + te−tj + sin(6t)k. (b) Find the unit tangent vector at the point t = 0. S
Tatiana [17]

The correct question is:

(a) Find the derivative of r(t) = (2 + t³)i + te^(−t)j + sin(6t)k.

(b) Find the unit tangent vector at the point t = 0.

Answer:

The derivative of r(t) is 3t²i + (1 - t)e^(-t)j + 6cos(6t)k

(b) The unit tangent vector is (j/2 + 3k)

Step-by-step explanation:

Given

r(t) = (2 + t³)i + te^(−t)j + sin(6t)k.

(a) To find the derivative of r(t), we differentiate r(t) with respect to t.

So, the derivative

r'(t) = 3t²i +[e^(-t) - te^(-t)]j + 6cos(6t)k

= 3t²i + (1 - t)e^(-t)j + 6cos(6t)k

(b) The unit tangent vector is obtained using the formula r'(0)/|r(0)|. r(0) is the value of r'(t) at t = 0, and |r(0)| is the modulus of r(0).

Now,

r'(0) = 3t²i + (1 - t)e^(-t)j + 6cos(6t)k; at t = 0

= 3(0)²i + (1 - 0)e^(0)j + 6cos(0)k

= j + 6k (Because cos(0) = 1)

r'(0) = j + 6k

r(0) = (2 + t³)i + te^(−t)j + sin(6t)k; at t = 0

= (2 + 0³)i + (0)e^(0)j + sin(0)k

= 2i (Because sin(0) = 0)

r(0) = 2i

Note: Suppose A = xi +yj +zk

|A| = √(x² + y² + z²).

So |r(0)| = √(2²) = 2

And finally, we can obtain the unit tangent vector

r'(0)/|r(0)| = (j + 6k)/2

= j/2 + 3k

8 0
3 years ago
This is #5 <br> Algebra-Find the value for x<br> I know it’s 11 but how do I get there.
Sergeeva-Olga [200]

Answer:

x = 11

Step-by-step explanation:

the line x + 5 is a mid segment of the triangle and thus is half the length of 3x - 1, that is

x + 5 = \frac{1}{2}(3x - 1)

multiply both sides by 2 to eliminate the fraction

2x + 10 = 3x - 1 ( subtract 3x from both sides )

- x + 10 = - 1 ( subtract 10 from both sides )

- x = - 11 ( multiply both sides by - 1 )

x = 11




3 0
3 years ago
Describe a vectors v = [x y] that are orthogonal to u = [a b]. If u is not the zero vector, then v is a multiple of [a b]. If u
hoa [83]

Answer:

Step-by-step explanation:

Sbdbshee

6 0
3 years ago
What is the value of x?<br> 6-2/3(x+5)=4x
gogolik [260]

It was 14

3

x + 8

3

= 0

Factorization:

−2

3

(7x − 4) = 0

Solutions:

x = 8

14

≈ 0.571429

7 0
3 years ago
HELP ASAP PLEASE
Liula [17]

distance : 15 units

coordinates :  (7,0) and (-8, 45)

slope:

\sf \rightarrow  \dfrac{y_2-y_1}{x_2-x_1}

\sf \rightarrow  \dfrac{45-0}{-8-7}

\sf \rightarrow  -3

equation:

\hookrightarrow \sf y - 0 = -3(x-7)

\hookrightarrow \sf y = -3x+21

the y-intercept of this function:

\hookrightarrow \sf y = -3(0)+21

\hookrightarrow \sf y =21

distance between both y-intercept :

  • 21 - 6
  • 15
3 0
2 years ago
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