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6 days ago

Find three different surfaces that contain the curve r(t) = t^2 i + lnt j + (1/t)k

1 answer:

7 0

Let’s consider the curve: r(t) = t²i +(int)j + 1/t k X = t², y = int,z = 1/t Utilizing x = t² and z = 1/t X = (1/z)² Xz² = 1 Now using y = int and z= 1/t Y = in│1/z│ By using x = t² and y = int Y = int = in(√x) Thus, the resulting surfaces are, Xz² = 1 Y = in│1/z│ Y= in(√x)

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A photocopy machine can reduce copies to 80% of their original size. By copying an already reduced copy, further reductions can

PIT_PIT [9121]

Part a) When a page is scaled down to 80%, how much enlargement is necessary to bring it back to its original size?

Let

x---------> the percent enlargement

Given the original size is 100%

This means:

x*80%=100%

x=(100%/80%)

x=1.25--------> 1.25=(125/100)=125%

Thus,

The answer to Part a) is

The percent enlargement required is 125%

Part b) Estimate how many successive copies of a page are needed to make the final copy less than 15% of its original size.

Since the photocopy machine reduces sizes to 80% of the original

Therefore:

Copy N 1

0.80*100%=80%

Copy N 2

0.80*80%=64%

Copy N 3

0.80*64%=51.2%

Copy N 4

0.80*51.2%=40.96%

Copy N 5

0.80*40.96%=32.77%

Copy N 6

0.80*32.77%=26.21%

Copy N 7

0.80*26.21%=20.97%

Copy N 8

0.80*20.97%=16.78%

Copy N 9

0.80*16.78%=13.42%-------------> 13.42% < 15%

Therefore,

The answer to Part b) is

The necessary number of copies to achieve this is 9

6 0

21 day ago

DOPO

AnnZ [9104]

Response:

$144,843.5

Detailed explanation:

In this scenario, we will utilize the compound interest formula

A= P(1+r)^t

A = final amount

P = initial principal

r = interest rate

t = number of periods

Given parameters

P= $27,000

R= 7.25%= 7.25/100= 0.0725

T= 24

A=27000(1+0.0725)^24

A= 27000(1.0725)^24

A= 27000*5.364

A= $144,843.5

By the end of 24 years, her account balance will reach $144,843.5

5 0

15 days ago

Triangle X Y Z is shown. The length of side X Y is (9 n + 12) feet and the length of side X Z is (15 n minus 6) feet. Angles X Y

babunello [8423]

Answer:

$n = 3$

$XY = 39$

$XZ = 39$

Step-by-step explanation:

Given

$XY = 9n + 12$

$XZ = 15n - 6$

Solving for (a): n

To find n;

We will utilize

$XY = XZ$

Substituting values for XY and XZ

$9n + 12 = 15n - 6$

$9n - 15n = -12 - 6$

$-6n = -18$

Dividing by -6

$n = 3$

Solving for (b) XY

$XY = 9n + 12$

Substituting 3 for n

$XY = 9 * 3 + 12$

$XY = 27 + 12$

$XY = 39$

Solving for (c): XZ

$XZ = XY$

$XZ = 39$

7 0

29 days ago

Sal recorded the number of crackers in each snack-sized package he opened. Which statement must be true according to the box plo

PIT_PIT [9121]

Response:

The data shows skewness, with the minimum amount of crackers in a pack being 7

Detailed explanation:

Hello,

Firstly, the question lacks completeness due to missing information from the box plot, which I have provided to assist you in answering your inquiry.

Considering the details from the attached image, a symmetric distribution would be centered evenly, but that is not the case here.

The image indicates a positive skew, with the lowest count recorded as 7.

7 0

12 hours ago

Read 2 more answers

A rocket was launched into the air from a podium 6 feet off the ground. The rocket path is represented by the equation h(t)=-16t

lawyer [9240]

Answer:

Step-by-step explanation:

The function provided is:

$h(t)=-16t^2+120t+6$

The average rate of change of h(t) as time goes from t=a to t=b is expressed as:

$\frac{h(b)-h(a)}{b-a}$

This function can be reformulated as: $h(t)=-16(t-3.75)^2+231$

The rocket's peak height is 231, which occurs at t=3.75 seconds.

$\implies h(3.75)=231$

The initial launch happens at: t=0

and $h(0)=-16(0)^2+120(0)+6=6$

The average rate of change from launch to max height is

$\frac{h(3.75)-h(0)}{3.75-0}=\frac{231-6}{3.75-0} =60$

6 0

1 month ago