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3 years ago

A damsel is in distress and is being

Mathematics

2 answers:

Katen [24]3 years ago

6 0

Answer:

30 feet

Step-by-step explanation:

Let x be the length of the ladder. Then, x cos(60) = 15

If we divide both sides by cos(60), then x = 30 feet.

tatyana61 [14]3 years ago

3 0

30 feet. I hope this helps!

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121+b^2=12.1^2<br> What is the value of b^2?

luda_lava [24]

$121 + b^2 = 12.1^2$
Square 12.1, and subtract 121 from both sides.
$b^2 = 146.41 - 121$
Complete the subtraction on the right side.
$b^2 = 25.41$
This is the solution.

$b^2 = 25.41$

5 0

4 years ago

Julie, a police officer, has the following work pattern. She works 3 days, has 4 days off, then works 4 days, then has 3 days of

zalisa [80]

Answer:

See below.

Step-by-step explanation:

For each day number, Y means working, and N means off

Day

1 Y

2 Y

3 Y

4 N

5 N

6 N

7 N

8 Y

9 Y

10 Y

11 Y

12 N

13 N

14 N

15 Y

16 Y

17 Y

18 N

19 N

20 N

21 N

22 Y

23 Y

24 Y

25 Y

26 N

27 N

28 N

29 Y

30 Y

31 Y

32 N

33 N

34 N

35 N

36 Y

37 Y

38 Y

39 Y

40 N

41 N

42 N

43 Y

44 Y

45 Y

46 N

a. Today is day 1. 30 days from today is day 31.

She works on day 31, so she does work 30 days from today.

b. 45 days from today is day 46. She is off on day 46, so she will be off 45 days from today.

8 0

3 years ago

Read 2 more answers

Find a solution to the initial value problem, y′′+18x=0,y(0)=5,y′(0)=1.

Serga [27]

We want to find a solution to the initial value problem:

$y'' + 18x = 0 \qquad,\qquad y(0) = 5 \qquad,\qquad y'(0)=1.$

We can start by integrating the equation once:

$\dfrac{\textrm{d}^2 y}{\textrm{d}x^2} + 18 x = 0 \iff \dfrac{\textrm{d}^2 y}{\textrm{d}x^2} = -18 x \iff\\\\\iff \dfrac{\textrm{d}y}{\textrm{d}x} = -18\displaystyle\int x\textrm{ d}x \iff \dfrac{\textrm{d}y}{\textrm{d}x}=-18\dfrac{x^2}{2} + C \iff\\\\\iff \dfrac{\textrm{d}y}{\textrm{d}x} = -9x^2 + C.$

Using the initial condition $y'(0) = 1$ , we can determine the integration constant $C$ :

$\dfrac{\textrm{d}y}{\textrm{d}x}\Big\vert_{x= 0} = 1 \iff -9 \times 0^2 + C = 1 \iff C = 1.$

Therefore, we have:

$\dfrac{\textrm{d}y}{\textrm{d}x} = -9x^2 + 1$

We can now integrate again:

$y(x) = \displaystyle\int\dfrac{\textrm{d}y}{\textrm{d}x}\textrm{ d}x = \int\left(-9x^2+1\right)\textrm{d}x = -9\int x^2\textrm{ d}x + \int\textrm{d}x =\\\\= -9\dfrac{x^3}{3} + x + K = -3x^3 + x + K.$

The integration constant $K$ is determined by using $y(0) = 5$ :

$y(0) = 5 \iff -3 \times 0^3 + 0 + K = 5 \iff K = 5.$

Finally, the solution is:

$\boxed{y(x) = -3x^3 + x + 5}.$

7 0

3 years ago

Clara created the poster shown below:

lana66690 [7]

Answer:

$length=4\ cm\\width=6\ cm$

Step-by-step explanation:

Given the rectangular poster shown in the picture, you know that its dimensions (its width and its lenght) are:

$w_1=24\ cm\\l_1=16\ cm$

In order to calculate the dimensions of the rectangular at $\frac{1}{4}$ times its current size, you need to multiply the original lenght by $\frac{1}{4}$ and multiply the original width by $\frac{1}{4}$ .

Knowing this, you get:

$w_2=w_1\frac{1}{4}\\\\w_2=(24\ cm)(\frac{1}{4})\\\\w_2=6\ cm\\\\\\l_2=l_1\frac{1}{4}\\\\l_2=(16\ cm)(\frac{1}{4})\\\\l_2=4\ cm$

6 0

3 years ago

Which points are reflections of each other across both axes? A coordinate plane. (–2, 8) and (2, –8) (–7, –1) and (–7, 1) (5, –6

Stells [14]

Answer: The answer is A: (-2,8) and (2,-8)

Step-by-step explanation:

I hope this helps!

8 0

3 years ago

Read 2 more answers