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Thank you! I have to say idk with part B however, I've redone it 3 times and entered it into wolfram and keep getting the same thing so yeah.

Very nice, Space Tsunami   !!!!

It appears  that  Space Tsunmai  is  using  the midpoint rule  for  the height of  the rectangles and the width of  a single rectangle  is  .2

If we use  this approach we  have  the area  as

.2  [  F(.1) + F(.3)  + F(.5) + F(.7) + F(.9) + F(1.1) + F(1.3)  + F(1.5) + F(1.7) + F(1.9)  +F(2.1) +

         F(2.3)  +  F (2.5)  +  F(2.7)  + F(2.9)  + F(3.1)  + F(3.3)  + F ( 3.5) + F(3.7) + F(3.9)  + F(4.1) +

         F(4.3)  + F(4.5) + F(4.7)  + F(4.9)  + F(5.1) + F(5.3) + F(5.5) + F(5.7) + F(5.9)  ]    =

.2  [ 1.19  + 3.51 + 5.75 + 7.91  + 9.99  + 11.99  + 13.91   + 15.75  + 17.51  + 19.19  + 20.79 +

     22.21  + 23.75  + 25.11  + 26.39 + 27.59  + 28.71 + 29.75  + 30.71  + 31.59  + 32.39 + 33.11 +

    33.75  + 34.31  + 34.79 + 35.19 + 35.51  + 35.75 + 35.91  + 35.99  ]       =

.2  [ 127.49  + 311.31  + 281.2  ]   ≈

144

Here's the approach for part A

Your integration for part B is correct.  (edited to correct my mistake!).

Nevermind lmao i'm dumb, it would just be \(\int _{-1.5}^{0.5}\left|\cos \left(x^2\right)-e^x\right|dx = .595\)

tan 42^o =   12/w

w =  12 / tan42 = 13.3

tan 27 =  12/ ( w+x)

tan 27 = 12/ (13.3 + x)

x = 10.2 units

Use pythagorean theorem for right triangles

hypotenuse ^2   = leg1^2 + leg2^2

          x^2             = 8^2      + 15 ^2

x = sqrt 289  = 17 units

There are more ways though. For example, there could be:

1, 3, 4, 5, 5

2, 2, 3, 5, 5

This gives another 90 ways:

1, 3, 4, 5, 5: 5!/2 = 60

2, 3, 3, 5, 5: 5!/4 = 30

If you add it with the previous one, we get 60+60+30 = 150

Hey there :) I'm not 100% sure what your lesson or teacher is wanting, whether it be a visible graph or just using a calculator, but the limit of the integral from 0 to 6, of F(x), can be modelled by this graph below, If using a calculator, you could simply enter the integral of the equation and let it do the work for you, resulting in an answer of 144 :)

Help ASAP pls

Thanks in advance

100%.....can't do much better than that  !!!

Glad  we could help   !!!

y =  .04 (500)  + 36

y = 56     (i.e.,  they should expect to win 56% of their games )

See I thought so, but my brain was thinking the gradient OF the derivative, but I felt that was wrong, but anyways yeah thats what I thought haha, it just seemed too simple! Lol my brain overthinking everything. Thank you :)

Thank you! This makes sense :)

we can say that one side length is a, another b, and the last c. We know that:

a+b>c

a+c>b

c+b>a

a+b+c=15

We also know that order matters. if a=1, b and c must be 7. if a=2, b must be 7, and c must be 6. we can continue counting:

a=1,b=7,c=7

a=2,b=7,c=6

a=3,b=6,c=6

a=3,b=7,c=5

a=4,b=6,c=5

a=4,b=7,c=4

a=5,b=5,c=5

those are all the possible solutions, so $\boxed{7}$ is our answer

a)  x intercepts occur when f(x)   (which is 'y' )  = 0 

              -(x+4)(x-1) = 0        so x = -4   and   1   are the 'zeroes'   (x intercepts)

      y intercept is when x = 0        - (0+4)(0-1) = 4

b) axis of symmetry is exactly between the zeroes      x =  - 1.5

c)  the x coordinate of the vertex is tha axis of symmetry    x = - 1.5     use this value in the equation to calculate the 'y' coordinate

d ) graph it with your tools  

If these five letters are each intended for the five persons (one per person), then, with random distribution, it is impossible for exactly four of the persons to get the correct letter.  If each of the four persons get the letters intended for him/her, then the fifth person will get the letter intended for him/her.

The probability is zero.

Opposite sides must be equal length    10x+9 = 14x-7

                                                                 4x = 16            x = 4

Thakk uu ...

Already answered ....NOW !   

Welll....from the diagram, you can see you have two triangles  (one on each side)

area of triangle = 1/2 base*height  = 1/2  * 2 x 10   = 10 ft²   each

  then you are left with a rectangle   13 ft x 10 ft = 130 ft^2

130 + 10 + 10 = 150 ft²

    ^{or you could just use the formula for area of parallelogram     base * height = 15 * 10 = 150 square feet}

But can't the $x, y,$ or $z$ be a decimal?

Pretty sure I will need a diagram of the mainsail.....

Since all of the parallel horizontal lines are the same distance apart      WY = YX = XV

WV = 2.8 + 2.8 + 2.8  = 8.4 units

my bad, the roations of cos(3x) would be bounded by [0,pi/6]

Point-slope form

(y- -1) = -2 (x-0)

y = -2x-1