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svlad2 [7]
1 year ago
15

Louie is trying to find a rectangular canvas for his art project. its width must measure 20 inches and form a 35° angle with the

diagonal of the canvas. what is the height of the canvas? round your answer to the nearest tenth.
Mathematics
1 answer:
sweet-ann [11.9K]1 year ago
8 0

The height of the canvas according to tangent is 14 inches.

According to the statement

we have given that the a rectangular canvas for his art project. its width must measure 20 inches and form a 35° angle with the diagonal of the canvas.

And we have to find the height of the canvas.

So, For this purpose,

The given information is:

The 35⁰ angle is part of a right triangle with a side of 20 inches.  The tangent of this angle (35⁰) is equal to the opposite side, x, over the adjacent side (20 inches).

Tan (35⁰) = x/20

0.7002 = x/20

x = 14.004 inches.

For more understanding of the statement please see the image below.

So, The height of the canvas according to tangent is 14 inches.

Learn more about tangent here

brainly.com/question/17040970

#SPJ4

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Colt1911 [192]

Answer:

b = -1

Step-by-step explanation:

7(3b-1): 7 goes into the numbers by multiplying. This will give you 21b-7.

So now the equation should be like 21b-7=2b-26.

-7 and 2b swap places, making 21b-2b=7-26. It will give you 19b= -19.

Finally divide the two numbers (-19 / 19) and the solution will be b= -1.

If I didn't make a clear answer or a good explanation, please comment. I sometimes mess up my steps, and this is my first time using this.

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Daniel rollerbladed 3 miles in 12 minutes. At this rate, how many miles will he rollerblade in 1 hour? Show your work.
Yakvenalex [24]

Answer:

Daniel is rollerblading at 15 miles per hour

Daniel can go 3 miles in 12 minutes so we do 12÷3 to find out how many minutes it takes to go 1 mile which is 4 now we do 60÷4 to get 15

Alternatively we could do 60÷12 to get 5 then do 3×5 to get 15

Step-by-step explanation:

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3 years ago
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mr Goodwill [35]

Answer:

Probably A.

Step-by-step explanation:

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2 years ago
Does anyone know how to simplify this expression? I know it has to do with properties of summation and special summation rules b
dusya [7]
<h3>Answer:     -n/(n+1)</h3>

============================================================

Explanation:

Let's expand this out up to say n = 6 terms

I'll write the summation in such a way that each (1/(k+1) - 1/k) grouping will get its own row. Each row has the same value of k.

If we plug in k = 1 through k = 6, but not evaluate just yet, we will have this:

1/(1+1) - 1/1

1/(2+1) - 1/2

1/(3+1) - 1/3

1/(4+1) - 1/4

1/(5+1) - 1/5

1/(6+1) - 1/6

All I've done so far is replace k with 1 through 6. Again, each row represents a different k value. Each row has the general format 1/(k+1)-1/k.

Let's simplify everything in the first column.

So the (1+1) turns into 2, the (2+1) turns into 3, and so on.

Doing that leads to...

1/2 - 1/1

1/3 - 1/2

1/4 - 1/3

1/5 - 1/4

1/6 - 1/5

1/7 - 1/6

Then note how we have the cancellations shown in the diagram below. The color coding shows how the terms pair up to cancel out. By "cancel out", I mean specifically that the fractions add up to 0. Eg: 1/2 + (-1/2) = 0.

Nearly everything cancels out. The only things left after the dust settles is the -1/1 in the first row and the 1/7 in the bottom row. This evaluates to 1/7-1/1 = 1/7 - 7/7 = (1-7)/1 = -6/7

If you were to try this with n = 7, then you should find that again nearly everything cancels but the fractions -1/1 and 1/8. Then 1/8 - 1/1 = -7/8.

For n = 8, you should end up with 1/9 - 1/1 = -8/9.

You can probably see the pattern.

A conjecture is that the answer is -n/(n+1). The general proof of this isn't too tricky. Simply follow the same ideas as mentioned above. Expand out a few terms and see how things cancel out. You'll find that everything cancels except for the -1/1 in the first row and the 1/(n+1) just one term before the very end. Then we can say:

1/(n+1) - 1/1

1/(n+1) - (n+1)/(n+1)

(1-(n+1))/(n+1)

(1-n-1)/(n+1)

-n/(n+1)

If we tried n = 6, then we find,

-n/(n+1) = -6/(6+1) = -6/7

which was the result we found earlier when we added the first n = 6 terms of this series. Trying out n = 7 should lead to -n/(n+1) = -7/8, and so on.

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iVinArrow [24]

Answer:

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