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3 years ago

Solve for x round to the newest 10th i’d necessary

Mathematics

1 answer:

docker41 [41]3 years ago

5 0

Answer:

x = 43.7°

Step-by-step explanation:

Reference angle (θ) = x°

Opposite side length = 43

Adjacent side length = 45

Apply the trigonometric function, TOA, which is:

Tan θ = Opp/Adj

Substitute

$Tan(x) = \frac{43}{45}$

$x = Tan^{-1}(\frac{43}{45})$

x = 43.7° (nearesth tenth)

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If 588 digits were used to number the pages of a book, how many pages are in this book?

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Answer:

294 pages are in this book

Step-by-step explanation:

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3 years ago

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A square has a diagonal measuring 19 centimeters in length.which of the following is closest to the length of each side of the s

nata0808 [166]

Answer:

13cm

Step-by-step explanation:

Let the length of each side be x;

Using the pythagoras theorem

l² = x² + x²

l is the length of the diagonal

l² = 2x²

19² = 2x²

361 = 2x²

x² = 361/2

x² = 180.5

x =√180.5

x = 13

hence the length of each side of the square is closest to 13cm

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4 years ago

How do you turn a mix number into a fraction?

Tomtit [17]

You must add or subtract, depending on which fraction your going for at that time.

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3 years ago

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Be sure to answer all parts. List the evaluation points corresponding to the midpoint of each subinterval to three decimal place

gayaneshka [121]

Answer:

The Riemann Sum for $\int\limits^5_4 {x^2+4} \, dx$ with n = 4 using midpoints is about 24.328125.

Step-by-step explanation:

We want to find the Riemann Sum for $\int\limits^5_4 {x^2+4} \, dx$ with n = 4 using midpoints.

The Midpoint Sum uses the midpoints of a sub-interval:

$\int_{a}^{b}f(x)dx\approx\Delta{x}\left(f\left(\frac{x_0+x_1}{2}\right)+f\left(\frac{x_1+x_2}{2}\right)+f\left(\frac{x_2+x_3}{2}\right)+...+f\left(\frac{x_{n-2}+x_{n-1}}{2}\right)+f\left(\frac{x_{n-1}+x_{n}}{2}\right)\right)$

where $\Delta{x}=\frac{b-a}{n}$

We know that a = 4, b = 5, n = 4.

Therefore, $\Delta{x}=\frac{5-4}{4}=\frac{1}{4}$

Divide the interval [4, 5] into n = 4 sub-intervals of length $\Delta{x}=\frac{1}{4}$

$\left[4, \frac{17}{4}\right], \left[\frac{17}{4}, \frac{9}{2}\right], \left[\frac{9}{2}, \frac{19}{4}\right], \left[\frac{19}{4}, 5\right]$

Now, we just evaluate the function at the midpoints:

$f\left(\frac{x_{0}+x_{1}}{2}\right)=f\left(\frac{\left(4\right)+\left(\frac{17}{4}\right)}{2}\right)=f\left(\frac{33}{8}\right)=\frac{1345}{64}=21.015625$

$f\left(\frac{x_{1}+x_{2}}{2}\right)=f\left(\frac{\left(\frac{17}{4}\right)+\left(\frac{9}{2}\right)}{2}\right)=f\left(\frac{35}{8}\right)=\frac{1481}{64}=23.140625$

$f\left(\frac{x_{2}+x_{3}}{2}\right)=f\left(\frac{\left(\frac{9}{2}\right)+\left(\frac{19}{4}\right)}{2}\right)=f\left(\frac{37}{8}\right)=\frac{1625}{64}=25.390625$

$f\left(\frac{x_{3}+x_{4}}{2}\right)=f\left(\frac{\left(\frac{19}{4}\right)+\left(5\right)}{2}\right)=f\left(\frac{39}{8}\right)=\frac{1777}{64}=27.765625$

Finally, use the Midpoint Sum formula

$\frac{1}{4}(21.015625+23.140625+25.390625+27.765625)=24.328125$

This is the sketch of the function and the approximating rectangles.

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4 years ago

Joe work 21 hours on his class project. He worked 3 times as long is Marie did. How long did Marie work on a project? Translate

MAXImum [283]

The answer is 21 ÷ 3 = 7 hrs

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3 years ago

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