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Klio2033 [76]
3 years ago
6

Use Stokes' Theorem to evaluate S curl F · dS. F(x, y, z) = x2z2i + y2z2j + xyzk, S is the part of the paraboloid z = x2 + y2 th

at lies inside the cylinder x2 + y2 = 16, oriented upward.
Mathematics
1 answer:
worty [1.4K]3 years ago
7 0

Answer:

0

Step-by-step explanation:

CHECK ATTACHMENT

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What is the height of a right triangle with an angle that measures 30 degrees adjacent to a base of 14
stepladder [879]

The height of the right triangle is 8.08

<h3>Calculating the height of a triangle </h3>

From the question, we are to determine the height of the described right triangle

From the given information,

The angle measure is 30 degrees adjacent to the base

and

The base is 14

Using SOH CAH TOA

Adjacent = 14

Opposite = height of the triangle

Let the height the h

∴ Opposite = h

Thus,

tan 30° = h/14

h = 14 × tan 30°

h = 8.08

Hence, the height of the right triangle is 8.08

Learn more on Calculating height of triangle here: brainly.com/question/10082088

#SPJ1

3 0
1 year ago
4x + 1 = 3 Would you describe this equation as always true, never true or Sometimes true?
rjkz [21]

Answer:

Sometimes true

Step-by-step explanation:

There is only one x value that satisfies the equation.

4x + 1 = 3

4x = 2

x = 1/2

4 0
2 years ago
Read 2 more answers
Please show the working and answer. you can take a picture for the working.
baherus [9]

Answer:

(a) The area of the triangle is approximately 39.0223 cm²

(b) ∠SQR is approximately 55.582°

Step-by-step explanation:

(a) By sin rule, we have;

SQ/(sin(∠SPQ)) = PQ/(sin(∠PSQ)), which gives;

5.4/(sin(52°)) = 6.8/(sin(∠PSQ))

∴ (sin(∠PSQ)) = (6.8/5.4) × (sin(52°)) ≈ 0.9923

∠PSQ = sin⁻¹(0.9923) ≈ 82.88976°

Similarly, we have;

5.4/(sin(52°)) = SP/(sin(180 - 52 - 82.88976))

Where, 180 - 52 - 82.88976 = ∠PQS = 45.11024

SP = 5.4/(sin(52°))×(sin(180 - 52 - 82.88976)) ≈ 4.8549

Given that RS : SP = 2 : 1, we have;

RS = 2 × SP = 2 × 4.8549 ≈ 9.7098

We have by cosine rule, \overline {RQ}² =  \overline {SQ}² +  \overline {SR}² - 2 × \overline {SQ} × \overline {SR} × cos(∠QSR)

∠QSR and ∠PSQ are supplementary angles, therefore;

∠QSR = 180° - ∠PSQ = 180° - 82.88976° = 97.11024°

∠QSR = 97.11024°

Therefore;

\overline {RQ}² =  5.4² +  9.7098² - 2 ×  5.4×9.7098× cos(97.11024)

\overline {RQ}² ≈ 136.42

\overline {RQ} = √(136.42) ≈ 11.6799

The area of the triangle = 1/2 ×\overline {PQ} × \overline {PR} × sin(∠SPQ)

By substituting the values, we have;

1/2 ×\overline {PQ} × \overline {PR} × sin(∠SPQ)

1/2 × 6.8 × (4.8549 + 9.7098) × sin(52°) ≈ 39.0223 cm²

The area of the triangle ≈ 39.0223 cm²

(b) By sin rule, we have;

\overline {RS}/(sin(∠SQR)) = \overline {RQ}/(sin(∠QSR))

By substituting, we have;

9.7098/(sin(∠SQR)) = 11.6799/(sin(97.11024))

sin(∠SQR) = 9.7098/(11.6799/(sin(97.11024))) ≈ 0.82493

∠SQR = sin⁻¹(0.82493) ≈ 55.582°.

8 0
3 years ago
Olivia goes shopping at the mall and buys a shirt that is on sale for 25% off. She also knows that the sales tax is 5%. If her f
Norma-Jean [14]

Answer:   The shirt originally cost 125 dollars.

Step-by-step explanation: The shirt on sale is 25% off. So first multiply 25 by 5 and you get 125. So 125 is the originall price. Her final cost is 25 dollars. Last step: 125 divided by 5 equals 25 dollars.

3 0
3 years ago
54% of 76.8 = ___ estimate
LekaFEV [45]
The answer is: 41.256 (You round it to the number that you're required to round it)

7 0
3 years ago
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