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valentinak56 [21]
3 years ago
8

Please simplify each expression for 18, 20, and 21

Mathematics
1 answer:
NeX [460]3 years ago
5 0
The answer to the questions

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Work out the volume of the cone, giving your answer
Gwar [14]

Answer:

If the given lengths of 7 cm, 24 cm, and 25 cm for the sides of a triangle satisfy the equation of the Pythagorean Theorem, then, yes, the given side lengths are those of a right triangle. Let's see if they are:

The well-known equation of the famous Pythagorean Theorem is:

a² + b² = c², which says that for a right triangle, the sum of the squares of the lengths of the two shorter sides of the triangle is equal to the square of the length of the longest side called the hypotenuse, where a and b are the lengths of the two shorter sides (also called the "legs") and c is the length of the hypotenuse (the side opposite the right angle).

We're given that a = 7 cm and b = 24 cm and that c = 25 cm. Substituting these values into the equation of the Pythagorean Theorem, we get:

a² + b² = c²

(7 cm)² + (24 cm)² = (25 cm)²

(7 cm)(7 cm) + (24 cm)(24 cm) = (25 cm)(25 cm)

49 cm² + 576 cm² = 625 cm²

625 cm² = 625 cm²

As we can see, the equation of the Pythagorean Theorem is satisfied, i.e., made a true statement, by the given lengths; therefore, if these three lengths, 7 cm, 24 cm, and 25 cm, are the lengths of the sides of a triangle, then the triangle is indeed a right triangle.

5 0
2 years ago
find the parametric equations for the line of intersection of the two planes z = x + y and 5x - y + 2z = 2. Use your equations t
Kaylis [27]

Answer:

You didn't give the points in which you want the parametric equations be filled, but I have obtained the parametric equations, and they are:

x = (1/3 + t)

y = (-1/3 - 7t)

z = -6t

Step-by-step explanation:

If two planes intersect each other, the intersection will always be a line.

The vector equation for the line of intersection is given by

r = r_0 + tv

where r_0 is a point on the line and v is the vector result of the cross product of the normal vectors of the two planes.

The parametric equations for the line of intersection are given by

x = ax, y = by, and z = cz

where a, b and c are the coefficients from the vector equation

r = ai + bj + ck

To find the parametric equations for the line of intersection of the planes.

x + y - z = 0

5x - y + 2z = 2

We need to find the vector equation of the line of intersection. In order to get it, we’ll need to first find v, the cross product of the normal vectors of the given planes.

The normal vectors for the planes are:

For the plane x + y - z = 0, the normal vector is a⟨1, 1, -1⟩

For the plane 5x - y + 2z = 2, the normal vector is b⟨5, -1, 2⟩

The cross product of the normal vectors is

v = a × b =

|i j k|

|1 1 -1|

|5 -1 2|

= i(2 - 1) - j(2 + 5) + k(-1 - 5)

= i - 7j - 6k

v = ⟨1, -7, -6⟩

We also need a point on the line of intersection. To get it, we’ll use the equations of the given planes as a system of linear equations. If we set z = 0 in both equations, we get

x + y = 0

5x - y = 2

Adding these equations

5x + x + y - y = 2 + 0

6x = 2

x = 1/3

Substituting x = 1/3 back into

x + y = 0

y = -1/3

Putting these values together, the point on the line of intersection is

(1/3, -1/3, 0)

r_0= (1/3) i - (1/3) j + 0 k

r_0​​ = ⟨1/3, -1/3, 0⟩

Now we’ll plug v and r_0​​ into the vector equation.

r = r_0​​ + tv

r = (1/3)i - (1/3)j + 0k + t(i - 7j - 6k)

= (1/3 + t) i - (1/3 + 7t) j - 6t k

With the vector equation for the line of intersection in hand, we can find the parametric equations for the same line. Matching up r = ai + bj + ck with our vector equation,

r = (1/3 + t) i + (-1/3 - 7t) j + (-6t) k

a = (1/3 + t)

b = (-1/3 - 7t)

c = -6t

Therefore, the parametric equations for the line of intersection are

x = (1/3 + t)

y = (-1/3 - 7t)

z = -6t

3 0
3 years ago
Write an expression 6 more than 5 times a n
polet [3.4K]
5 + 6 hahahahaha hahhahhahaha
5 0
3 years ago
Read 2 more answers
Georg invests $5000 for 14 years at a rate of 2% per year compound interest.
Rufina [12.5K]

Answer:

\frac{1}{50} or 0.02

Step-by-step explanation:

2% x 1 to give the answer

or

reduce it to faction like

<h2>\frac{2}{100} = \frac{1}{50}</h2>
8 0
3 years ago
A copy machine makes 136 copies in 4 minutes and 15 seconds. How many copies does it make per minute?
Dahasolnce [82]

Answer:

The copy machine makes 32 copies per minute.

Step-by-step explanation:

Given that a copy machine makes 136 copies in 4 minutes and 15 seconds, to determine how many copies does it make per minute, the following calculation must be performed:

15 seconds = 0.25 minutes

136 / 4.25 = X

32 = X

Therefore, the copy machine makes 32 copies per minute.

8 0
3 years ago
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