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nirvana33 [79]
3 years ago
5

Need help with this math problem

Mathematics
1 answer:
-BARSIC- [3]3 years ago
3 0

z = 37°

Step-by-step explanation:

The exterior angle theorem says that the sum of two internal angles is equal to the exterior angle

In this case the sum of z and z+4 will be equal to z+41

Writing mathematically

z + z+ 4 = z + 41\\2z+4 = z + 41\\2z -z = 41 -4\\z = 37

Hence

z = 37°

Keywords: Angles, Triangles

Learn more about angles at:

  • brainly.com/question/10800566
  • brainly.com/question/10808021

#LearnwithBrainly

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X+y=1 If x=0, then y=
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1

Step-by-step explanation:

x+y=1 if x=0, then y=1

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A flow meter is attached in a hydraulic line that measures 18 gal/min. The line has an inside diameter of 1.0 in. What is the fl
snow_tiger [21]

The flow velocity measured as in/min at the meter is 5924.13 in/min

<h3 /><h3>Volumetric flow rate</h3>

We know that the volume flow rate Q = Av where

  • A = cross-sectional area of pipe and
  • v = flow velocity

Now, Q = 18 gal/min

Converting this to in³/min, we have

Q = 18 gal/min = 18 × 1 gal/min = 18 × 231 in³/min = 4158 in³/min

A = πd²/4 where d = diameter of pipe = 1.0 in.

<h3 /><h3>Flow velocity, v</h3>

Since Q = Av, making v subject of the formula, we have

v = Q/A

v = 4Q/πd²

Substituting the values of the variables into the equation, we have

v = 4Q/πd²

v = 4 × 4158 in³/min ÷ π × (1.0 in)²

v = 16632 in/min ÷ π

v = 5924.13 in/min

So, the flow velocity measured as in/min at the meter is 5924.13 in/min

Learn more about flow velocity here:

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5 0
2 years ago
What is the slope of y-4=5/2(x-2)
OLEGan [10]
The answer is 5/2. The equation is already in point slope form. If you recall, the equation for point slope form is y-y1 = m(x-x1) where y1 and x1 are points on the graph, and m is the slope. In the given equation, m is 5/2 so we know it is the slope.
Alternatively, if you are not familiar with the point slope for equation, you can manipulate the equation to the form of y=mx+b where m is the slope and b is the constant. If you solve for y, you get y=5/2x-1 since 5/2 is in the place of m, we know 5/2 is the slope.

6 0
3 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
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