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Sphinxa [80]
2 years ago
11

If f(x)=3x-1 and g(x)=x+5, find (f o g)(x) and (g o f)(x) (f o g)(x)= (g o f)(x)

Mathematics
1 answer:
Nuetrik [128]2 years ago
3 0

Answer:

(f o g)(x)= 3x + 14

(g o f)(x) = 3x + 4

Step-by-step explanation:

(f o g)(x) = f(g(x)) = f(x + 5) = 3(x + 5) - 1 = 3x + 15 - 1 = 3x + 14

(g o f)(x) = g(f(x)) = g(3x - 1) = 3x - 1 + 5 = 3x + 4

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1025 + 503 – 1412 – 7
Andreyy89

Answer: a

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Can anyone help me ?
gtnhenbr [62]
The formula for the volume of a sphere is V=(4/3) (pi) r^3. if r is doubled then you get 2r as the radius and V=(4/3) (pi) * 8r^3 so the volume is eight times bigger than the original  r  value. if r is tripled the r =3r  and (3r)^3 so the volume is 27 times bigger. If r  is multiplied by  n  the radius is  nr  and (nr)^3 =n^3  r^3, Therefore, the volume is n^3 times bigger than the original.
7 0
3 years ago
Evaluate the triple integral ∭ExydV where E is the solid tetrahedon with vertices (0,0,0),(5,0,0),(0,9,0),(0,0,4).
Elan Coil [88]

Answer: \int\limits^a_E {\int\limits^a_E {\int\limits^a_E {xy} } \, dV = 1087.5

Step-by-step explanation: To evaluate the triple integral, first an equation of a plane is needed, since the tetrahedon is a geometric form that occupies a 3 dimensional plane. The region of the integral is in the attachment.

An equation of a plane is found with a point and a normal vector. <u>Normal</u> <u>vector</u> is a perpendicular vector on the plane.

Given the points, determine the vectors:

P = (5,0,0); Q = (0,9,0); R = (0,0,4)

vector PQ = (5,0,0) - (0,9,0) = (5,-9,0)

vector QR = (0,9,0) - (0,0,4) = (0,9,-4)

Knowing that cross product of two vectors will be perpendicular to these vectors, you can use the cross product as normal vector:

n = PQ × QR = \left[\begin{array}{ccc}i&j&k\\5&-9&0\\0&9&-4\end{array}\right]\left[\begin{array}{ccc}i&j\\5&-9\\0&9\end{array}\right]

n = 36i + 0j + 45k - (0k + 0i - 20j)

n = 36i + 20j + 45k

Equation of a plane is generally given by:

a(x-x_{0}) + b(y-y_{0}) + c(z-z_{0}) = 0

Then, replacing with point P and normal vector n:

36(x-5) + 20(y-0) + 45(z-0) = 0

The equation is: 36x + 20y + 45z - 180 = 0

Second, in evaluating the triple integral, set limits:

In terms of z:

z = \frac{180-36x-20y}{45}

When z = 0:

y = 9 + \frac{-9x}{5}

When z=0 and y=0:

x = 5

Then, triple integral is:

\int\limits^5_0 {\int\limits {\int\ {xy} \, dz } \, dy } \, dx

Calculating:

\int\limits^5_0 {\int\limits {\int\ {xyz}  \, dy } \, dx

\int\limits^5_0 {\int\limits {\int\ {xy(\frac{180-36x-20y}{45} - 0 )}  \, dy } \, dx

\frac{1}{45} \int\limits^5_0 {\int\ {180xy-36x^{2}y-20xy^{2}}  \, dy } \, dx

\frac{1}{45} \int\limits^5_0  {90xy^{2}-18x^{2}y^{2}-\frac{20}{3} xy^{3} } \, dx

\frac{1}{45} \int\limits^5_0  {2430x-1458x^{2}+\frac{94770}{125} x^{3}-\frac{23490}{375}x^{4}  } \, dx

\frac{1}{45} [30375-60750+118462.5-39150]

\int\limits^5_0 {\int\limits {\int\ {xyz}  \, dy } \, dx = 1087.5

<u>The volume of the tetrahedon is 1087.5 cubic units.</u>

3 0
3 years ago
Answer the question in the picture please
iogann1982 [59]

Answer:

B

Step-by-step explanation:

Since 1.5 is the y-intercept, B (0,1.5) is the only option.

~theLocoCoco

5 0
2 years ago
Graph (x-2)^2 + (y-1)^2 = 9
Alex787 [66]

Step-by-step explanation:

Given the following question:

(x-2)^2+(y-2)^2=9

First thing we need to keep in mind is the fact that this graph is indeed a circle. We know this because we are adding two cubic roots to each other which makes the graph a circle. We know the two separate functions are cubic roots because they each have an exponent of two. Not only is this function whose graph is a circle, but the midpoint of this circle is (2,2).

Hope this helps.

5 0
2 years ago
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