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3 years ago

(5x-25)+(3x+9)=180 please answer right now

Mathematics

1 answer:

jok3333 [9.3K]3 years ago

6 0

Answer:

$x=24.5\\$

Step-by-step explanation:

So we have the equation:

$(5x-25)+(3x+9)+180$

Combine like terms:

$(5x+3x)+(-25+9)=180$

Add:

$8x-16=180$

Add 16 to both sides:

$8x=196$

Divide both sides by 8:

$x=24.5\\$

So, our answer is 24.5 :)

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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. Normal vector 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

The volume of the tetrahedon is 1087.5 cubic units.

3 0

2 years ago

What is the volume of the pyramid?

madreJ [45]

Answer:

$volume=1/3 ~BH$

$=1/3(16)^{2} \sqrt{17^{2} -8^{2} }$

$=1/3\times256\times15$

$=1280 ~ft^{3}$

------------------------

hope it helps...

have a great day!!

3 0

2 years ago

WILL GIVE BRAINLIEST

kumpel [21]

Range is output or y values
(x,y)
just the 2nd number of each pair
so it is 2,4,-5,-3

B is answer

7 0

3 years ago

An item originally costs $10. It's on sale for 50% off with and additional 20% off. If the sales tax is 10.1%, what is the final

Sergio039 [100]

Answer:

Final Cost = $4.01

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3 years ago

Which equation shows the quadratic formula used correctly to solve 5x2 + 3x – 4 = 0 for x?

ludmilkaskok [199]

5x^2+3x-4=0
x^2+3x/5-4/5=0 
x^2+3x/5=4/5 
x^2+3x/5+9/100=89/100 
(x+3/10)^2=89/100 
x+3/10=±(√89)/10 
x=-3/10±√89/100 
x=-3±(√89/10)

7 0

2 years ago

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