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3 years ago

What is the answer to this question?(3+√5)^2

2 answers:

6 0

14 + 6√5 because foil method

(3+√5)^2 = (3+√5)(3+√5)

3(3) = 9
3(√5) = 3√5
√5(3) = 3√5
√5(√5) = 5

9 + 3√5 + 3√5 + 5
= 14 + 6√5

slavikrds [6]3 years ago

4 0

Answer:

the answer to this is

14 + 6√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

3 years ago

If you get it right I’ll give brainliest!!!!

aksik [14]

Answer:

The slope is undefined.

Step-by-step explanation:

A slope of zero would be a horizontal line, this is a vertical line, which would mean it's undefined.

3 0

3 years ago

Steve is about to take his fifth math test. His scores on the first four test were 84, 92, 71, and 94. What score does Steve nee

lyudmila [28]

Answer:

Step-by-step explanation:

The sum of the differences of the current scores from average is ...

(84 -85) +(92 -85) +(71-85) +(94 -85) = -1 +7 -14 +9 = 1

So, to make the total of all differences from average be zero, Steve must get a score of 85 -1 = 84 on his 5th test.

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3 years ago

Which of the following choices describe the bases of a cylinder?

nataly862011 [7]

Answer:

they are parallel to each other is the best choice to describe the bases of a cylinder. The answer is PARALLEL

7 0

2 years ago

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The number of visitors to an art museum increases each year. The function V(t) = N(1 + r)t represents the number of visitors to

IrinaVladis [17]

Answer:

Option A - The number of visitors is multiplied by (1+r) each year

Step-by-step explanation:

Given : The number of visitors to an art museum increases each year. The function $V(t) = N(1 + r)^t$ represents the number of visitors to the museum at year t, where N is the number of visitors in year 0 and r is the rate of increase.

To find : Select the correct statement?

Solution :

We have given an exponential function,

The function $V(t) = N(1 + r)^t$ represents the number of visitors to the museum at year t, where N is the number of visitors in year 0 and r is the rate of increase.

As In year 0,

The initial visitors is $V(t) = N(1 + r)^0=N$

In year 1,

$V(t) = N(1 + r)^1=N(1+r)$

In year 2,

$V(t) = N(1 + r)^2$

So, According to this the number of visors is multiplied by (1+r) each year.

Therefore, Option A is correct.

7 0

3 years ago

Read 2 more answers