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3 years ago

The product of two mixed numbers that are each between 4 and 5 is between 16 and 25

1 answer:

8 0

Correct the whole #s 4 x4 is 16 and the whole #s 5 x5 is 25 so 2 #s that are 4 and something x4 and something will be over 16 and if the numbers are less than 5 it can not be greater than 25

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The quantity that is arrived at by taking the highest score minus the lowest score is referred to as the?

Delicious77 [7]

Answer:

B) standard range

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3 0

3 years ago

the weekly salaries for 7 employees of a small business are given below 632, 750, 829, 839, 841, 881, 954 suppose the 632 salary

PolarNik [594]

I don't understand your question.. Is this multiple choice or something else?

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. 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

What is incorrect in this? And how do I correct it?

german

$\bf \begin{cases} y=3x+2\\ -3x+y=2\\ 3x-y=-2\\ ------\\ 6x-2y=10 \end{cases}\implies \begin{cases} 3x-y=-2\\ 6x-2y=10 \end{cases}\implies \begin{bmatrix} 3&-1&|&-2\\ 6&-2&|&10 \end{bmatrix}\\\\ -------------------------------$

$\bf \stackrel{\textit{system's determinant}}{ \begin{bmatrix} 3&-1\\6&-2 \end{bmatrix}\implies (3\cdot -2)-(6\cdot -1)}\implies -6-(-6)\implies -6+6\implies 0 \\\\\\ \stackrel{\textit{systerm determinant of 0 means}}{\textit{the system has \underline{no solutions } or \underline{infinitely many solutions}}}$

7 0

3 years ago

Ac is tangent to circle at point c what is the measure of oac?

Norma-Jean [14]

Answer: 27 degrees

Step-by-step explanation: 180-90 because its perpendicular -63=27

3 0

3 years ago