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3 years ago

7

Al tom and Joe share €3000. The ratio of the amount Al gets to the amount tom gets is in the ratio 5:4. Joe gets 1.5 times the a

mount tom gets work out the amount tom gets.

1 answer:

suter [353]3 years ago

8 0

Answer:

€1333.33

Step-by-step explanation:

Al Tom ratio to Joe=5:4

Joe gets 1.5 times the amount Al gets

€3000 in the ratio 5:4

Al share

5/9×3000

=€1666.67

Joe share

4/9×3000

=€1333.33

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Step-by-step explanation:

$7(A - 6) \\ = 7A - 7 \times 6 \\ = 7A - 42$

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Step-by-step explanation:

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2 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:

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

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

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

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

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

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3 years ago

A rectangle is 3 times as long as it is wide and its perimeter is 120 centimeters. find area.

valentina_108 [34]

The formula for perimeter is
P = 2l + 2w
In this particular case you are given that the length is three times the width:
3l = w
In this case, you are also given:
P = 120
Therefore,
120 = 2l + 2w
At this point you have a system of equations:
120 = 2l + 2w
l = 3w
Now you can use substitution (plug in 3w for l in the perimeter equation)
120 = 2(3w) + 2w
Simplify:
120 = 6w + 2w
120 = 8w
120/8 = 8w/8
15 = w
Plug in the width into one of your original equations to get the length:
l = 3*15
l = 45
Now you know that l = 45 and w = 15
Now, you plug this information in for your equation for area:
A = l*w
A = 45*15
A = 675
The area of the rectangle is 675 cm²

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3 years ago

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