The volume of a prism is given by:
We know that the height is x. The length is 25 shorter than x, this can be express as:
The width is 14 longer than x, this can be express as:
Plugging the expressions for the length, the width and the height we have that:
Therefore, the volume of the prism is:
-2x + 2y + 3z = 0 → 2x - 2y - 3z = 0 → 2x - 2y - 3z = 0
-2x - 1y + 1z = -3 → 2x + 1y - 1z = 3 → 2x + 1y - 1z = 3
2x + 3y + 3z = 5 → 2x + 3y + 3z = 5 -3y - 2z = -3
-2x + 2y + 3z = 0 → 2x - 2y - 3z = 0
-2x - 1y + 1z = -3 → 2x + 1y - 1z = 3 → 2x + 1y - 1z = 3
2x + 3y + 3z = 5 → 2x + 3y + 3z = 5 → 2x + 3y + 3z = 5
-2y - 4z = -2
-3y - 2z = -3 → -6y - 4z = -6
-2y - 4z = -2 → -2y - 4z = -2
-4y = -4
-4 -4
y = 1
-3y - 2z = -3
-3(1) - 2z = -3
-3 - 2z = -3
+ 3 + 3
-2z = 0
-2 -2
z = 0
-2x + 2y + 3z = 0
-2x + 2(1) + 3(0) = 0
-2x + 2 + 0 = 0
-2x + 2 = 0
- 2 - 2
-2x = -2
-2 -2
x = 1
(x, y, z) = (1, 1, 0)
By understanding and applying the characteristics of <em>piecewise</em> functions, the results are listed below:
- r (- 3) = 15
- r (- 1) = 11
- r (1) = - 7
- r (5) = 13
<h3>How to evaluate a piecewise function at given values</h3>
In this question we have a <em>piecewise</em> function formed by three expressions associated with three respective intervals. We need to evaluate the expression at a value of the <em>respective</em> interval:
<h3>r(- 3): </h3>
-3 ∈ (- ∞, -1]
r(- 3) = - 2 · (- 3) + 9
r (- 3) = 15
<h3>r(- 1):</h3>
-1 ∈ (- ∞, -1]
r(- 1) = - 2 · (- 1) + 9
r (- 1) = 11
<h3>r(1):</h3>
1 ∈ (-1, 5)
r(1) = 2 · 1² - 4 · 1 - 5
r (1) = - 7
<h3>r(5):</h3>
5 ∈ [5, + ∞)
r(5) = 4 · 5 - 7
r (5) = 13
By understanding and applying the characteristics of <em>piecewise</em> functions, the results are listed below:
- r (- 3) = 15
- r (- 1) = 11
- r (1) = - 7
- r (5) = 13
To learn more on piecewise functions: brainly.com/question/12561612
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S= 15
3s=45
3s/3=45/3
S=15
You have to divide both sides
Answer:
k = -6/35
Step-by-step explanation:
To make the function continuous
kx^2 = x+k
These must be equal where the function is defined for two different intervals
This is at the point x=-6 so let x=-6
k(-6)^2 = -6+k
36k = -6+k
Subtract k from each side
36k-k = -6+k-k
35k = -6
Divide by 35
35k/35 = -6/35
k = -6/35
