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dem82 [27]
2 years ago
12

Three Linear Variables​

Mathematics
1 answer:
azamat2 years ago
8 0

Answer:

23 yellow, 30 pink and 12 blue balls

Step-by-step explanation:

Let the number of yellow, pink, blue, and black balls be y, p, b, and x respectively.

<em>From 1st sentence:</em>

y +p +b +x= 90

<em>"</em><em>60</em><em> </em><em>of</em><em> </em><em>them</em><em> </em><em>are</em><em> </em><em>not</em><em> </em><em>pink</em><em>"</em><em> </em>

➜ y +b +x= 60

Given that 25 are black, x= 25.

<em>"</em><em>67</em><em> </em><em>of</em><em> </em><em>them</em><em> </em><em>are</em><em> </em><em>not</em><em> </em><em>yellow"</em>

➜ p +b +x= 67

Subst. x= 25 into the above equations:

y +p +b +25= 90

y+ p +b= 65 -----(1)

y +b +25= 60

y +b= 35 -----(2)

p +b +25= 67

p +b= 42 -----(3)

I will rewrite the 3 equations for better clarity:

y +p +b= 65 -----(1)

y +b= 35 -----(2)

p +b= 42 -----(3)

(1) -(2):

p= 65 -35

p= 30

(1) -(3):

y= 65 -42

y= 23

Substitute p= 30 and y= 23 into (1):

23 +30 +b= 65

b= 65 -53

b= 12

Thus, there 23, 30 and 12 yellow, pink and blue balls respectively.

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<span>y' = 9x^-1 =9/x</span>
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curvature k = |y''| / (1 + (y')^2)^(3/2) 

<span>= |-9/x^2| / (1 + (9/x)^2)^(3/2) 
= (9/x^2) / (1 + 81/x^2)^(3/2) 
= (9/x^2) / [(1/x^3) (x^2 + 81)^(3/2)] 
= 9x(x^2 + 81)^(-3/2). 

To maximize the curvature, </span>

we find where k' = 0. <span>
k' = 9 * (x^2 + 81)^(-3/2) + 9x * -3x(x^2 + 81)^(-5/2) 
...= 9(x^2 + 81)^(-5/2) [(x^2 + 81) - 3x^2] 
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Setting k' = 0 yields x = ±9/√2. 

Since k' < 0 for x < -9/√2 and k' > 0 for x > -9/√2 (and less than 9/√2), 
we have a minimum at x = -9/√2. 

Since k' > 0 for x < 9/√2 (and greater than 9/√2) and k' < 0 for x > 9/√2, 
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x=9/√2=6.36

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the answer is
(x,y)=(6.36,16.66)
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Answer:

untere Tabelle gibt an, wie Oberfläche und Volumen der Pyramide berechnet werden. Grundsätzlich gilt:

Oberfläche = Grundfläche + Mantelfläche

Volumen = Grundfläche · Pyramidenhöhe : 3

Generell ist darauf zu achten, dass mit unterschiedlichen Höhenangaben gerechnet wird. Für die Berechnung der Oberfläche wird die Höhe der schrägliegenden Seitendreiecke benötigt (Grafik unten: ha; hb). Für die Berechnung des Volumens wird die Höhe der Pyramide benutzt (Grafik unten: h).

JSXGraph v0.95 Copyright (C) see http://jsxgraph.org

ha = 5.83 cm

h = 5.00 cm

a = 6.00 cm

b = 6.01 cm

hb = 5.83 cm

V = 60.10 cm³

Ap = 106.11 cm²

AM = 70.05 cm²

AG = 36.06 cm²

 –  o  +  ←  ↓  ↑  → 

rechteckige Grundflächequadratische GrundflächeOberfläche = Grundfläche + Mantelfläche

OP = AG + AMOP = a · b + a · ha + b · hbOP = a² + a · ha · 2 Volumen = Grundfläche · h : 3

VP = AG · h : 3

VP = a · b · h : 3VP = a² · h : 3

Step-by-step explanation:

#semogamembantu

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