Answer:
Answer:
h = \frac{2A}{b}
Step-by-step explanation:
Given
A = \frac{1}{2} bh
Multiply both sides by 2 to clear the fraction
2A = bh ( isolate h by dividing both sides by b )
h = \frac{2A}{b}
1 and 3 I believe sorry if it’s incorrect
It is given in the question that
A rectangular box has a square base with an edge length of x cm and a height of h cm. The volume of the box is given by
And the edge length of the base is 12 cm, the edge length of the base is decreasing at a rate of 2 cm/min, the height of the box is 6 cm, and the height is increasing at a rate of 1 cm/min.
Here we differentiate V with respect to t, and we use product rule, that is
Substituting the given values , we will get
![[tex]dV/dt = 2(12)(6)(-2)+ 12^2(1)](https://tex.z-dn.net/?f=%5Btex%5DdV%2Fdt%20%3D%202%2812%29%286%29%28-2%29%2B%2012%5E2%281%29)
[/tex]
So at that moment, the volume is decreasing at the rate of
8^2 /2+5(15-7)
=64/2+75-35
=32+40
=72
<span><span>3<span>(<span>5−9</span>)</span></span>+<span>4<span>(<span>4−9</span>)
</span></span></span><span>=<span><span><span>(3)</span><span>(<span>−4</span>)</span></span>+<span>4<span>(<span>4−9</span>)
</span></span></span></span><span>=<span><span>−12</span>+<span>4<span>(<span>4−9</span>)
</span></span></span></span><span>=<span><span>−12</span>+<span><span>(4)</span><span>(<span>−5</span>)
</span></span></span></span><span>=<span><span>−12</span>+<span>−20
</span></span></span><span>=<span>−32
</span></span><span><span>10<span>(<span>9−18</span>)</span></span>−<span>32
</span></span><span>=<span><span><span>(10)</span><span>(<span>−9</span>)</span></span>−<span>32
</span></span></span><span>=<span><span>−90</span>−<span>32
</span></span></span><span>=<span><span>−90</span>−9
</span></span><span>=<span>−<span>99
</span></span></span><span><span>−<span>12<span>(<span>5−7</span>)</span></span></span>−<span>10<span>(<span>2−5</span>)
</span></span></span><span>=<span><span><span>(<span>−12</span>)</span><span>(<span>−2</span>)</span></span>−<span>10<span>(<span>2−5</span>)
</span></span></span></span><span>=<span>24−<span>10<span>(<span>2−5</span>)
</span></span></span></span><span>=<span>24−<span><span>(10)</span><span>(<span>−3</span>)
</span></span></span></span><span>=<span>24−<span>(<span>−30</span>)
</span></span></span><span>=<span>54</span></span>
