Answer:
y
=1
/3
x
+
14
/3
Step-by-step explanation:
The solutions to the inequalities are x >1 and x < 6
<h3>How to solve the inequalities?</h3>
The inequality expression is given as:
-2x + 5 < 3x + 10
Collect the like terms in the above inequality
-2x - 3x < 10 - 5
Evaluate the like terms
-5x < 5
Divide by -5
x >1
Also, we have
5(x - 2) <3x + 2
Open the bracket
5x - 10 < 3x + 2
Evaluate the like terms
2x < 12
Divide by 2
x < 6
Hence, the solutions to the inequalities are x >1 and x < 6
Read more about inequalities at
brainly.com/question/24372553
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We can find this using the formula: L= ∫√1+ (y')² dx
First we want to solve for y by taking the 1/2 power of both sides:
y=(4(x+1)³)^1/2
y=2(x+1)^3/2
Now, we can take the derivative using the chain rule:
y'=3(x+1)^1/2
We can then square this, so it can be plugged directly into the formula:
(y')²=(3√x+1)²
<span>(y')²=9(x+1)
</span>(y')²=9x+9
We can then plug this into the formula:
L= ∫√1+9x+9 dx *I can't type in the bounds directly on the integral, but the upper bound is 1 and the lower bound is 0
L= ∫(9x+10)^1/2 dx *use u-substitution to solve
L= ∫u^1/2 (du/9)
L= 1/9 ∫u^1/2 du
L= 1/9[(2/3)u^3/2]
L= 2/27 [(9x+10)^3/2] *upper bound is 1 and lower bound is 0
L= 2/27 [19^3/2-10^3/2]
L= 2/27 [√6859 - √1000]
L=3.792318765
The length of the curve is 2/27 [√6859 - √1000] or <span>3.792318765 </span>units.
Answer:
<h2> <em><u>384</u></em></h2>
Step-by-step explanation:
<em><u>Given</u></em><em><u>, </u></em>
Dimensions of the rectangular prism = 9ft, 12ft and 4ft
<em><u>Therefore</u></em><em><u>, </u></em>
Surface area of the rectangular prism
= 2( lb + bh + lh)




<em><u>Hence</u></em><em><u>,</u></em>
<em><u>Surface</u></em><em><u> </u></em><em><u>area</u></em><em><u> </u></em><em><u>of</u></em><em><u> </u></em><em><u>rectangular</u></em><em><u> </u></em><em><u>prism</u></em><em><u> </u></em><em><u>is</u></em><em><u> </u></em><em><u>384</u></em><em><u> </u></em><em><u>sq</u></em><em><u>.</u></em><em><u> </u></em><em><u>ft</u></em><em><u> </u></em><em><u>(</u></em><em><u>Ans</u></em><em><u>)</u></em>