<h3>
Answer: ds/dt = 11</h3>
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Work Shown:
Before we can use derivatives, we need to find the value of s when (x,y) = (15,20)
s^2 = x^2+y^2
s^2 = 15^2+20^2
s^2 = 225+400
s^2 = 625
s = sqrt(625)
s = 25
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Now we can apply the derivative to both sides to get the following. Don't forget to use the chain rule.
s^2 = x^2 + y^2
d/dt[s^2] = d/dt[x^2 + y^2]
d/dt[s^2] = d/dt[x^2] + d/dt[y^2]
2s*ds/dt = 2x*dx/dt + 2y*dy/dt
2(25)*ds/dt = 2(15)*5 + 2(20)*(10)
50*ds/dt = 150 + 400
50*ds/dt = 550
ds/dt = 550/50
ds/dt = 11
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Side note: The information t = 40 is never used. It's just extra info.
Answer:
x can be 14 or more
Step-by-step explanation:
Answer:
13.7477270849 to 19.7230829233.
Step-by-step explanation:
1. Using the pythagorean theorem, a²+b²=c², we try different combinations of given lengths 10 and 17.
2. If 10 and 17 are legs and 10²+17²=√389 = 19.7230829233, then c=19.7230829233.
3. If 10 is a leg and 17 is a hypotenuse,
10²+b²=17²
100+b²=289
b²=189
b=13.7477270849
4. The case of 17 is a leg and 10 is a hypotenuse is not possible because the hypotenuse is the longest side.
5. The range of the length of the 3rd side is 13.7477270849 to 19.7230829233.
Answer: Yes it is possible to construct a triangle and it will be an isosceles triangle.
Step-by-step explanation:
The triangle inequality says that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.
The given sides of the triangle is 4 inches, 4 inches, and 7 inches.
Here,
So by triangle inequality, a triangle with sides 4 inches, 4 inches, and 7 inches. is possible.
Since it has two equal sides as 4 inches , then it must be an isosceles triangle.
To divide fractions you multiply the reciprocal
480 ÷ 1/3 =
480 × 3/1 = 1,440