Let the constant term be represented by a constant "c" and the term that varies directly as the square of v be represented by "kv²", where k is a constant.
Given that u = c + kv².
When v = 2, u = 203:
203 = c + k(2)²
203 = c + 4k ----- (Equation 1)
Now we need to find the value of v when u = 515.
515 = c + kv² ----- (Equation 2)
To solve for the value of v, we need to eliminate the constant term "c" and solve for k using the given information.
From Equation 1, we can express c in terms of k:
c = 203 - 4k
Substituting this value for c in Equation 2:
515 = (203 - 4k) + kv²
515 = 203 - 4k + kv²
312 = kv² - 4k
Rearranging the equation:
kv² - 4k = 312
Factoring out k:
k(v² - 4) = 312
Divide both sides by (v² - 4):
k = 312 / (v² - 4)
Now we can substitute this value of k back into Equation 1 to solve for c:
203 = c + 4k
203 = c + 4(312 / (v² - 4))
203 = c + 1248 / (v² - 4)
Multiply both sides by (v² - 4) to eliminate the fraction:
203(v² - 4) = c(v² - 4) + 1248
203v² - 812 = cv² - 4c + 1248
Since the first term of the equation has a v² term and the constant term is a number, we can equate the coefficients:
203 = c
-812 = -4c + 1248
Solving the second equation for c:
-4c + 1248 = -812
-4c = -812 - 1248
-4c = -2060
c = -2060 / -4
c = 515
Therefore, the constant term "c" is 515.
Substituting this back into Equation 1:
203 = c + 4k
203 = 515 + 4k
Solving for k:
4k = 203 - 515
4k = -312
k = -312 / 4
k = -78
Now we have the values of "c" and "k" which we can substitute into Equation 2 to solve for v when u = 515:
515 = c + kv²
515 = 515 + (-78)v²
0 = -78v²
This equation has no real solutions.
Therefore, there is no value of v for which u = 515.
A quantity u is the sum of two terms , one partly constant and the other varies directly as the square of v . If v =2 when u=203. Find the value of v when u=515
3 answers
An octagon has interior angle of 120, 110, 130, 114 , 90.if the remaining angles are equal . what is the size of the equal angles
To find the size of the equal angles in the octagon, we need to first calculate the sum of the known interior angles.
Given that the octagon has interior angles measuring 120°, 110°, 130°, 114°, and 90°, we can add these angles:
120° + 110° + 130° + 114° + 90° = 564°.
The sum of the known interior angles is 564°.
Since an octagon has 8 interior angles, we subtract the sum of the known angles from the sum of all the interior angles of the octagon to determine the measure of the remaining equal angles:
Sum of all interior angles of an octagon = (8 - 2) * 180° = 1080°.
1080° - 564° = 516°.
We now have the measure of the remaining equal angles as 516°.
Since an octagon has 8 equal interior angles, we divide the total measure of the equal angles by 8 to find the measure of each equal angle:
516° / 8 = 64.5°.
Therefore, the size of the equal angles in the octagon is 64.5°.
Given that the octagon has interior angles measuring 120°, 110°, 130°, 114°, and 90°, we can add these angles:
120° + 110° + 130° + 114° + 90° = 564°.
The sum of the known interior angles is 564°.
Since an octagon has 8 interior angles, we subtract the sum of the known angles from the sum of all the interior angles of the octagon to determine the measure of the remaining equal angles:
Sum of all interior angles of an octagon = (8 - 2) * 180° = 1080°.
1080° - 564° = 516°.
We now have the measure of the remaining equal angles as 516°.
Since an octagon has 8 equal interior angles, we divide the total measure of the equal angles by 8 to find the measure of each equal angle:
516° / 8 = 64.5°.
Therefore, the size of the equal angles in the octagon is 64.5°.