Answer:
Thnx
Step-by-step explanation:
have a great day
Answer:
straight angle
Step-by-step explanation:
The value
maximizes angle APB.
In this question we need to determine the <em>maximum possible</em> angle APB, which can be determined by definition of dot product, that is to say:
(1)
Where:
,
- Magnitudes of
and
.
- Internal angle, in sexagesimal degrees.
The magnitudes of each are respectively defined by line segment length formula:
,
, ![P(x, y) = (x, 0)](https://tex.z-dn.net/?f=P%28x%2C%20y%29%20%3D%20%28x%2C%200%29)
![\overrightarrow{PA} = \sqrt{(3-x)^{2}+1^{2}}](https://tex.z-dn.net/?f=%5Coverrightarrow%7BPA%7D%20%3D%20%5Csqrt%7B%283-x%29%5E%7B2%7D%2B1%5E%7B2%7D%7D)
(2)
![\overrightarrow{PB} = \sqrt{(5-x)^{2}+3^{2}}](https://tex.z-dn.net/?f=%5Coverrightarrow%7BPB%7D%20%3D%20%5Csqrt%7B%285-x%29%5E%7B2%7D%2B3%5E%7B2%7D%7D)
(3)
By (1), (2) and (3) we have the following expression:
![(3-x)\cdot (5-x) +3 = \sqrt{10-6\cdot x + x^{2}}\cdot \sqrt{34-10\cdot x + x^{2}}](https://tex.z-dn.net/?f=%283-x%29%5Ccdot%20%285-x%29%20%2B3%20%3D%20%5Csqrt%7B10-6%5Ccdot%20x%20%2B%20x%5E%7B2%7D%7D%5Ccdot%20%5Csqrt%7B34-10%5Ccdot%20x%20%2B%20x%5E%7B2%7D%7D)
![15-8\cdot x +x^{2} = \sqrt{(10-6\cdot x +x^{2})\cdot (34-10\cdot x + x^{2})}\cdot \cos \theta](https://tex.z-dn.net/?f=15-8%5Ccdot%20x%20%2Bx%5E%7B2%7D%20%3D%20%5Csqrt%7B%2810-6%5Ccdot%20x%20%2Bx%5E%7B2%7D%29%5Ccdot%20%2834-10%5Ccdot%20x%20%2B%20x%5E%7B2%7D%29%7D%5Ccdot%20%5Ccos%20%5Ctheta)
(4)
From geometry we know that sum of internal angles in triangles equals 180°, which means that angle APB must meet this condition:
![0 < \angle APB < 180](https://tex.z-dn.net/?f=0%20%3C%20%5Cangle%20APB%20%3C%20180)
In addition, we know that <em>cosine</em> function is a bounded function between -1 and 1, where
,
, ![\theta = 180^{\circ}\to -1](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20180%5E%7B%5Ccirc%7D%5Cto%20-1)
A quick approach consists in graphing (4) against x. Outcome is described in the second image attached. By direct inspection, we see that
maximizes angle APB.
We kindly invite to check this question on optimization: brainly.com/question/4302495
Get a common denominator for the two, whcih would be 12 soooo.
5 2/12 - 1 9/12 = your answer (3 5/12)
Answer:
2201.8348 ; 3 ; x / (1 + 0.01)
Step-by-step explanation:
1)
Final amount (A) = 2400 ; rate (r) = 6% = 0.06, time, t = 1.5 years
Sum = principal = p
Using the relation :
A = p(1 + rt)
2400 = p(1 + 0.06(1.5))
2400 = p(1 + 0.09)
2400 = p(1.09)
p = 2400 / 1.09
p = 2201.8348
2.)
12000 amount to 15600 at 10% simple interest
A = p(1 + rt)
15600 = 12000(1 + 0.1t)
15600 = 12000 + 1200t
15600 - 12000 = 1200t
3600 = 1200t
t = 3600 / 1200
t = 3 years
3.)
A = p(1 + rt)
x = p(1 + x/100 * 1/x)
x = p(1 + x /100x)
x = p(1 + 1 / 100)
x = p(1 + 0.01)
x = p(1.01)
x / 1.01 = p
x / (1 + 0.01)