Answer:
Step-by-step explanation:
We khow that the equation of a circle is written this way :
(x-a)²+(y-b)²=r² where (x,y) are the coordinates of the cercle's points and (a,b) the coordinates of the cercle's center and r the radius .
Our task is to khow the values of a and b :
- We khow that the center is lying on the line 3x+2y=16⇒ 2y=-3x+16⇒ y=
x+8 - We khow that the points P and Q are two points in the cercle
- Let Ω be the center of this cercle
- we can notice that : PΩ AND QΩ are both equal to the radius ⇒ PΩ=QΩ= r
- So let's write the expression of this distance using vectors KHOWING THAT Ω(a,b)
- Vector PΩ(a-4,b-6) and Vector QΩ(a-8,b-2)
- PΩ=
and QΩ=
- Let's substitute a by x and b by y
- PΩ=QΩ we substitute each distance by its expression
- After simplyfying the expressions we get finally : -12+8x-8y=0
- now we have -12x +8x-8y=0 and the line equation 3x+2y-16=0
- these are simultanious equations so after solving them we get x=3.8 wich is approximatively 4 and y=2
- we substitute a by 4 and y by 2 in PΩ to get the radius
- we get r =
= 4 - so r²= 16
- then the equation is : (x-4)²+(y-2)²=16
i think this is the answer Simplifying h(t) = -16t2 + 20t + 6 Multiply h * t ht = -16t2 + 20t + 6 Reorder the terms: ht = 6 + 20t + -16t2 Solving ht = 6 + 20t + -16t2 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Divide each side by 't'. h = 6t-1 + 20 + -16t Simplifying h = 6t-1 + 20 + -16t Reorder the terms: h = 20 + 6t-1 + -16t
Given that triangles MON and POQ are similar triangles, the length of PO is 30 units.
<h3>What are Similar Triangles?</h3>
The triangles that are similar to each other will have their corresponding sides proportional to each other.
Given:
MP = 25
PQ = 18
MN = 33
Triangles MON and POQ are similar triangles.
Let PO = x
Therefore:
MN/PQ = MO/PO
Substitute
33/18 = (25 + x)/x
Cross multiply
33x = 18(25 + x)
33x = 450 + 18x
33x - 18x = 450
15x = 450
x = 30
Therefore, given that triangles MON and POQ are similar triangles, the length of PO is 30 units.
Learn more about similar triangles on:
brainly.com/question/21874653
Composite is a number that is NOT prime. So we want to find an odd perfect square that IS prime to be a counterexample.
√36 = Not odd
√49 = 7 Factors only 1 * 7 so it is prime
√81 = 9 Factors 1, 3, 9 composite
√225 = 15 Factors 1,3, 5,9,15, 25, 45, 75, 225 composite
Counterexample for 2∧n - 1 Is prime
2^6 - 1 = 64 - 1 = 63 NOT PRIME Factors are: 1, 3, 7, 9,21, 63
2^5 - 1 = 32 - 1 = 31 Prime
2^3 - 1 = 8 - 1 = 7 Prime
2^2 - 1 = 4 - 1 = 3 Prime
Answer:
1. θ = 34.85°
2. x = 36.31°
3. x = 39.80°
Step-by-step explanation:
1. Determination of θ.
Adjacent = 11.9
Hypothenus = 14.5
Angle θ =?
Cos θ = Adjacent /Hypothenus
Cos θ = 11.9 / 14.5
Cos θ = 0.8207
Take the inverse of Cos
θ = Cos¯¹ 0.8207
θ = 34.85°
2. Determination of x
Opposite = 9 m
Hypothenus = 15.2 m
Angle x =?
Sine x = Opposite /Hypothenus
Sine x = 9 / 15.2
Sine x = 0.5921
Take the inverse of Sine
x = Sine¯¹ 0.5921
x = 36.31°
3. Determination of x
Opposite = 10 in
Adjacent = 12 in
Angle x =?
Tan x = Opposite / Adjacent
Tan x = 10 / 12
Tan x = 0.8333
Take the inverse of Tan
x = Tan¯¹ 0.8333
x = 39.80°
