Answer:
Step-by-step explanation:
There are two sides on a coin, heads and tails. So, the probability of flipping heads is going to be 1/2, as there is one chance out of the two options that you will flip a head. As for spinning blue, there are 3 options that are blue out of the four color options given. So, the probability of spinning blue would be 3/4. Hope this helped :) Take this with a grain of salt, though. It's been a while since I reviewed probabilities.
Answer:
The height of the hill = h = 580.7 feet
Step-by-step explanation:
Let height of the hill = h
From the triangle A B D
Tan 22 = 
⇒ AB = h & B D = y + 700
⇒ Tan 22 = 
------------(1)
From triangle ABC
Tan 38 = 
⇒ AB = h & BC = y
⇒ Tan 38 = 
------------------(2)
⇒ h = y tan 38 -----------------(3)
Put the value of h from equation (3) into equation (1) we get
⇒ (tan 22) × (y + 700) = y × tan 38
⇒ 0.40 y + 282.82 = y × 0.78
⇒ y = 742.12 feet -----------------(4)
Put this value of y in equation 3 we get
⇒ h = 742.12 × tan 38
⇒ h = 580.7 feet
This is the height of the hill.
2cos²x+cos x-1=0
cos x=t
2t²+t-1=0
t=[-1⁺₋√(-1+8)]/2=(-1⁺₋3)/4
We have two possible set solutions:
First set solutions.
t₁=(-1-3)/2=-4/4=-1
cos x=-1 ⇒x=cos⁻¹ (-1)=π +2kπ or 180º+360ºk (k=(...-2,-1,0,1,2...)
Second set solutions:
t₂=(-1+3)/4=2/4=1/2
cos x=1/2 ⇒ x=cos⁻¹ 1/2=π/3+2kπ U 5π/3+ 2kπ or
60º+360ºK U 300º+360ºK (k=...-2,-1,0,1,2,...)
solutions: first set solutions U second set solutions:
Answer in radians : π +2kπ U π/3+2kπ U 5π/3+ 2kπ (k=...-1,0,1,...)
Answer is degrees: 180º+360ºk U 60º+360ºK U 300º+360ºK (k=...-2,-1,0,1,2,...)
Answer:
(x - 3)^2 + (y - 4)^2 = 3^2
Step-by-step explanation:
Notice that both endpoints are on the vertical line x = 3. Thus, to determine the diameter of this circle, we need only subtract 1 from 7, obtaining 6. The diameter is 6, so the radius is 3.
The center is on the vertical line x = 3 and is halfway between the endpoints of the diameter, that is, at y = 4. (3, 4) describes this point.
Then we insert the known quantities into the general equation for a circle with center at (h, k) and radius r: 3 for h, 4 for k and 3 for r:
(x - 3)^2 + (y - 4)^2 = 3^2 is the desired equation.
Answer:
y = 107°
Step-by-step explanation:
As you can see from the markings on the triangle, this is an isosceles triangle (two sides are congruent).
An isosceles triangle has the base angles congruent too.
So at this point,
34 = x - 5
Solve for x,
34 = x - 5
x = 34 + 5
x = 39
Now, the total angle measure of triangle is 180°.
There are two angles ready to solve for y.
34 + 39 + y = 180
73 + y = 180
y = 180 - 73
y = 107°
