so since the ratio of red paint to blue paint is 2:4 and you can simplify 2:4 into 1:2 and because 5 liters of paint is used you would have to multiply the 2 from the simplified ratio by 5 so you could get the answer 2*5 and that equals 10
2 hours at 65 mph makes 130 miles. Subtract 130 from 185 and you get 55
Answer:
132 feet
Step-by-step explanation:
Given that Alejandro is standing at a distance of 140 feet from the base of the tree and his eyes are 6 feet above the ground.
Let AB is the height of the tree and point E is the location of his eyes which is 6 feet above from C on the ground as shown in the figure.
The distance between points A and C, AC=140 feet.
Drawing a horizontal line from point E which meets AB at point D as shown.
As ACED forms a rectangle, so
AC=DE=140 feet ...(i)
CE=AD= 6 feet ...(ii)
The height of the tree, AB=AD+DB
By using equation (ii), AB=6+DB ...(iii)
Now, given that the on watching the top of the tree, the reading on the clinometer is 42 degrees.
So,
In triangle DEB,
[from (i)]
feet
From equation (iii) the height of the tree is
AB=6+126=132 feet.
Hence, the height of the tree is 132 feet.
9514 1404 393
Answer:
(a) 75.5
Step-by-step explanation:
There are two ways you can work this.
<u>Pythagorean theorem</u>
Triangle CMP is a right triangle. CM = AC = 55. CP = CB -PB = 55 -15 = 40. Then length PM can be found from ...
PM² +CP² = CM²
PM = √(CM² -CP²) = √(55² -40²) = √1425 ≈ 37.749
The length MN is twice the length of PM, so is ...
MN = 2×PM = 2×37.349 = 75.498
The length of MN is about 75.5.
__
<u>Using chord relationships</u>
The products of the different lengths for the same chord are the same for the crossed chords.
AP×PB = MP×PN
We know MP = PN, so ...
MP = √(AP×PB) = √((55+40)(15)) = √1425
As before, MN = 2×MP = 2√1425
MN ≈ 75.5
Answer:
y = -1/√3 (x − 4)
Step-by-step explanation:
Let's say the point where the tangent line intersects the circle is B (bₓ, bᵧ). Therefore:
bₓ² + bᵧ² = 4
The slope of the tangent line at that point is dy/dx, which we can find with implicit differentiation:
x² + y² = 4
2x + 2y dy/dx = 0
2y dy/dx = -2x
dy/dx = -x/y
At point B, the slope of the tangent line is m = -bₓ/bᵧ.
We can also write that as the slope between the points A(4, 0) and B(bₓ, bᵧ).
m = (bᵧ − 0) / (bₓ − 4)
m = bᵧ / (bₓ − 4)
Setting the expressions equal:
-bₓ / bᵧ = bᵧ / (bₓ − 4)
bᵧ² = -bₓ (bₓ − 4)
bᵧ² = 4 bₓ − bₓ²
Substituting this into the first equation:
bₓ² + (4 bₓ − bₓ²) = 4
4 bₓ = 4
bₓ = 1
Therefore, bᵧ = √3. So the slope of the line is -1/√3. The equation of the line is:
y − 0 = -1/√3 (x − 4)
y = -1/√3 (x − 4)
Graph: desmos.com/calculator/sornb1ajgp
