Answer:
cot θ = √15 / 7
Explanation:
csc θ = 1 / sin θ
In a right angled triangle, sin θ = opposite / hypotenuse
This means that:
csc θ = hypotenuse / opposite = 8 / 7
So, we have:
opposite = 7 units and hypotenuse = 8 units
We will use the Pythagorean theorem to get the adjacent side as follows:
(hypotenuse)^2 = (opposite)^2 + (adjacent)^2
(8)^2 = (7)^2 + (adjacent)^2
(adjacent)^2 = 15
adjacent = √15 units
Now, we want to get the value of cot θ.
We know that:
cot θ = 1 / tan θ
Since tan θ = opposite / adjacent
Therefore:
cot θ = adjacent / opposite = √15 / 7
Hope this helps :)
Step-by-step explanation:
Well first let's find the derivative in using the power rule
h'(t) = (-4.9)t + 157
h'(t) = -9.8t + 157
we can see from the image above that the maximum height is 1452.602 so that is the answer to the second question.
h'(1452.602) = -9.8(1452.602) + 157
h' = 14,078.500
This is a equilateral triangle because all the sides are equal.
The 10 tons should have 37.9% cement.
Let the 25% mixture be x tons
Then the 68% mixture will be (10 -x) tons.
Using formula for mixtures:
Let p for percentage and w for weight in tons.
p₁w₁ + p₂w₂ = pw
25*x + 68*(10-x) = 37.9*10
25x + 680 - 68x = 379
680 - 43x = 379
680 - 379 = 43x
301 = 43x
43x = 301
x = 301/43
x = 7
Recall that x, was for the 25% mixture, 7 tons.
a) For the 68% mixture, = 10 - x = 10 -7 = 3 tons.
b) For the 25% mixture = x = 7 tons.
That they are the exact same shape. Some of the sides will be longer and shorter than the other figure, but same shape.
