Step-by-step explanation:
=99*9/11
- -
_____
=891/11
=81
Answer:
35/37
Step-by-step explanation:
In this question, we are to calculate the ratio that represents the cosine of angle O
Firstly, please check attachment for diagram of the triangle.
Mathematically, the trigonometric term Cos means the ratio of the length of the adjacent to that of the hypotenuse
The hypotenuse is the longest length which is 37 which represents the length ON
The side adjacent to angle O is the side OP which is 35
Thus, the ratio representing the cosine of angle O is 35/37
Answer:
E(29/4,3)
Step-by-step explanation:
Given that,
Segment CD has point E located on it such that CE:ED = 3:5
The coordinates of C and D are (5, -6) and (11,18) respectively.
We need to find the coordinates of E. Let the coordinates are (x,y). Using section formula to find it as follows :
So, the coordinates of E are (29/4,3).
Answer:
Step-by-step explanation:
This is simply a units conversion problem. It gives us for the number of passengers, the number of seats per carriage and the number of carriages per train. To change the units from passengers to trains without changing the value, we use the multiplicative identity (that is, 1).
350000 passengers
(350000 passengers) * 1
(350000 passengers) * ((1 carriage)/(32 passengers)) * ((1 train)/(15 carriages)
[note: passengers and carriages cancel. Leaving only trains]
(350000)*(1/32)*(1/15) trains [note: I write this way to paste into MS Excel]
729.1667 trains [oh, but don’t just round this number either up or down]
729 full trains can carry 729*32*15 = 349920 passengers
730 full trains can carry 730*32*15 = 350400 passengers
Now, we can say that 730 trains are adequate to carry 350000 passengers.
Answer:
We conclude that:
h(f(-1)) = -2
∴ option D i.e. -2 is correct.
Step-by-step explanation:
Given
f(x) = 4x² - 1
g(x) = 1/2x + 5
h(x) = 2(x - 4)³
To determine
h(f(-1)) = ?
In order to determine h(f(-1)) first we need to determine f(-1).
substitute x = -1 in the function f(x) = 4x² - 1
f(-1) = 4(-1)² - 1
f(-1) = 4(1) - 1
f(-1) = 4-1
f(-1) = 3
so
h(f(-1)) = h(3)
now substitute h = 3 in the function h(x) = 2(x - 4)³
h(x) = 2(x - 4)³
h(3) = 2(3 - 4)³
h(3) = 2(-1)³
h(3) = 2(-1)
h(3) = -2
Thus,
h(f(-1)) = h(3) = -2
Hence, we conclude that:
h(f(-1)) = -2
∴ option D i.e. -2 is correct.
