Answer:
a=30
b=15
c=3
d=30
e=10
Step-by-step explanation:
Solve for A first and continue solving for one variable at a time
Numbers are related in all of them
Since both α and β are in the first quadrant, we know each of cos(α), sin(α), cos(β), and sin(β) are positive. So when we invoke the Pythagorean identity,
sin²(x) + cos²(x) = 1
we always take the positive square root when solving for either sin(x) or cos(x).
Given that cos(α) = √11/7 and sin(β) = √11/4, we find
sin(α) = √(1 - cos²(α)) = √38/7
cos(β) = √(1 - sin²(β)) = √5/4
Now, recall the sum identity for cosine,
cos(x + y) = cos(x) cos(y) - sin(x) sin(y)
It follows that
cos(α + β) = √11/7 × √5/4 - √38/7 × √11/4 = (√55 - √418)/28
Answer:
793 liters of washing fluid is needed
Step-by-step explanation:
step 1
Find the slant height of the triangular faces of pyramid
we know that
The lateral area of a square pyramid is equal to the area of its four triangular faces
so
where
b is the base of triangle (is the same that the length of the square base)
l is the slant height
To find out the slant height we need to apply the Pythagorean Theorem
so
we have
substitute
step 2
Find the lateral area of the pyramid
we have
substitute
step 3
Find out how much window washing fluid is needed
we know that
2 L of washing fluid cover 5 square meters
so
using proportion
Round up
793 liters of washing fluid is needed
Answer:
y = 3/2 x + 9/2
Step-by-step explanation:
3x - 2y = 5
3x - 5 = 2y
3/2 x - 5/2 = y
y = 3/2 x - 5/2, slope of this line m = 3/2.
For parallel line slope is the same.
y = mx + b
y = 3/2 x + b
Using point (-1,3) , we can find b.
3 = (3/2)*(-1) + b
3 = -3/2 + b
b = 3 + 3/2 = 6/2 + 3/2 = 9/2
y = 3/2 x + 9/2