Answer:
35/12
Step-by-step explanation:
The tangent in a triangle is always the opposite side divided by the adjacent side. In this triangle, BC is the side opposite to angle a, and AC is the side adjacent to angle A.
However, we do not know what AC is, but we can use the pythagorean theorem to solve. 
, which is 12 squared. Therefore, AC is 12 units in length.
Now we have all the sides of the triangle and we can divide the opposite side by the adjacent side. We get 35/12.
Hope this helps!
Answer:
Step-by-step explanation:
Base of triangle = b = 8 cm
Height of triangle = h = 6 cm
Length of rectangle = l = 6 cm
Sides of the triangle : S1 = 6 cm ; S2 = 8 cm and S3 = 10 cm
Surface area of triangular prism= bh + l *(s1+ S2 + S3)
= 8 * 6 + 6*(6+8+10)
= 48 + 6*24
= 48 + 144
= 192 square cm
Answer:
The proof is detailed below.
Step-by-step explanation:
We will first prove that if H(x) is a differentiable function in [a,b] such that H'(x)=0 for all x∈[a, b] then H is constant. For this, take, x,y∈[a, b] with x<y. By the Mean Value Theorem, there exists some c∈(x,y) such that H(y)-H(x)=H'(c)(x-y). But H'(c)=0, thus H(y)-H(x)=0, that is, H(x)=H(y). Then H is a constant function, as it takes the same value in any two different points x,y.
Now for this exercise, consider H(x)=F(x)-G(x). Using differentiation rules, we have that H'(x)=(F-G)(x)'=F'(x)-G'(x)=0. Applying the previous result, F-G is a constant function, that is, there exists some constant C such that (F-G)(x)=C.
Answer:
2.36
Step-by-step explanation:
order of operations : pemdas
parenthesis, exponents
multiplication, division
addition, substraction
first parenthesis, so
(32-4) = 28
parenthesis again
[10+28] = 38
now you have
90/38 = 45/19 = 2.36
