Answer:
d = k·sin(2θ)·sin(α)/(sin(θ)·sin(β))
Step-by-step explanation:
The Law of Sines tells us that sides of a triangle are proportional to the sine of the opposite angle. This can be used along with a trig identity to demonstrate the required relation.
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<h3>top triangle</h3>
The law of sines applied to the top triangle is ...
BC/sin(A) = AC/sin(θ)
Triangle ABC is isosceles, so the base angles at B and C are congruent. Then the angle at vertex A is ...
∠A = 180° -θ -θ = 180° -2θ
A trig identity tells us the sine of an angle is equal to the sine of its supplement. That means the sine of angle A is ...
sin(A) = sin(180° -2θ) = sin(2θ)
and our above Law of Sines equation tells us ...
BC = sin(A)/sin(θ)·AC = k·sin(2θ)/sin(θ)
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<h3>bottom triangle</h3>
The law of sines applied to the bottom triangle is ...
DC/sin(B) = BC/sin(D)
d/sin(α) = BC/sin(β)
Multiplying by sin(α) we have ...
d = BC·sin(α)/sin(β)
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Using our expression for BC gives the desired relation:
d = k·sin(2θ)·sin(α)/(sin(θ)·sin(β))
Answer:
B. 4 imaginary; 1 real
Step-by-step explanation:
Given the polynomial:
x^5 + 7*x^4 + 2*x^3 + 14*x^2 + x + 7
it can be reordered as follows
(x^5 + 2*x^3 + x ) + (7*x^4 + 14*x^2 + 7)
Taking greatest common factor at each parenthesis
x*(x^4 + 2*x^2 + 1) + 7*(x^4 + 2*x^2 + 1)
Taking again the greatest common factor
(x + 7)*(x^4 + 2*x^2 + 1)
Replacing x^2 = y in the second parenthesis
(x + 7)*(y^2 + 2*y + 1)
(x + 7)*(y + 1)^2
Coming back to x variable
(x + 7)*(x^2 + 1)^2
There are two options to find the roots
(x + 7) = 0
or
(x^2 + 1)^2 = 0 which is the same that (x^2 + 1) = 0
In the former case, x = -7 is the real root. In the latter, (x^2 + 1) = 0 has no real solution. Therefore, there is only 1 real root in the polynomial.
Let the amount deposited by each of them in march be m.
in April, Isaiah deposited 210$, this means the amount in his account became m+210
Freddie increased the amount by 15%, this means that the amount of money in his account became: m+0.15m
since both values are still equal, we will equate both equations and solve for m.
m+210 = m+0.15m
0.15m = 210
m = 1400$
Answer:
Step-by-step explanation:
Remark
I suppose the question is what is Thaddeus' time to make the trip. This is a fairly common question but not everyone knows how to solve it.
Derivation of the Formula
Prescott + Thaddeus = 1 trip
So the logic of the equation is this.
distance = 1 trip
time = number of dates
rate = ?
rate = distance / time
To find out what the contribution of Thaddeus is set up a distance time formula.
1/21 days is the rate for Prescott
1/x days is the rate for Thaddeus
Together the rate is 1/9
Solution
1/21 + 1/x = 1/9
Subtract 1/21 from both sides
1/x = 1/9 - 1/21
It's not obvious what the LCM is.
9 = 3 * 3
21 = 3 * 7
LCM: 7 * 3 *3 = 63
1/x = 7/63 - 3/63 = 4/63
1/x = 4/63 Cross Multiply
4x = 63 Divide by 4
x = 63/4
Answer
x = 15 3/4
x = 15.75
C. 705.25 minutes
First, estimate the learning curve rate by calculating the average learning rate with each dou- bling of production
