You invest 5000 dollars in an account at 1.6% interest is compounded annually (once a year) a) write an equation that shows the
1 answer:
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Answer:
x-intercept = 0.956
Step-by-step explanation:
You have the function f(x) given by:
(1)
Furthermore you have that at the point (a,f(a)) the tangent line to that point has a slope of -1.
You first derivative the function f(x):
(2)
To solve this derivative you use the following derivative formula:
For the derivative in (2) you have that b=2 and u=2x. You use the last expression in (2) and you obtain:
You equal the last result to the value of the slope of the tangent line, because the derivative of a function is also its slope.
Next, from the last equation you can calculate the value of "a", by doing x=a. Furhtermore, by applying properties of logarithms you obtain:
With this value you calculate f(a):
Next, you use the general equation of line:
for xo = a = 0.235 and yo = f(a) = 0.721:
The last is the equation of the tangent line at the point (a,f(a)).
Finally, to find the x-intercept you equal the function y to zero and calculate x:
hence, the x-intercept of the tangent line is 0.956
Answer:
Yes, △ABC ∼ △FED by AA postulate.
Step-by-step explanation:
Given:
Two triangles ABC and FED.
m∠A = m∠B
m∠C = m∠A + 30°
m∠E = m∠F =
m∠D = °.
Now, let m∠A = m∠B =
So, m∠C = m∠A + 30° =
Now, sum of all interior angles of a triangle is 180°. Therefore,
m∠A + m∠B + m∠C = 180
Therefore, m∠A = 50°, m∠B = 50° and m∠C = m∠A + 30° = 50 + 30 = 80°.
Now, consider triangle FED,
m∠D+ m∠E + m∠F = 180
Therefore, m∠F = 50°
m∠E = 50° and
m∠D =
So, both the triangles have congruent corresponding angle measures.
m∠A = m∠F = 50°
m∠B = m∠E = 50°
m∠C = m∠D = 80°
Therefore, the two triangles are similar by AA postulate.