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lina2011 [118]
3 years ago
6

A function f is described by f(x)=A*exp(kx)+B, where A, B and k are constants. Given f(0)=1, f(1)=2, and that the horizontal asy

mptote of f is -4, the value of k is
Mathematics
1 answer:
s2008m [1.1K]3 years ago
8 0

Answer:

k = ln (6/5)

Step-by-step explanation:

for

f(x)=A*exp(kx)+B

since f(0)=1, f(1)=2

f(0)= A*exp(k*0)+B = A+B = 1

f(1) = A*exp(k*1)+B =  A*e^k + B = 2

assuming k>0 , the horizontal asymptote H of f(x) is

H= limit f(x) , when x→ (-∞)

when x→ (-∞) , limit f(x) =  limit (A*exp(kx)+B) = A* limit [exp(kx)]+B* limit = A*0 + B = B

since

H= B = (-4)

then

A+B = 1 → A=1-B = 1 -(-4) = 5

then

A*e^k + B = 2

5*e^k + (-4) = 2

k = ln (6/5)    ,

then our assumption is right and k = ln (6/5)  

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The radius of a circle is 9 feet. What is the length of a 90° arc?
maks197457 [2]

Answer:

\frac{9\pi }{2} feet, or 14.14 feet

Step-by-step explanation:

Use the arc length formula:

s = rθ

To use the formula, we have to convert the central angle to radians.

90° is equivalent to \frac{\pi }{2} radians, so plug this and the radius into the formula:

s = rθ

s = (9)(\frac{\pi }{2})

s = \frac{9\pi }{2}

So, the length of the arc is \frac{9\pi }{2}\\ feet, or approximately 14.14 feet

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3 years ago
Please help with problem 8. (ONLY IF YOU KNOW)
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3x$2.49+2x$3.19+4x$4.99=$33.81
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Harlon recorded this set of data, which contains an outlier. 163, 97, 184, 199, 169, 175 What is the range of this set of data?
maks197457 [2]
Hey there!

To find the range, first put the numbers in order from smallest to largest. 
97, 163, 169, 175, 184, 199

Then take the largest number, 199, and subtract the smallest number (in this case, the outlier) which is 97.

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Thanks for using Brainly! Hope this helps :)


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last month Stephanie spent $57 on 4 allergy shots and 1 office visit .This month she spent $9 after 1 office visit and a refund
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Visit $25 allergy shot $8

4a + 1v =57

-2a +1v= 9

I will multiply the second by -1 to cancel v variable (elimination method)

4a +1v =57

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add both

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v= 25

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