MATHEMATICS COLLEGE

Use the product rule to answer each of the questions below. Throughout, be sure to carefully label any derivative you find by name. It is not necessary to algebraically simplify any of the derivatives you compute.a. Let m (w) = 3 w^17 4^w. Find m ′(w) .
b. Let h (t) = ( sin (t) + cos (t)) t 4. Find h ′(t).
c. Determine the slope of the tangent line to the curve y = f (x) at the point where a = 1 if f is given by the rule f(x) = e^x sin (x).
d. Find the tangent line approximation L(x) to the function y = g (x) at the point where a = − 1 if g is given by the rule g (x) = ( x^2 + x ) 2^x .

Answers

Answer 1

Answer:

Answer:

A) M'(w) = w^16 * 4^w [ 51 + 3w In4 ]

B) h'(t) = [ cos (t) - sin (t) ] t^4 + [ sin(t) + cos (t) ] 4t^3

C) f'(1) = e' [sin(1) + cos(1) ]

D) g'(a) = 0 - 1/2

L(x) = - 1/2 ( x + 1 )

Step-by-step explanation:

Attached below is the detailed solution of the problem

A) m(w) = 3w^17 * 4^w

M'(w) = w^16 * 4^w [ 51 + 3w In4 ]

B) h(t) = [sin(t) + cos(t) ] t^4

h'(t) = [ cos (t) - sin (t) ] t^4 + [ sin(t) + cos (t) ] 4t^3

C) f(x) = e^x sin (x). at a = -1

f'(1) = e' [sin(1) + cos(1) ]

D) g (x) = ( x^2 + x ) 2^x .

g'(a) = 0 - 1/2

L(x) = - 1/2 ( x + 1 )

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A cell site is a site where electronic communications equipment is placed in a cellular network for the use of mobile phones. The numbers y of cell sites from 1985 through 2011 can be modeled byy = 269573/1+985e^-0.308t where t represents the year, with t = 5 corresponding to 1985. Use the model to find the numbers of cell sites in the years 1998, 2003, and 2006.

Answers

Answer:

(a) 3178

(b) 14231

Step-by-step explanation:

Given

$y = (269573)/(1+985e^(-0.308t))$

Solving (a): Year = 1998

1998 means t = 8 i.e. 1998 - 1990

So:

$y = (269573)/(1+985e^(-0.308*8))$

$y = (269573)/(1+985e^(-2.464))$

$y = (269573)/(1+985*0.08509)$

$y = (269573)/(84.81365)$

$y = 3178$ --- approximated

Solving (b): Year = 2003

2003 means t = 13 i.e. 2003 - 1990

So:

$y = (269573)/(1+985e^(-0.308*13))$

$y = (269573)/(1+985e^(-4.004))$

$y = (269573)/(1+985*0.01824)$

$y = (269573)/(18.9664)$

$y = 14213$ --- approximated

Solving (c): Year = 2006

2006 means t = 16 i.e. 2006 - 1990

So:

$y = (269573)/(1+985e^(-0.308*16))$

$y = (269573)/(1+985e^(-4.928))$

$y = (269573)/(1+985*0.00724)$

$y = (269573)/(8.1314)$

$y = 33152$ --- approximated

What is the area of this figure? :)

Answers

there are 4 semicircles, each radius is 8cm, so we get the total areas of these semicircles: 4×0.5× $8^(2)$ π
and the square area: 16²
so the total area of figure: 16²+4×0.5× $8^(2)$ π=256+128π

What does it mean to evaluate?

Answers

Answer:

Means to simply solve, sometimes you may need to show your thinking, depending on the question.

Step-by-step explanation:

Answer:

Evaluate means to assess or determine something.

Step-by-step explanation:

Gabrielle is 5 years older than Mikhail. The sum of their ages is 53 . What is Mikhail's age?

Answers

Let, the Age of Mikhail = x
Age of Gabrielle = x + 5

It is given that, x + x+ 5 = 53
2x = 53 - 5
x = 48/2
x = 24

In short, Mikhail is 24 years old.

Hope this helps!

The following table shows claim amounts and their probabilities for an insurance company that offers homeowners’ insurance policies. Calculate the expected claim amount. That is, on average, how much will the insurance company have to pay in claims per policy holder?$2250

$5000

$7500

$3250

Answers

the answer is $5000.

if a cyclist rides at a constant rate of 24 miles per hour, how long would it take the cyclist to ride 156 miles

Answers

Answer:

6.5 hours

Step-by-step explanation:

156 ÷ 24 = 6.5

have a nice dayyy :)

It would take the cyclist 6.5 hours

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