All categories

2 years ago

Find (a) the slope of the curve at the given point P, and (b) an equation of the tangent line at P: y = 9x^2 + 5 ; P (2,41)

Mathematics

1 answer:

Flauer [41]2 years ago

6 0

Answer:

(a) 36

(b) y = 36x-31

Step-by-step explanation:

(a) dy/dx = 18x

slope of tangent at (2, 41) = 18(2)

= 36

(b) using y-y1 = m(x-x1)

y-41 = 36(x-2)

y = 36x-31

You might be interested in

10-2x -x for x<1 f(x) 3 + 4e^x-1 for x> 1 f(x) be the function defined above. Is f continuous at x=1? Why or why not? Find

8090 [49]

it can not be a function because functions only have ONE input to each output

5 0

2 years ago

In the year 2002, the world population was estimated at 6 billion people. Based on research from the World Bank, about 20% lived

olga_2 [115]

In the given question all the information's are provided based on which the answer to the question can be easily deduced. It is already given that the population of the world in the year 2002 was estimated to about 6 billion. Among them 20% of the people lived on an an income of less that $1 per day.Firstly let us convert 6 billion from words to numbers.
6 billion = 6000000000
Now
Number of people earning less that $1 per day = (20/100) * 6000000000
= 6000000000/5
= 1200000000
So the number of people earning less than $1 per day is 1200000000

8 0

2 years ago

Which of these values for p and a will cause the function f(x)=Pax to be an exponential growth function

vovikov84 [41]

The option are missing in the question. The options are :

A. P = 2, a = 1

B. $P=\frac{1}{2} ; a =\frac{1}{3}$

C. $P=\frac{1}{2} ; a =1$

D. P = 2, a = 3

Solution :

The given function is $f(x)= Pa^x$

So for the function to be an exponential growth, a should be a positive number and should be larger than 1. If it less than 1 or a fraction, then it is a decay. If the value of a is negative, then it would be between positive and negative alternately.

When the four option being substituted in the function, we get

A). It is a constant function since $2(1^x)=2$

B). Here, the value of a is a fraction which is less than 1, so it is a decay function. $f(x)=\frac{1}{2}\left(\frac{1}{3}\right)^x$

C). It is a constant function since the value of a is 1.

D). Here a = 3. So substituting, as the value of x increases by 1, the value of the function, f(x) increases by 3 times.

$f(x)=2(3)^x$

Therefore, option (D). represents an exponential function.

4 0

2 years ago

What is a two dementional figure that has one endpoint.PLEASE HELP ME!!!!!

Ivanshal [37]

Answer:

A two dimensional figure that has only one endpoint is a ray

Step-by-step explanation:

A ray has one endpoint and then goes on for infinite time in the other direction.

7 0

3 years ago

what's the least positive integer that has the same number of positive factors as 175? I know there are 6 positive factors. But

GarryVolchara [31]

How many positive factors does it have?
175=1*5*5*7
it depends on whether you count 1 or not
how many are there
3 or 4

same number of positive factors
didn't say the factors had to be different
1*1*1*1=1
answer is 1

8 0

2 years ago