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3 years ago

If the tangent line to y = f(x) at (7, 4) passes through the point (0, 3), find f(7) and f '(7).

1 answer:

4 0

Hello :
f'(7) = the slope of the tangent line : let A(7,4) B(0,3)
the slope is : (YB - YA)/(XB -XA)= (3-4)/(0-7) = -1/-7 = 1/7=f'(7)
the equation of the tangent line is :
y-3 = 1/7 (x-0)
y = (1/7)x+3
the line tangent and the graph of : f passes through the point A(7, 4)
x= 7 y=4 so : f(7) =4

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Determine o x 2x+15 3x-25

Papessa [141]

2x+15 = 3x-25
2x-3x = -25 -15
-x = -40
x = 40

7 0

3 years ago

The South Coast Air Basin (Los Angeles, Orange, and San Bernardino counties) does not meet the air quality standards for carbon

Archy [21]

Answer:

0.2225 gr/mile

Step-by-step explanation:

Let's work out first the amount of CO sent out in 1990.

The population we estimated in 12.5 million people with a total of driven miles per year of about

12.5 million*8,700 = 108,750 million miles.

With an CO emission factor of 0.9 g per mile, we would have a total of CO emitted rounding 0.9*180,750 = 97,875 million grams

Now, we must estimate the population for 2020.

Since we are assuming an exponential growth, the population in year t is given by a function

$\bf P(t)= Ce^{kt}$

where C and k are constants to be determined.

We can take 1980 as year 0. This way calculations are lighter. 1990 is year 10 and 2020 is year 20.

So P(0) = 10.3 and C=10.3

So far we have

$\bf P(t)= 10.3e^{kt}$

Given that P(10)=12.5

$\bf 10.3e^{k*10}=12.5\rightarrow e^{10k}=\frac{12.5}{10.3}=1.21359\rightarrow \\10k=log(1.21359)\rightarrow k=0.01936$

And the function that models the population growth is

$\bf P(t)= 10.3e^{0.01936t}$

We need P(20)

$\bf P(20)= 10.3e^{0.01936*20}=10.3e^{0.38717}=15.17\;million$

If the miles driven per person per year remains constant at 8700 mi/yr.person, then we have a total miles driven of

15.17*8,700=131,979 million miles, so the CO emitted would be 0.9*131,979=118,781.1 million grams.

The 30% of the CO sent out in 1990 is 0.3*97,875=29,362.5 million grams.

We must reduce 118,781.1 down to 29,362.5

Hence the new CO emission factor would be

29,362.5/131,979 = 0.2225 gr/mile

6 0

3 years ago

Sir Ving Spoon earned $5,436 on his $7,550 certificate of deposit. If he had the CD for 12 years, what simple interest rate did

Lilit [14]

6% or 0.06 is the simple interest rate the bank pays him.

Step-by-step explanation:

Sir Ving Spoon earned $5,436 on his $7,550 certificate of deposit.

From this given information,

It can be determined that the Principal amount is $7550 and the interest amount is $5436.

The CD is for 12 years. Therefore, the number of years is 12.

To find the interest rate (r) :

Using the simple interest formula,

Interest = P×r×t

where,

P is the principal amount = $7550
r is the rate of interest.
t is the number of years = 12

⇒ 5436 = 7550 × r × 12

⇒ 5436 = 90600 × r

⇒ r = 5436 / 90600

⇒ r = 0.06

Multiply by 100 to represent in rate %

⇒ r = 0.06 × 100

⇒ r = 6%

∴ 6% or 0.06 is the simple interest rate the bank pays him.

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3 years ago

Factor the given polynomial 2z-22z+48 completely.

____ [38]

The GCF here is 2

2(z - 11z + 24)

i assume your question is wrong.. or you printed it inaccurately
because the 1st term should indicate the highest exponent however the 1st and 2nd terms are having the same exponent!!

7 0

3 years ago

Read 2 more answers

PLEASE HELP ME QUICKLY!!!!

LiRa [457]

For each, you'll use the slope formula
m = (y2-y1)/(x2-x1)

For function f, you'll use the two points (1,6) and (2,12) since x ranges from x = 1 to x = 2 for function f

The slope through these two points is
m = (y2-y1)/(x2-x1)
m = (12-6)/(2-1)
m = 6/1
m = 6

-------------------------------------------

For function g, you'll use (2,4) and (3,20)

The slope through these two points is
m = (y2-y1)/(x2-x1)
m = (20-4)/(3-2)
m = 16/1
m = 16

-------------------------------------------

For function h, you'll use (0,-6) and (2,-18). The y coordinates can be found by plugging in x = 0 and x = 2 respectively into h(x)

The slope through these two points is
m = (y2-y1)/(x2-x1)
m = (-18-(-6))/(2-0)
m = (-18+6)/(2-0)
m = (-12)/(2)
m = -6

-------------------------------------------

The order from left to right is: h, f, g

6 0

3 years ago