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Finger [1]
3 years ago
8

Finding an Equation of a Tangent Line In Exercise, find an equation of the tangent line to the graph of the function at the give

n point.
y = xe^x - e^x, (1, 0)
Mathematics
1 answer:
neonofarm [45]3 years ago
3 0

Answer:

Equation of tangent:

y = xe^{x}

At point (1,0):

y = 2.713

Step-by-step explanation:

The equation of tangent line to the function can be calculated by taking the first derivative.

We have,

y = xe^{x}-e^{x}\\\frac{dy}{dx}=\frac{d}{dx}[ xe^{x} ]-\frac{d}{dx} [e^{x}]\\

Applying Product Rule:

d/dx [u.v] = (d/dx u) . (v) + (u) . (d/dx v)

Therefore,

\frac{dy}{dx}=\frac{d}{dx}(x) . e^{x}+x .\frac{d}{dx}(e^{x})- \frac{d}{dx}(e^{x})\\\\\frac{dy}{dx}=(1)(e^{x})+(x)(e^{x})-e^{x}\\ \frac{dy}{dx}=xe^{x}\\\\

The above equation is the equation of tangent line.

The point given is (1,0):

So,

\frac{dy}{dx} = (1)e^{1}\\ \frac{dy}{dx} = e\\\frac{dy}{dx} = 2.713

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Please help!! ASAP!!!!
Softa [21]
Tan(theta)= pi

Now, in order for you to find the angle (theta), you would inverse tan both the left and the right to find the value. The inverse of tan is tan^-1.

tan(theta)=pi ---> theta = tan^-1(pi)

Then, you would plug tan^-1(pi) into a calculator, giving you the value 

1.26
8 0
3 years ago
Use the number line below, where RS = 7y +3, ST = 5y +8, and RT = 83.
Llana [10]

Answer:

Step-by-step explanation:

Given the vectors based on the number line as RS = 7y +3, ST = 5y +8, and RT = 83, the equation RS+ST = RT will be used to get the unknown.

Substituting the given equation into the expression we will have;

7y +3+5y +8 = 83

collect like terms'

7y+5y+3+8 = 83

12y + 11 = 83

12y = 83-11

12y = 72

y = 72/12

y = 6

b) Substitute y = 6 into RS and ST

Given RS = 7y+3

RS = 7(6)+3

RS = 42+3

RS = 45

For ST;

ST = 5y+8

ST = 5(6)+8

ST = 30+8

ST = 38

6 0
3 years ago
Alex paid $17,520 for a new car.he will make equal payments each month for 4 years. What will be Alex’s monthly car payments?
timurjin [86]

Answer:

$365.00

Step-by-step explanation:

4 years times 12 months equals 48 months.

$17520.00 / 48=$365.00

6 0
3 years ago
There are 100 runners entered in a marathon. How many different groups of three runners can finish in first, second, and third?
DIA [1.3K]
Permutations and Every runner except for the one that was 1st could be 2nd hoep this helps
4 0
4 years ago
HELP TIMED QUIZ AND I DONT KNOW THE ANSWER!!
GuDViN [60]

Answer:

18 women

Step-by-step explanation:

What we know:

5/8 of the orchestra are male player, and 3/8 are female.

5/8 is a 1/4 more than 3/8.

If 12 is 1/4 of x, then x is 48.

Multiply 48 by 3/8 to get your answer.

48*3/8 = 144/8 = 18 women

3 0
3 years ago
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