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enyata [817]
3 years ago
5

Find the slope of the tangent line to the curve f(x)=e^(x) at (0.4,1.49)

Mathematics
1 answer:
almond37 [142]3 years ago
8 0

Answer:

1.49

Step-by-step explanation:

In order to find the slope of the tangent line to a given equation, and in a given point, we need to:

1. Find the first derivative of the given function.

2. Evaluate the first derivative function in the given point.

1. Let's find the first derivative of the given function:

The original function is f(x)=e^{x}

But remeber that the derivative of  e^{x} is  e^{x}

so, f'(x)=e^{x}

2. Let's evaluate the first derivative function in the given point

The given point is (0.4,1.49) so:

f'(x)=e^{x}

f'(0.4)=e^{0.4}

f'(x)=1.49

Notice that the calculated slope of the tangent line is equal to the y-coordinate of the given point because f'(x)=f(x). In conclusion, the slope of the tangent line is equal to 1.49.

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A farmer sells 8.3 kg of apples and pears at the farmers market this way is apples and Restless Paris how many kilograms of Pari
Serga [27]

Answer:

She sell <u>2.075 kilograms</u> of pears at the farmer's market.

Step-by-step explanation:

<u><em>There is a mistake in the question some data is missing, so the correct question is below: </em></u>

<em>A farmer sells 8.3 kg of apples and pears at the farmer's market. 3 /4 of this weight is apples, and the rest is pears. How many kilograms of pears did she sell at the farmer's market?</em>

Now, to find the kilograms of pears.

Total weight of apples and pears = 8.3 kg.

Weight of apples = \frac{3}{4} of 8.3 kg.

So, to get the weight of apples:

  \frac{3}{4} \times 8.3

=0.75\times 8.3

=6.225\ kg.

Thus, the weight of apples = 6.225 kg.

Now, to get the weight of pears we subtract the weight of apples from the total weight of apples and pears:

8.3-6.225\\\\=2.075\ kg.

Therefore, she sell 2.075 kilograms of pears at the farmer's market.

5 0
3 years ago
6. Calculate the value of tan (48°19'23").
lisov135 [29]

Answer:

C. 1.12

Step-by-step explanation:

There are 60' (minutes) in a degree and 60" in a minute meaning that we have (60×60) seconds in a degree.

Therefore to convert seconds to degrees we divide by 3600. and minutes to degrees we divide by 60.

The angle 48°19'23'' can be converted into a decimal as follows

48°+(19/60+23/3600)°

=48.323°

Tan 48.323= 1.12

4 0
3 years ago
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