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marta [7]
3 years ago
13

Evaluate the indefinite integral. (Use C for the constant of integration.) ex 5 ex dx.

Mathematics
1 answer:
melisa1 [442]3 years ago
8 0

Answer:

  5 e^{x} +C

where C is constant of integration

Step-by-step explanation:

<u><em>Explanation:-</em></u>

<em>Given f(x) = 5 eˣ</em>

Now integrating with respective to 'x' , we get

                                                      I =  \int\limits {5 e^{x} } \, d x

<em> By using integration formula</em>

                                       \int\limits { e^{x} } \, d x = e^{x} +C

                                     I =  \int\limits {5 e^{x} } \, d x  = 5 e^{x} +C

<em>where C is constant of integration</em>

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Need help with some practice questions since all are different types I'm asking alot sorry!​
sasho [114]

Answer:

Yes

Step-by-step explanation:

If they're perpendicular, that means that angle ECM = 90 degrees and angle ACE = 90 degrees. To figure out if this works, plug that into the two equations they give:

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90 = 3x + 15

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90 = 4x - 10

100 = 4x

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The corners of a meadow are shown on a coordinate grid. Ethan wants to fence the meadow. What length of fencing is required?
Nuetrik [128]

Answer:

34.6 units

Step-by-step explanation:

The lenght of fencing required is the total distance between point A to B, B to C, C to D, and D to A. That is the distance between all 4 corners of the meadow.

The coordinates of the corners of the meadow is shown on a coordinate plane in the attachment. (See attachment below).

Let's use the distance formula to calculate the distance between the 4 corners of the meadow using their coordinates as follows:

Distance between point A(-6, 2) and point B(2, 6):

AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

Let,

A(-6, 2)) = (x_1, y_1)

B(2, 6) = (x_2, y_2)

AB = \sqrt{(2 - (-6))^2 + (6 - 2)^2}

AB = \sqrt{(8)^2 + (4)^2}

AB = \sqrt{64 + 16} = \sqrt{80}

AB = 8.9 (nearest tenth)

Distance between B(2, 6) and C(7, 1):

BC = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

Let,

B(2, 6) = (x_1, y_1)

C(7, 1) = (x_2, y_2)

BC = \sqrt{(7 - 2)^2 + (1 - 6)^2}

BC = \sqrt{(5)^2 + (-5)^2}

BC = \sqrt{25 + 25} = \sqrt{50}

BC = 7.1 (nearest tenth)

Distance between C(7, 1) and D(3, -5):

CD = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

Let,

C(7, 1) = (x_1, y_1)

D(3, -5) = (x_2, y_2)

CD = \sqrt{(3 - 7)^2 + (-5 - 1)^2}

CD = \sqrt{(-4)^2 + (-6)^2}

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Distance between D(3, -5) and A(-6, 2):

DA = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

Let,

D(3, -5) = (x_1, y_1)

A(-6, 2) = (x_2, y_2)

DA = \sqrt{(-6 - 3)^2 + (2 - (-5))^2}

DA = \sqrt{(-9)^2 + (7)^2}

DA = \sqrt{81 + 49} = \sqrt{130}

DA = 11.4 (nearest tenth)

Length of fencing required = 8.9 + 7.1 + 7.2 + 11.4 = 34.6 units

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Answer:

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