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3 years ago

I have an interesting intergral that seems pretty challenging. After attempting to solve it for some time, I've come up empty ha

nded. Can you solve this integral?
Indefinite Integral of:
${x}^{4} { {e}^{x} }^{3}$

Mathematics

1 answer:

serious [3.7K]3 years ago

3 0

${x}^{4} { {e}^{x} }^{3} = 0 \\ \Leftrightarrow {x}^{4} = 0 \: \vee \: { {e}^{x} }^{3} = 0 \\ \Leftrightarrow x = 0\: \vee \:x \in \emptyset \\ \Leftrightarrow x = 0$

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The volume of a rectangular prism is 270 cubic centimeters the height of the prism is 5 centimeters. What could the length and w

kotegsom [21]

Answer:

The answer to your question is below

Step-by-step explanation:

Data

Volume = 270 cm³

height = 5 cm

length = ?

width = ?

Formula

Volume of a rectangular prism = height x length x width

- Solve for Area of the base (height x length)

Area of the base = Volume / height

-Substitution

Area of the base = 270 / 5

-Result

Area of the base = 54 m²

2.- Find the prime factors of 54

54 2

27 3

9 3

3 3

3.- The possible values of the sidas of the rectangle are:

Combining the prime factor of 54.

Length Width

2 x 3 = 6 and 3 x 3 = 9

or 2 x 3 x 3 = 18 and 3 x 1 = 3

or 3 x 3 x 3 = 27 and 2 x 1 = 2

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3 years ago

An airplane is flying from New York City to Los Angeles. The distance it travels in miles, d, is related to the time in seconds,

yuradex [85]

Answer:

Step-by-step explanation:

Given the expression that relates the distance and the time with the expression:

d = 0.15t

d is the distance

t is the time

To determine how fast it is flying (Speed), we will need to use the formula

Speed = distance/time

s = d/t

From the given equation we can se that 0.15 = d/t

Comparing this to the general equation, we will see that s = 0.15

<em>Hence the airplane is flying at 0.15</em>

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2 years ago

Consider h(x)=x^2+8+15. identify its vertex and y-intercept.

OleMash [197]

Answer:

Vertex: (-4, -1)

Y-intercept: (0, 15)

Step-by-step explanation:

Given the quaratic function, h(x) = x² + 8x + 15:

In order to determine the vertex of the given function, we can use the formula, $[x = \frac{-b}{2a}, h(\frac{-b}{2a})]$ .

<h3>Use the equation: $[x = \frac{-b}{2a}, h(\frac{-b}{2a})]$ </h3>

In the quadratic function, h(x) = x² + 8x + 15, where:

a = 1, b = 8, and c = 15:

Substitute the given values for <em>a</em> and <em>b</em> into the equation to solve for the x-coordinate of the vertex.

$x = \frac{-b}{2a}$

$x = \frac{-8}{2(1)}$

x = -4

Subsitute the value of the x-coordinate into the given function to solve for the <u>y-coordinate of the vertex</u>:

h(x) = x² + 8x + 15

h(-4) = (-4)² + 8(-4) + 15

h(-4) = 16 - 32 + 15

h(-4) = -1

Therefore, the vertex of the given function is (-4, -1).

<h3>Solve for the Y-intercept:</h3>

The <u>y-intercept</u> is the point on the graph where it crosse the y-axis. In order to find the y-intercept of the function, set x = 0, and solve for the y-intercept:

h(x) = x² + 8x + 15

h(0) = (0)² + 8(0) + 15

h(0) = 0 + 0 + 15

h(0) = 15

Therefore, the y-intercept of the quadratic function is (0, 15).

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2 years ago

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LuckyWell [14K]

Answer:

x=-1

Step-by-step explanation:

just like 8/8 is 1 the same concept only you add a negative

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Flauer [41]

4,398,200 is your answer

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