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3 years ago

6

Help with 48 thanks

1 answer:

Ne4ueva [31]3 years ago

6 0

Geez... I did this lesson today... I think it´d be A.

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Integrate the following. ∫<img src="https://tex.z-dn.net/?f=5x%5E%7B4%7D%20dx" id="TexFormula1" title="5x^{4} dx" alt="5x^{4} dx

Vadim26 [7]

Answer:

$\displaystyle D) {x}^{5} + \rm C$

Step-by-step explanation:

we would like to integrate the following Integral:

$\displaystyle \int 5 {x}^{4} \, dx$

well, to get the constant we can consider the following Integration rule:

$\displaystyle \int c{x} ^{n} \, dx = c\int {x}^{n} \, dx$

therefore,

$\displaystyle 5\int {x}^{4} \, dx$

recall exponent integration rule:

$\displaystyle \int {x} ^{n} \, dx = \frac{ {x}^{n + 1} }{n + 1}$

so let,

$n = 4$

Thus integrate:

$\displaystyle = 5\left( \frac{ {x}^{4+ 1} }{4 + 1} \right)$

simplify addition:

$\displaystyle = 5\left( \frac{ {x}^{5} }{5} \right)$

reduce fraction:

$\displaystyle = {x}^{5}$

finally we of course have to add the constant of integration:

$\displaystyle \boxed{ {x}^{5} + \rm C}$

hence,

our answer is D)

7 0

2 years ago

Read 2 more answers

Find the value of 4x2 + 2y where y= 0.5 and x= 3

Citrus2011 [14]

Answer:

37

Step-by-step explanation:

substitute the given values for x and y into the expression

4x² + 2y

= 4(3)² + 2( $\frac{1}{2}$ )

= 4(9) + 1

= 36 + 1

= 37

7 0

2 years ago

Pls help im really bad at math no links pls

lawyer [7]

Answer:

$-\frac{1}{2}$

Step-by-step explanation:

$-\frac{5}{6} +\frac{6}{18}$

$-\frac{5}{6} +\frac{2}{6}$ reduced

$\frac{-5+2}{6}$ transformed the expression to make it easier

$-\frac{3}{6}$ add

$-\frac{1}{2}$ reduce

8 0

2 years ago

The circumference of the equator of a sphere was measured to be 82 82 cm with a possible error of 0.5 0.5 cm. Use linear approxi

True [87]

Answer:

The maximum error in the calculated surface area is approximately 8.3083 square centimeters.

Step-by-step explanation:

The circumference ( $s$ ), in centimeters, and the surface area ( $A_{s}$ ), in square centimeters, of a sphere are represented by following formulas:

$A_{s} = 4\pi\cdot r^{2}$ (1)

$s = 2\pi\cdot r$ (2)

Where $r$ is the radius of the sphere, in centimeters.

By applying (2) in (1), we derive this expression:

$A_{s} = 4\pi\cdot \left(\frac{s}{2\pi} \right)^{2}$

$A_{s} = \frac{s^{2}}{\pi^{2}}$ (3)

By definition of Total Differential, which is equivalent to definition of Linear Approximation in this case, we determine an expression for the maximum error in the calculated surface area ( $\Delta A_{s}$ ), in square centimeters:

$\Delta A_{s} = \frac{\partial A_{s}}{\partial s} \cdot \Delta s$

$\Delta A_{s} = \frac{2\cdot s\cdot \Delta s}{\pi^{2}}$ (4)

Where:

$s$ - Measure circumference, in centimeters.

$\Delta s$ - Possible error in circumference, in centimeters.

If we know that $s = 82\,cm$ and $\Delta s = 0.5\,cm$ , then the maximum error is:

$\Delta A_{s} \approx 8.3083\,cm^{2}$

The maximum error in the calculated surface area is approximately 8.3083 square centimeters.

6 0

2 years ago

Graph the parabola y=-3x^2-18x+22

Luden [163]

<span> x y
</span><span><span>−5</span><span>−9
</span></span><span><span>−4 -0</span></span><span>
</span><span><span>−3 3</span></span><span><span>
-2 0
-1-9</span></span>

4 0

3 years ago