Th= 7 units X = 7 units Y = 4 units, and Z = 20 units, what is the volume of the triangular prism shown above?

Can someone explain to me this derivative : y=3x√x

dimaraw [331]

Answer:

(9/2)√x.

Step-by-step explanation:

Convert the radical to an exponent.

x√x = x^1 * x^1/2

= x^(1 + 1/2)

= x^3/2

So the derivative of 3x^3/2 is found as follows:

y' = 3 * 3/2x^(3/2 - 1)

= (9/2)x^1/2

= (9/2)√x.

6 0

3 years ago

(2,-1) y-intercept -3 slope 1/2 Write an equation with the given info above.

jek_recluse [69]

y-intercept -3

slope 1/2

is sufficient info with which to write an equation for a straight line:

y = mx + b becomes y = (1/2)x - 3.

You should check this by determining whether or not (2,-1) satisfies this equation.

4 0

3 years ago

The range of typical total prices for an American tourist traveling on the European continent is $20.70 to $25.00. What is the a

Nuetrik [128]

For this case what we should do is find an average value of the total prices for a trip to europe
We look for the average of the prices by means of the following expression:
P = (20.70 + 25) / (2)
P = 22.8 $
Answer:
the average price is $ 22.8

8 0

3 years ago

Read 2 more answers

To train for a bike race, Sandi rode her bike a total of 16 miles each day. Brian was training for the same race, but only rode

MaRussiya [10]

So the first thing you're gonna wanna know is how many miles Brian is riding per day so
16/2= 8

Then you'll want to do the following steps

16 × 5 = 80

8 × 5 = 40

80-40 = 40

Sandi rode 40 more miles then Brian in five days

Hope this helped!

3 0

3 years ago

Substitution to evaluate the indefinite integral

gregori [183]

Answer:

$\displaystyle \int {e^{5x}} \, dx = \boxed{ \frac{e^{5x}}{5} + C }$

General Formulas and Concepts:
Calculus

Differentiation

Derivatives
Derivative Notation

Derivative Property [Multiplied Constant]:
$\displaystyle (cu)' = cu'$
Derivative Rule [Basic Power Rule]:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Integration

Integrals

Integration Rule [Reverse Power Rule]:
$\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C$

Integration Property [Multiplied Constant]:
$\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

Integration Methods: U-Substitution

Step-by-step explanation:

Step 1: Define

Identify given.

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

Step 2: Integrate Pt. 1

Identify variables for u-substitution.

Set u:
$\displaystyle u = 5x$
[u] Differentiate [Derivative Rules and Properties]:
$\displaystyle du = 5 \ dx$

Step 3: Integrate Pt. 2

[Integral] Rewrite [Integration Property - Multiplied Constant]:
$\displaystyle \begin{aligned}\int {e^{5x}} \, dx & = \frac{1}{5} \int {5e^{5x}} \, dx \\\end{aligned}$
[Integral] Apply Integration Method [U-Substitution]:
$\displaystyle \begin{aligned}\int {e^{5x}} \, dx & = \frac{1}{5} \int {5e^{5x}} \, dx \\& = \frac{1}{5} \int {e^u} \, du \\\end{aligned}$
[Integral] Apply Exponential Integration:
$\displaystyle \begin{aligned}\int {e^{5x}} \, dx & = \frac{1}{5} \int {5e^{5x}} \, dx \\& = \frac{1}{5} \int {e^u} \, du \\& = \frac{e^u}{5} + C \\\end{aligned}$
[u] Back-substitute:
$\displaystyle \begin{aligned}\int {e^{5x}} \, dx & = \frac{1}{5} \int {5e^{5x}} \, dx \\& = \frac{1}{5} \int {e^u} \, du \\& = \frac{e^u}{5} + C \\& = \boxed{ \frac{e^{5x}}{5} + C } \\\end{aligned}$

∴ we have used substitution to evaluate the indefinite integral.

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Learn more about integration: brainly.com/question/27746495

Learn more about Calculus: brainly.com/question/27593180

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Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

3 0

2 years ago