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Mathematics

1 answer:

Aleonysh [2.5K]3 years ago

7 0

Answer:

C is answer

Step-by-step explanation:

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Ex 4.8 14) integrate 3^(2x-1)

sesenic [268]

Take the integral:

$\large\begin{array}{l} \mathsf{\displaystyle\int\!3^{2x-1}\,dx}\\\\ =\mathsf{\displaystyle\int\!\frac{1}{2}\cdot 2\cdot 3^{2x-1}\,dx}\\\\ =\mathsf{\displaystyle\frac{1}{2}\int\!3^{2x-1}\cdot 2\,dx\qquad(i)} \end{array}$

$\large\begin{array}{l} \textsf{Substitute}\\\\ \mathsf{2x-1=u\quad\Rightarrow\quad 2\,dx=du}\\\\\\ \textsf{so (i) becomes}\\\\ =\mathsf{\displaystyle\frac{1}{2}\int\!3^u\,du}\\\\ =\mathsf{\dfrac{1}{2}\cdot \dfrac{1}{\ell n\,3}\,3^u+C}\\\\ =\mathsf{\dfrac{1}{2\,\ell n\,3}\,3^{2x-1}+C} \end{array}$

$\large\begin{array}{l} \boxed{\begin{array}{c}\mathsf{\displaystyle\int\!3^{2x-1}\,dx=\frac{1}{2\,\ell n\,3}\,3^{2x-1}+C} \end{array}}\qquad\checkmark \end{array}$

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$\large\textsf{I hope it helps. :-)}$


Tags: integrate indefinite integral substitution exponential base logarithm log ln composite integral calculus

4 0

3 years ago

A quadratic function y=f(x) is plotted on a graph and the vertex of the resulting parabola is (−5,−3). What is the vertex of the

Licemer1 [7]

Answer:

(-5 , 6)

Step-by-step explanation:

f(x) = (x - (-5))² - 3 ... vertex (h , k) : (-5 , -3) y = (x-h)² + k

g(x) = -f(x) + 3 = -((x+5)² - 3) + 3 = -(x + 5)² + 6

vertex of g(x) is : (-5 , 6)

4 0

3 years ago

A.) 15.7in B.) 31.4in C.) 40in D.) 62.8in

IrinaK [193]

Answer:

31.4 in

Step-by-step explanation:

This is a tricky question,

if you observe the shape carefully, you will notice that if you mirror (flip outward) each curve surface of each quardrant, what you will end up with is a complete circle with a radius of 5 inches.

Hence the combined length of all the curved surfaces is simply the circumference of the circle, given by:

Circumference = 2πr

= 2 x 3.14 x 5

= 31.4 in

4 0

3 years ago

Read 2 more answers

How do you solve this ?

snow_tiger [21]

a and c are the anwsers to this it if you look at the back of the book it will give you anwsers

3 0

4 years ago