I need help please.

laila [671]

Take log of both sides
$\ln y = \ln(2^{\sin \pi x})$
Use log property to get "x" out of the exponent
$\ln y = (\ln 2) (\sin \pi x)$
Differentiate
$\frac{dy}{y} = (\pi \ln 2)(cos \pi x) dx$
Move y to Right side (Note y = original expression)
$\frac{dy}{dx} = (\pi \ln 2) (\cos \pi x) 2^{\sin \pi x}$

In general, whenever you have a function in the form
$y = a^{f(x)}$
The derivative will be
$\frac{dy}{dx} = (\ln a) (f'(x))a^{f(x)}$

3 0

3 years ago

It took a 3D priner 10528 minutes to print 87 percent of a 3D print job. At this rate of speed how much time will take for the p

11Alexandr11 [23.1K]

The time it would take for the print to reach 100 percent completion is 12,101 minutes 9 seconds.

<h3>What is time it would take to reach 100%?</h3>

The mathematical operations that would be used to determine the required value are division and multiplication. Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷. Multiplication is the process of determining the product of two or more numbers. The sign used to denote multiplication is ÷.

Other mathematical operations that are used to solve problems include addition and subtraction.

Time it would take to reach 100% completion = (minutes it takes to print 87% of the words x 100%) / 87%

Time it would take to reach 100% completion = (10,528 x 1) / 0.87 =

10.528 / 0.87

= 12,101. 15

= 12,101+ (0.15 x 60)

= 12,101 minutes 9 seconds

To learn more about division, please check: brainly.com/question/13281206

#SPJ1

7 0

1 year ago

Find all zeros of f(x)=x^4-3x^3+6x^2+2x-60 given that 1+3i is a zero of f(x)

Triss [41]

Answer:

The roots of f(x) are: -2, 3, (1+3i) and (1-3i)

Step-by-step explanation:

We are given an expression:

$f(x)=x^4-3x^3+6x^2+2x-60$

(1+3i) is a root of f(x)

We have to find the remaining roots of f(x).

Since, (1+3i) is a root of f(x),

$x-(1+3i)$

is a factor of given expression.

Now, we check if (1 - 3i) is a root of given function.

$f(x)=x^4-3x^3+6x^2+2x-60\\f(1-3i)=(1-3i)^4-3(1-3i)^3+6(1-3i)^2+2(1-3i)-60\\= (28+96i)-3(-26+18i)+6(-8-6i)+2(1-3i)-60 = 0$

Thus, (1-3i) is also a root of given function.

Since, (1-3i) is a root of f(x),

$x-(1-3i)$

is a factor of given expression.

Thus, we can write:

$(x-(1+3i))(x-(1-3i))\text{ is a factor of f(x)}\\x^2-x(1-3i)+x(1+3i)+(1-3i)(1+3i)\text{ is a factor of f(x)}\\x^2-2x+10\text{ is a factor of f(x)}$

Dividing f(x) by above expression:

$\displaystyle\frac{x^4-3x^3+6x^2+2x-60}{x^2-2x+10} = x^2-x-6$

To find the root, we equate it to zero:

$x^2-x-6 = 0\\x^2 - 3x+2x-6=0\\x(x-3)+2(x-3)=0\\(x+2)(x-3) = 0\\x = -2, x = 3$

Thus, the roots of f(x) are: -2, 3, (1+3i) and (1-3i)

4 0

4 years ago

Write an expression to represent the perimeter of a rectangle with one side is x=4 and

Ksju [112]

Answer:

que njsnskdkd

Step-by-step explanation:

qylikqunwjsmsnsj

5 0

3 years ago

Simplify radical using the exponent rule. Show work

katen-ka-za [31]

Answer:

$\frac{1}{x^{4} }$

Step-by-step explanation:

( $\sqrt[3]{x^{2} }$ × $\sqrt[6]{x^{4}}$ )⁻³

$\sqrt[3]{x^{2} }$ is the same thing as $x^{\frac{2}{3} }$

you can think of the numerator as the power and the denominator as the root

rewrite both terms:

( $x^{\frac{2}{3} }$ × $x^{\frac{4}{6} }$ )⁻³

simplify the 4/6:

( $x^{\frac{2}{3} }$ × $x^{\frac{2}{3} }$ )⁻³

bases are the same, add the exponents:

( $x^{\frac{4}{3} }$ )⁻³

multiply the exponents:

$x^{\frac{-12}{3} }$

simplify:

x⁻⁴

negative power rule:

$\frac{1}{x^{4} }$

8 0

3 years ago