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ddd [48]
3 years ago
11

Find the derivative with respect to x of the integral from 2 to x^3 of ln(x^2)dx

Mathematics
1 answer:
strojnjashka [21]3 years ago
5 0

The derivative follows from the fundamental theorem of calculus:

\displaystyle\frac{\mathrm d}{\mathrm dx}\int_c^{g(x)}f(t)\,\mathrm dt=f(g(x))\dfrac{\mathrm dg}{\mathrm dx}

where c is any constant in the domain of f.

We have

g(x)=x^3\implies\dfrac{\mathrm dg}{\mathrm dx}=3x^2

so

\displaystyle\frac{\mathrm d}{\mathrm dx}\int_2^{x^3}\ln(t^2)\,\mathrm dt=3x^2\ln((x^3)^2)=18x^2\ln x

(applying the property \ln a^b=b\ln a)

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Find the diameter of the circle with the given circumference.use 3.14 for pi<br><br> C=23 cm
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Answer:

7.324840764

Step-by-step explanation:

23/3.14=7.324840764

7 0
2 years ago
Which statement below about roots is false.Immersive Reader (5 Points) Simplified radicals have a positive and a negative root.
scoray [572]

Answer:

Statement (B)

Step-by-step explanation:

Which statement below about roots is false?

Let's arrange the statements by assigning option-letters a, b, c, d to them.

(A) Simplified radicals have a positive and a negative root.

This is true, as the root of any number is either a positive or a negative; especially if the rooting index is an even number like 2 or 4. For example, the square root (when the index is 2) of 9 is either +3 or -3. To check, find their squares. +3 x +3 = 9 and -3 x -3 = 9.

(B) A radicand is the symbol used when working with roots.

This statement is false, as the name for the symbol used in root operations is "radical symbol". A radicand is the number or expression whose roots are about to be found. It is the expression that lies under or inside the radical symbol!

(C) Exponents and Roots are inverses.

Exponents are the powers to which mathematical expressions are raised. Roots are the indexes by which mathematical expressions are divided. Exponents are hence the opposites or inverses of roots.

(D) Roots can be squared, cubed, quadrupled, or raised to higher powers.

Yes! The root of a mathematical expression or figure can be raised to any number or power, be it 2 (square), 3 (cube), 4 (quadruple), 5 (quintuple) or 100 (cent).

4 0
3 years ago
Please help!!!! D:<br><br>(grades 7-8 probability)​
dmitriy555 [2]

Answer:

1/4 ch a chance of a car any color

Step-by-step explanation:

if you only have 4 cars and they are different colors, you get 1/4 chance to pick one

6 0
3 years ago
A carpenter lays 16 square feet of tile in 2/3 of an hour. How many square feet of tile does the carpenter lay per hour?
r-ruslan [8.4K]
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3 0
3 years ago
One of the roots of the quadratic equation 4mnx^2 – 6m^2x – 6n^2x + 9mn = 0 (m, n ≠ 0) is a)-3m/2n b)3m/2n c)2m/3n d)-2m/3n
maxonik [38]

Answer:

B.\ \frac{3m}{2n}

Step-by-step explanation:

Given

4mnx^2 - 6m^2x - 6n^2x + 9mn = 0\ (m, n \neq  0)

Required

Calculate one of the root of the equation

4mnx^2 - 6m^2x - 6n^2x + 9mn = 0

Factorize

2mx(2nx - 3m) -3n(2nx - 3m) = 0

(2mx - 3n)(2nx - 3m) = 0

Split equation

2mx - 3n = 0\ or\ 2nx - 3m = 0

Make x the subject of formula in both expressions

2mx = 3n\ or\ 2nx = 3m

x = \frac{3n}{2m}\ or\ x = \frac{3m}{2n}

<em>From the list of given options, one of the roots of the equation is</em> \frac{3m}{2n}

4 0
3 years ago
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