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3 years ago

ITS QUESTION 21 !!!! Please help !

Mathematics

2 answers:

s2008m [1.1K]3 years ago

7 0

He doesn't know where x is

____ [38]3 years ago

6 0

Answer:

Should the line be dotted since X is not less than or equal to -3. The start point is left unshaded which is correct since x is not less than or equal to -3.

Step-by-step explanation:

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Use the following steps to prove that log b(xy)- log bx+ log by.

borishaifa [10]

Answer with Step-by-step explanation:

a. $x=b^p$

$y=b^q$

Taking both sides log

$log x=plog b$

Using identity: $logx^y=ylogx$

$p=\frac{logx}{log b}=log_b x$

Using identity: $log_x y=\frac{log y}{log x}$

$log y=qlog b$

$q=\frac{log y}{log b}=log_b y$

b. $xy=b^pb^q$

We know that

$x^a\cdot x^b=x^{a+b}$

Using identity

$xy=b^{p+q}$

c. $log_b(xy)=log_b(b^{p+q})$

$log_b(xy)=(p+q)log_b b$

Substitute the values then we get

$log_b(xy)=(log_b x+log_b y)$

By using $log_b b=1$

Hence, $log_b(xy)=log_b x+log_b y$

3 0

3 years ago

The base of a solid in the region bounded by the two parabolas y2 = 8x and x2 = 8y. Cross sections of the solid perpendicular to

Usimov [2.4K]

The two curves intersect at two points, (0, 0) and (8, 8):

$x^2=8y\implies y=\dfrac{x^2}8$

$y^2=\dfrac{x^4}{64}=8x\implies\dfrac{x^4}{64}-8x=0\implies\dfrac{x(x-8)(x^2+8x+64)}{64}=0$

$\implies x=0,x=8\implies y=0,y=8$

The area of a semicircle with diameter $d$ is $\dfrac{\pi d^2}8$ . The diameter of each cross-section is determined by the vertical distance between the two curves for any given value of $x$ between 0 and 8. Over this interval, $y^2=8x\implies y=\sqrt{8x}$ and $\sqrt{8x}>\dfrac{x^2}8$ , so the volume of this solid is given by the integral