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2 years ago

(log a)(log b) = log(a + b) Is it true or false?

Mathematics

1 answer:

Semmy [17]2 years ago

6 0

Answer:

False

Step-by-step explanation:

The correct rule should be:

log(A*B) = log(A) + log(B)

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Evaluate the integral. W (x2 y2) dx dy dz; W is the pyramid with top vertex at (0, 0, 1) and base vertices at (0, 0, 0), (1, 0,

In-s [12.5K]

Answer:

$\mathbf{\iiint_W (x^2+y^2) \ dx \ dy \ dz = \dfrac{2}{15}}$

Step-by-step explanation:

Given that:

$\iiint_W (x^2+y^2) \ dx \ dy \ dz$

where;

the top vertex = (0,0,1) and the base vertices at (0, 0, 0), (1, 0, 0), (0, 1, 0), and (1, 1, 0)

As such , the region of the bounds of the pyramid is: (0 ≤ x ≤ 1-z, 0 ≤ y ≤ 1-z, 0 ≤ z ≤ 1)

$\iiint_W (x^2+y^2) \ dx \ dy \ dz = \int ^1_0 \int ^{1-z}_0 \int ^{1-z}_0 (x^2+y^2) \ dx \ dy \ dz$

$\iiint_W (x^2+y^2) \ dx \ dy \ dz = \int ^1_0 \int ^{1-z}_0 ( \dfrac{(1-z)^3}{3}+ (1-z)y^2) dy \ dz$

$\iiint_W (x^2+y^2) \ dx \ dy \ dz = \int ^1_0 \ dz \ ( \dfrac{(1-z)^3}{3} \ y + \dfrac {(1-z)y^3)}{3}] ^{1-x}_{0}$

$\iiint_W (x^2+y^2) \ dx \ dy \ dz = \int ^1_0 \ dz \ ( \dfrac{(1-z)^4}{3}+ \dfrac{(1-z)^4}{3}) \ dz$

$\iiint_W (x^2+y^2) \ dx \ dy \ dz =\dfrac{2}{3} \int^1_0 (1-z)^4 \ dz$

$\iiint_W (x^2+y^2) \ dx \ dy \ dz =- \dfrac{2}{15}(1-z)^5|^1_0$

$\mathbf{\iiint_W (x^2+y^2) \ dx \ dy \ dz = \dfrac{2}{15}}$

7 0

2 years ago

A graph of a linear function is shown on the grid. Which of these best represents 0 of the function? A 8. B 10. C 16. D 24.

harina [27]

answer:

C. 16

explanation:

when x is 0, the y-intercept is 8

coordinates: (0,8) and (4,6)

slope:

$\sf \frac{y2-y1}{x2-x1}$

$\sf \frac{6-8}{4-0}$

$\sf \frac{-2}{4}$

$\sf -\frac{1}{2}$

equation:

$\sf y = mx +b$ [ where m is slope and b is y-intercept ]

$y = \sf -\frac{1}{2}x +8$

solve for x-intercept:

note: zeros of a function are the values of x when f(x) is equal to 0

$y = \sf -\frac{1}{2}x +8$

$0= \sf -\frac{1}{2}x +8$

$-8= \sf -\frac{1}{2}x$

$\sf x = -8 * -2$

$\sf x = 16$

3 0

2 years ago

Read 2 more answers

The measure of the angle's supplement is 60

Sever21 [200]

Answer:

80°

Step-by-step explanation:

Let the angle be x then four times it's complement plus 60, that is

4(90 - x) + 60 ← is it's supplement

Supplementary angles sum to 180°

Sum the angle and it's supplement and equate to 180

x + 4(90 - x) + 60 = 180 ← distribute and simplify left side

x + 360 - 4x + 60 = 180

- 3x + 420 = 180 ( subtract 420 from both sides )

- 3x = - 240 ( divide both sides by - 3 )

x = 80

The required angle = x = 80°

supplement = 4(90 - 80) + 60 = 4 × 10 + 60 = 40 + 60 = 100°

4 0

2 years ago

PLS HELP ME ASAP FOR 39 (SHOW WORK!) + LOTS OF POINTS!! *CORRECT ANSWER ONLY!*

Nady [450]

The straight line ON has the following equation :
(x - 18)/(x - 0) = (y - 12)/(y - 0)
Where (18,12) are coordinates of N and (0,0) are coordinates of O.
x - 18/x = y - 12/y
-18y = - 12x
y =12x/18 - - - - - (a)

The coordinates satisfy equation (a) are (7.5, 5)

Therefore D is the correct answer.

Good luck

7 0

3 years ago

Read 2 more answers

What is the correct definition for cot theta?

NemiM [27]

The correct definition for cot theta is (cos theta)/(sin theta). <span>Cotangent </span><span>(in a right-angled triangle) the ratio of the side (other than the hypotenuse) adjacent to a particular acute angle to the side opposite the angle. </span>I am hoping that this answer has satisfied your query and it will be able to help you in your endeavor, and if you would like, feel free to ask another question.

5 0

3 years ago

Read 2 more answers