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3 years ago

E^x=0.5 what is the answer to question

Mathematics

1 answer:

Anastasy [175]3 years ago

7 0

Answer:

x = ln(0.5)

Step-by-step explanation:

$e^x = 0.5$

Take the ln of both sides

$ln(e^x) = ln (0.5)$

Apply the log rule

$xln(e) = ln(0.5)\\$

Know that $ln(e) = 1$

hence,

$x = ln(0.5)$

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50 points

JulsSmile [24]

Answer:

b. w= 8x^2-2y / y

Step-by-step explanation:

Given:

(2*x^2)/y = (w+2)/4

Isolating w, we get:

w = (8*x^2)/y - 2

Multiplying and dividing the second term in the right-side of the equality by y, we get:

w = (8*x^2)/y - 2*y/y

Subtracting the fractions:

w = (8*x^2 - 2y)/y

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3 years ago

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Monica earned a total of $82.50 for helping at the carwash for 15 hours. If she works for 10 hours the next week, how much will

Yuki888 [10]

Answer:

$137.50

Step-by-step explanation:

82.50 divided by 15 gives you $5.50

Then you would multiply that by 10 and you would get $55.00

Last all you have to do is add $82.50 and $55.00 and you get $137.50

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2 years ago

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The base of a solid is the region in the first quadrant bounded by the line x=-2y+6 and the coordinate axes. What is the volume

nika2105 [10]

Answer:

$V = \frac{4y^3}{3} -12y^2 +36 y \Big|_0^3$

$V= \frac{4(3)^3}{3} -12(3)^2 +36 (3) -0 = 36-108+108= 36$

Step-by-step explanation:

For this case we have the following plot on the figure attached.

We know on this case that $x = -2y+6$ represent our radius for the square, since we need cross sections perpendicular to the y axis.

We find the intersection points like this:

$x= 0 , y=3$

$y=0, x=6$

Since we are assuming squares for the cross sections the area is given by $A = r^2$ where r = x= -2y+6.

Since our radius is on terms of x we can create a integral with limits on x in order to find the volume, And we can use the following integral in order to find the volume.

$V = \int_{0}^3 (-2y+6)^2 = \int_{0}^3 4y^2 -24y +36 dy$

On the left part we are using the following property from algebra:

$(a+b)^2 = a^2 +2ab +b^2$

$(-2y+6)^2 = (-2y)^2 +2*(-2y)(6) +(6)^2 = 4y^2 -24y+36$

And after do the integral we got this:

$V = \frac{4y^3}{3} -12y^2 +36 y \Big|_0^3$

$V= \frac{4(3)^3}{3} -12(3)^2 +36 (3) -0 = 36-108+108= 36$

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3 years ago

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Svetradugi [14.3K]

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4 years ago

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saveliy_v [14]

$3n+10=43 \\\\ 3n=43-10 \\\\ 3n=33 \\\\ \boxed{n=\frac{33}{3}=11}$

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4 years ago

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