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3 years ago

Use Natural Logarithms to solve the equation

Mathematics

1 answer:

Rus_ich [418]3 years ago

7 0

Answer:

A) 0.106

Step-by-step explanation:

8e^3x + 4 = 15

Subtract 4 from each side

8e^3x + 4-4 = 15-4

8e^3x = 11

Divide each side by 8

8/8e^3x = 11/8

e^(3x) = 11/8

Take the natural log of each side

ln(e^(3x)) = ln(11/8)

3x = ln(11/8)

Divide by 3

3x/3 = 1/3 ln(11/8)

x = 1/3 ln(11/8)

x =.106151244

To the nearest thousandth

x = .106

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x+2y+2z=3. 2x-2y-z=3. x-2z=-5

d1i1m1o1n [39]

Answer:

x = 1, y = -2, z = 3.

Step-by-step explanation:

x + 2y + 2z = 3 A

2x -2y - z = 3 B

x - 2z = -5 C

If we add equations A and B we eliminate y:

3x + z = 6 E

Multiply E by 2 :

6x + 2z = 12 F

Adding C and F we get:

7x = 7

x = 1.

Plug this into equaton C:

1 - 2z = -5

-2z = -5 - 1 = -6

z = 3.

Now plugging x = 1 and z = 3 in equation A:

1 + 2y + 2(3) = 3

2y = 3 - 1 - 6 = -4

y = -2.

8 0

2 years ago

I don’t understand number 5

yarga [219]

Multiply what’s on the outside to the inside, the variable is always a lower case letter such as x,

4 0

3 years ago

Triangle X Y Z is shown. Angle Y X Z is a right angle. The length of Y X is 12 inches and the length of X Z is 10 inches. Angle

mario62 [17]

The best approximation for the measure of angle XYZ is 39.8° ⇒ 2nd answer

Step-by-step explanation:

Let us revise the trigonometry ratios in the right triangle ABC, where B is the right angle, AC is the hypotenuse, AB and BC are the legs of the triangle

The trigonometry ratios of the angle BAC, the opposite side to this angle is BC and the adjacent side to it is AB are

$sin(BAC)=\frac{opposite}{hypotenuse}=\frac{BC}{AC}$
$cos(BAC)=\frac{adjacent}{hypotenuse}=\frac{AB}{AC}$
$tan(BAC)=\frac{opposite}{adjacent}=\frac{BC}{AB}$

In Δ XYZ

∵ ∠ YXZ is a right angle

∴ The hypotenuse is YZ

∵ The adjacent side to ∠XYZ is XY

∵ The opposite side to ∠XYZ is XZ

∵ YX = 12 units

∵ XZ = 10 units

- Use tan ratio to find the measure of the angle because you

have the adjacent and opposite sides of the angle XYZ

∵ m∠XYZ is x

∵ $tan(x)=\frac{XZ}{XY}$

∴ $tan(x)=\frac{10}{12}$

- To find x use the inverse of tan(x)

∵ $x=tan^{-1}(\frac{10}{12})$

∴ x = 39.8°

∴ m∠XYZ = 39.81°

The best approximation for the measure of angle XYZ is 39.8°

Learn more:

You can learn more about the trigonometry ratios in brainly.com/question/4924817

#LearnwithBrainly

4 0

3 years ago

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Answer quick for brainliest

erma4kov [3.2K]

Answer:

equation: y - 730 = 95*(x - 4)

or y = 95x + 350

Step-by-step explanation:

190/2 = slope

point (4, 730)

y - 730 = 95*(x - 4)

5 0

3 years ago

over six games, a hockey team scored 18 goals. On average, how many goals did the team score each game

Ede4ka [16]

Answer:

Step-by-step explanation:

Average = total sum of all numbers/number of items in set

Average = 18/6

Average = 3

4 0

3 years ago

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