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Darina [25.2K]
3 years ago
13

Solve the exponential equation use a calculator to obtain a decimal approximation correct to two decimal place for the solution.

Mathematics
1 answer:
svetlana [45]3 years ago
3 0
6^(8x) = 4
log 6^(8x) = log 4
8x log 6 = log 4
x = log 4 / 8log 6 = 0.10 to two decimal places.
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Which equation does this image represent?
nirvana33 [79]

Given:

Image of the ellipse

To find:

The equation of the image

Solution:

The given image is a ellipse.

Center of the ellipse = (0, 0)

x-axis points are (-3, 0) and (3, 0).

y-axis points are (2, 0) and (-2, 0).

Standard form of equation of ellipse:

$\frac{(x-h)^{2}}{a^{2}}+\frac{(y-k)^{2}}{b^{2}}=1

where (h, k) is the center = (0,0)

a is the point on x-axis where y = 0. Hence a = 3.

b is the point on y-axis where x = 0. Hence b = 2.

Substitute this in the standard form of ellipse.

$\frac{(x-0)^{2}}{3^{2}}+\frac{(y-0)^{2}}{2^{2}}=1

$\frac{x^{2}}{9}+\frac{y^{2}}{4}=1

To make the denominator same multiply 1st term by \frac{4}{4} and 2nd term by \frac{9}{9}.

$\frac{4x^{2}}{4\times9}+\frac{9y^{2}}{9\times4}=1

$\frac{4x^{2}}{36}+\frac{9y^{2}}{36}=1

$\frac{4x^{2}+9y^{2}}{36}=1

Multiply by 36 on both sides

$\frac{4x^{2}+9y^{2}}{36}\times 36=1\times 36

${4x^{2}+9y^{2}}={36}

The equation of the image is ${4x^{2}+9y^{2}}={36}.

8 0
4 years ago
Trigonometry
schepotkina [342]

The area of the triangle ABC is 207.5 square units.

Explanation:

The measurements of the sides of the triangle are AB=19, AC=24 and m\angle A=65^{\circ}

We need to determine the area of the triangle ABC.

<u>Area of the triangle:</u>

The area of the triangle can be determined using the formula,

{Area}=\frac{1}{2} b c \sin A

where b=19, c=24 and m\angle A=65^{\circ}

Substituting these values in the above formula, we get,

{Area}=\frac{1}{2}(19)(24)  \sin 65^{\circ}

Simplifying the values, we get,

{Area}=\frac{1}{2}(456) (0.91)

{Area}=\frac{1}{2}(414.96)

{Area}=207.48

Rounding off to the nearest tenth, we get,

{Area}=207.5

Thus, the area of the triangle ABC is 207.5 square units.

5 0
3 years ago
Read 2 more answers
The diameter of a circle is 16 cm. Find its area in terms of Pi
babymother [125]

Answer:

A= 201.06

Step-by-step explanation:

A=πr^2

d=2r

Input the information into those formulas. Im honestly not sure if thats the right answer but its better than nothing.

6 0
3 years ago
Forty percent of students in a class of 35 students are the girls. How many girls are in the class?
ad-work [718]
40% of 35 would be 14. Therefore 14 girls are in the class. Hope that helps! 
5 0
4 years ago
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A 100-inch board is cut into two pieces one peice is three times the length of the other find the length of the shorter peice
Masteriza [31]

Answer:

5 ?

Step-by-step explanation:

8 0
3 years ago
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