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satela [25.4K]
3 years ago
15

URGENT!!! Picture included

Mathematics
1 answer:
ch4aika [34]3 years ago
4 0
The correct answer is the fourth one, 3x^3 :)
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Find the exponential equation for the given information. Pls help
nikitadnepr [17]

Answer:

y = 12 (2.9)^{x}

Step-by-step explanation:

The standard form of the exponential function is

y = a (b)^{x}

Find a and b by substituting ordered pairs from the table into the equation

Using (0, 12 ), then

12 = ab^{0} ( b^{0} = 1 ), so

a = 12, then

y = 12 b^{x}

Using (1, 34.8 ) , then

34.8 = 12 b^{1} ( divide both sides by 12 )

b = 2.9

Thus exponential function is

y = 12 (2.9)^{x}

3 0
3 years ago
If 2tanA=3tanB then prove that,<br>tan(A+B)= 5sin2B/5cos2B-1​
Fed [463]

By definition of tangent,

tan(A + B) = sin(A + B) / cos(A + B)

Using the angle sum identities for sine and cosine,

sin(x + y) = sin(x) cos(y) + cos(x) sin(y)

cos(x + y) = cos(x) cos(y) - sin(x) sin(y)

yields

tan(A + B) = (sin(A) cos(B) + cos(A) sin(B)) / (cos(A) cos(B) - sin(A) sin(B))

Multiplying the right side by 1/(cos(A) cos(B)) uniformly gives

tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A) tan(B))

Since 2 tan(A) = 3 tan(B), it follows that

tan(A + B) = (3/2 tan(B) + tan(B)) / (1 - 3/2 tan²(B))

… = 5 tan(B) / (2 - 3 tan²(B))

Putting everything back in terms of sin and cos gives

tan(A + B) = (5 sin(B)/cos(B)) / (2 - 3 sin²(B)/cos²(B))

Multiplying uniformly by cos²(B) gives

tan(A + B) = 5 sin(B) cos(B) / (2 cos²(B) - 3 sin²(B))

Recall the double angle identities for sin and cos:

sin(2x) = 2 sin(x) cos(x)

cos(2x) = cos²(x) - sin²(x)

and multiplying uniformly by 2, we find that

tan(A + B) = 10 sin(B) cos(B) / (4 cos²(B) - 6 sin²(B))

… = 10 sin(B) cos(B) / (4 (cos²(B) - sin²(B)) - 2 sin²(B))

… = 5 sin(2B) / (4 cos(2B) - 2 sin²(B))

The Pythagorean identity,

cos²(x) + sin²(x) = 1

lets us rewrite the double angle identity for cos as

cos(2x) = 1 - 2 sin²(x)

so it follows that

tan(A + B) = 5 sin(2B) / (4 cos(2B) + 1 - 2 sin²(B) - 1)

… = 5 sin(2B) / (4 cos(2B) + cos(2B) - 1)

… = 5 sin(2B) / (4 cos(2B) - 1)

as required.

5 0
2 years ago
Which of the following expressions is equivalent to the expression a^2/3
vladimir1956 [14]

∛a² → C

From the ' law of exponents '

a^{\frac{m}{n} } = \sqrt[n]{a^{m} }


3 0
3 years ago
What is the area of this composite figure?
Gelneren [198K]

Answer:

249 centimeters squared

Step-by-step Explanation:

The area of the rectangle: l x w, where l is the length and w is the width.

= 15.5 x 18

= 279

Area of the smaller rectangle: l x w, where l is the length and w is the width.

= 4 x 7.5

= 30

We do not need this 30.

Area of the shaded region:

= 279 - 30

= 249 cm²

5 0
2 years ago
Find the circumference in inches
Alborosie

Answer:

Step-by-step explanation:

2×radius with pi, 28*pi=28 pi or 87.92

3 0
2 years ago
Read 2 more answers
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