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3 years ago

Write an exponential function in the form y=ab^xy=ab x that goes through points (0,8) and (2,288)

Mathematics

1 answer:

timofeeve [1]3 years ago

4 0

Answer:

y = 8•6^x

Step-by-step explanation:

Here, we want to write an exponential equation

To fully write this, we need the values of a and b

From the first coordinates given;

8 = a•b^0

a = 8 since b^0 = 1

Furthermore;

288 = 8•b*2

b^2 = 36

b = √36

b = 6

So we have ;

y = 8•6^x

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Sin∅=√3-1/2 find approximate value of sec∅(sec∅+tan∅)/1+tan²∅

Neko [114]

Answer:

The approximate value of $f(\theta) = \frac{\sec \theta \cdot (\sec \theta+\tan \theta)}{1+\tan^{2}\theta}$ is 1.366.

Step-by-step explanation:

Let $f(\theta) = \frac{\sec \theta \cdot (\sec \theta+\tan \theta)}{1+\tan^{2}\theta}$ , we proceed to simplify the formula until a form based exclusively in sines and cosines is found. From Trigonometry, we shall use the following identities:

$\sec \theta = \frac{1}{\cos \theta}$ (1)

$\tan\theta = \frac{\sin\theta}{\cos \theta}$ (2)

$\cos^{2}+\sin^{2} = 1$ (3)

Then, we simplify the given formula:

$f(\theta) = \frac{\left(\frac{1}{\cos \theta} \right)\cdot \left(\frac{1}{\cos \theta}+\frac{\sin \theta}{\cos \theta}\right) }{1+\frac{\sin^{2}\theta}{\cos^{2}\theta} }$

$f(\theta) = \frac{\left(\frac{1}{\cos^{2} \theta} \right)\cdot (1+\sin \theta)}{\frac{\sin^{2}\theta + \cos^2{\theta}}{\cos^{2}\theta} }$

$f(\theta) = \frac{\left(\frac{1}{\cos^{2}\theta}\right)\cdot (1+\sin \theta)}{\frac{1}{\cos^{2}\theta} }$

$f(\theta) = 1+\sin \theta$

If we know that $\sin \theta =\frac{\sqrt{3}-1}{2}$ , then the approximate value of the given function is:

$f(\theta) = 1 +\frac{\sqrt{3}-1}{2}$

$f(\theta) = \frac{\sqrt{3}+1}{2}$

$f(\theta) \approx 1.366$

5 0

3 years ago

What does y= 4x+rx+6 equal? (Solve for x) show all steps please!!

polet [3.4K]

Move all terms to the left side and set equal to zero. then set each factor equal to zero .

x = - 6 - y
______
4 + r

7 0

3 years ago

The system of equations y = negative one-fifth x minus 6 and y = –2x + 3 is shown on the graph below.

Dmitriy789 [7]

Answer: (5, -7)

Step-by-step explanation:

On a graph, the solution(s) of two equations is/are the points at which they intersect.

For the graph shown, there is only one intersection point, (5, -7). This set of coordinates satisfies both equations, so it is a solution to the system.

4 0

3 years ago

Can I get an example of systems of equations that represent the solution of this situation below? Thank you! ^ ^

Alenkinab [10]

Answer:

1x+ 1y =11

10x + 5y = 80

x = the cost of a taco = $5

y = the cost of a burrito = $6

Step-by-step explanation:

x = the cost of a taco

y = the cost of a burrito

1x+ 1y =11

10x + 5y = 80

rearange 1st equation as y = 11 -x and plug in into the 2nd one for y:

10x + 5( 11-x) = 80 distribute left side

10x + 55 - 5x = 80 combine like terms

10x - 5x = 5x

5x + 55 = 80 subtract 55 from both sides

5x = 80 - 55

5x = 25 divide by 5

x = 5

plug in for y in 1st equation y = 11--x =11-5 = 6

7 0

4 years ago

Solve the exponential equation<br> help, it's for homework

swat32

Answer: x = 3

Step-by-step explanation:

When the base is the same, the exponents are the same:

3-2x = -x

solve fore x

add 2x to both sides

3-2x = -x

+2x +2x

x = 3

6 0

3 years ago