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4 years ago

Write a possible exponential function in y=ab^x form for the graph described below.

Mathematics

1 answer:

Nuetrik [128]4 years ago

5 0

Answer:

see explanation

Step-by-step explanation:

Substitute the given points into the equation and solve for a and b

Using (0, 2 ), then

2 = a. $b^{0}$ → $b^{0}$ = 1, thus

a = 2

The equation is

y = 2 $b^{x}$

Using (3, 0.25 ), then

0.25 = 2. b³ ( divide both sides by 2)

b³ = 0.125 ( take the cube root of both sides )

b = 0.5

Hence a possible exponential function is

y = 2 $(0.5)^{x}$

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How to solve this trigonometric equation cos3x + sin5x = 0

mrs_skeptik [129]

Answer:

x = {nπ -π/4, (4nπ -π)/16}

Step-by-step explanation:

It can be helpful to make use of the identities for angle sums and differences to rewrite the sum:

cos(3x) +sin(5x) = cos(4x -x) +sin(4x +x)

= cos(4x)cos(x) +sin(4x)sin(x) +sin(4x)cos(x) +cos(4x)sin(x)

= sin(x)(sin(4x) +cos(4x)) +cos(x)(sin(4x) +cos(4x))

= (sin(x) +cos(x))·(sin(4x) +cos(4x))

Each of the sums in this product is of the same form, so each can be simplified using the identity ...

sin(x) +cos(x) = √2·sin(x +π/4)

Then the given equation can be rewritten as ...

cos(3x) +sin(5x) = 0

2·sin(x +π/4)·sin(4x +π/4) = 0

Of course sin(x) = 0 for x = n·π, so these factors are zero when ...

sin(x +π/4) = 0 ⇒ x = nπ -π/4

sin(4x +π/4) = 0 ⇒ x = (nπ -π/4)/4 = (4nπ -π)/16

The solutions are ...

x ∈ {(n-1)π/4, (4n-1)π/16} . . . . . for any integer n

5 0

3 years ago

The wind speed s (in miles per hour) is related to the distance (in miles) the tornado travels by the equation s = 93log d + 65.

Vesnalui [34]

Answer:

The distance the tornado traveled was approximately 205 miles.

Step-by-step explanation:

The equation representing the relationship between the wind speed (in miles per hour) and the distance the tornado travels (in miles) is:

$s=93\log d+65$

Compute the value of d for s = 280 as follows:

$s=93\log d+65$

$280=93\log d+65$

$93\log d=280-65\\93\log d=215$

$\log d=2.312\\$

$d=10^{2.312}\\d=205.035\\d\approx 205$

Thus, the distance the tornado traveled was approximately 205 miles.

7 0

3 years ago

What is the slope of the graph? (PLEASE HELP)

Snowcat [4.5K]

to calculate the slope m , use the ' gradient formula '

m = $\frac{y_{2-y_{1} } }{x_{2-x_{1} } }$

with ( $x_{1}$ , $y_{1}$ ) = (0, - 1 ) and ( $x_{2}$ , $y_{2}$ ) = (1, 5 )

m = $\frac{5+1}{1-0}$ = 6

4 0

3 years ago

Read 2 more answers

Identify the type of sequence 1/10, 3/20, 5/30, 7/40...

Dafna11 [192]

Arithmetic sequence: must have a constant common difference.
3/20-1/10=(3-2)/20=1/20
5/30-3/20=(10-9)/60=1/60
Difference is not constant, so no.

Geometric sequence: must have a common ratio
30/20 / (1/10) = 15
5/30 / (3/20) = 100/90 = 10/9
ratio is not constant, so no.

The answer is (c) neither geometric nor arithmetic

4 0

4 years ago

Evaluate the expression below. (8 - 7)- 4 + 3(-1) 1 -7 -1 7

Masja [62]

Answer:

answer is -1 according to calculation

4 0

3 years ago