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2 years ago

PLEASE HELP!

Mathematics

2 answers:

yuradex [85]2 years ago

5 0

Answer:

Options B and D

Step-by-step explanation:

Phrase shift of a trignometric function is the horizontal shift of the function towards right or left.

Vertical shift is shift up or down.

The graph of y = sin x is translated three units down.

-- This is vertical shift and not phase shift.

The graph of y = csc x is translated three units to the right

-- This is a phase shift as y = csc (x+3)

The graph of y = cos x is translated three units up. -- No, vertical shift.

The graph of y = sec x is translated three units to the left. -- Yes, phase shift

The graph of y = cot x is reflected over the horizontal axis. -- No, reflection

The graph of y = tan x is reflected over the vertical axis.-- No, reflection

Only options B D are phase shifts.

Anettt [7]2 years ago

4 0

Answer: 2,3 and 4

Step-by-step explanation:

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Answer: Bea has $30 saved

Step-by-step explanation:

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2 years ago

A person invest $1200 in an account that earns 2% interest compound quarterly. Find when the value of the investment reaches $15

Basile [38]

Answer:

After 11 years the value of the investment reaches $1500.00

Step-by-step explanation:

The formula used for finding time (when the value reaches certain amount) is:

$A= P(1+\frac{r}{n})^{nt}$

where A= Future VAlue

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r= rate of interest (in decimal)

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t= time

Putting the values given and finding Time t,

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Dividing both sides by 1200 and solving 0.02/4 = 0.005

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$1.25= (1.005)^{4t}$

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The rule of logarithm says that the exponent can be multiplied with the base when taking log

$\ln1.25=ln( 1.005)^{4t}\\\ln1.25=4t * ln( 1.005)\\0.22 = 4t * 0.005\\Solving\,\,\\\frac{0.22}{4*0.005} = t\\=> t= 11\, years$

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2 years ago

Suppose m is in the line given by the equation 6x-3y=7, and suppose n is the line perpendicular to m and passing Nd through the

stealth61 [152]

Answer:

The x co-ordinate o intersection of line k and n is $\frac{8}{11}$

Step-by-step explanation:

Given as :

The equation of line m is 6 x - 3 y = 7

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y = a x + c , where a is the slope

So, 6 x - 3 y = 7 can be written as

3 y = 6 x - 7

or, y = 2 x - $\frac{7}{3}$ ........1

So, slope of this line = a = 2

Now, The line n is perpendicular to line m and passing through line ( 6 , 2 )

So, Slope of line n = b

For , perpendicular lines , products of slope = - 1

Or, a × b = -1

∴ b = - $\frac{1}{a}$

I.e b = - $\frac{1}{2}$

So,equation of line n with slope b and passing through line ( 6 , 2 ) is

y - $y_1$ = b ( x - $x_1$ )

or, y - 2 = - $\frac{1}{2}$ ( x - 6 )

or, 2 × ( y - 2 ) = - 1 ( x - 6 )

or, 2 y - 4 = - x + 6

or, x + 2 y -10 = 0 ........2

Again, equation of line k with slope 5 and y intercept = 1

For y intercept , x coordinate = 0

y = c x + c

or, 1 = c× ( 0 ) + c

Or, c = 1

Or, equation of line k is

y = 5 x + 1 ..........3

Now intersection of line k and n is

put the value of y from eq 3 into eq 2

I.e x + 2 × ( 5 x + 1 )-10 = 0

Or, x + 10 x + 2 - 10 = 0

or, 11 x - 8 = 0

or 11 x = 8

∴ x = $\frac{8}{11}$

Hence The x co-ordinate o intersection of line k and n is $\frac{8}{11}$ Answer

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