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3 years ago

Identify the functions that have the given property.

Mathematics

2 answers:

mestny [16]3 years ago

7 0

The function could be y = -cos x

Step-by-step explanation:

One x-intercept is (pi,0): We can use a trigonometric function like cosine that has x-intercept (pi/2,0).

The domain of the cosine function is the set of all real numbers.

The domain of f(x) = cos(x) is all real numbers.

The minimum value is -1, then the amplitude must be -1: y = - 1 cos x

The y-intercept is (0,1) then it is the function y = cos x, reflected around the x-axis: y = cos x

vivado [14]3 years ago

7 0

Answer:

this is right!

Step-by-step explanation:

i got it right on edge

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For the following amount at the given interest rate compounded continuously, find (a) the future value after 9 years, (b) the

Stella [2.4K]

Answer:

(a) The future value after 9 years is $7142.49.

(b) The effective rate is $r_E=4.759 \:{\%}$ .

(c) The time to reach $13,000 is 21.88 years.

Step-by-step explanation:

The definition of Continuous Compounding is

If a deposit of $P$ dollars is invested at a rate of interest $r$ compounded continuously for $t$ years, the compound amount is

$A=Pe^{rt}$

(a) From the information given

$P=4700$

$r=4.65\%=\frac{4.65}{100} =0.0465$

$t=9 \:years$

Applying the above formula we get that

$A=4700e^{0.0465\cdot 9}\\A=7142.49$

The future value after 9 years is $7142.49.

(b) The effective rate is given by

$r_E=e^r-1$

Therefore,

$r_E=e^{0.0465}-1=0.04759\\r_E=4.759 \:{\%}$

(c) To find the time to reach $13,000, we must solve the equation

$13000=4700e^{0.0465\cdot t}$

$4700e^{0.0465t}=13000\\\\\frac{4700e^{0.0465t}}{4700}=\frac{13000}{4700}\\\\e^{0.0465t}=\frac{130}{47}\\\\\ln \left(e^{0.0465t}\right)=\ln \left(\frac{130}{47}\right)\\\\0.0465t\ln \left(e\right)=\ln \left(\frac{130}{47}\right)\\\\0.0465t=\ln \left(\frac{130}{47}\right)\\\\t=\frac{\ln \left(\frac{130}{47}\right)}{0.0465}\approx21.88$

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3 years ago

5x-3y=1,3x+2y=1 solve the simultaneous equation above

ryzh [129]

Answer:

The solution to the equation is as follows;

$x = \frac{5}{19} ,\ and \ y= \frac{2}{19}$

Step-by-step explanation:

Given;

5x - 3y = 1

3x + 2y = 1

Solving both equation simultaneously;

2: 10x - 6y = 2

3: 9x + 6y = 3

--------------------------

19x + 0 = 5

x = 5/19

substitute the value of x in any of the equations above and solve for y;

5x - 3y = 1

5 (5/19) - 3y = 1

25/19 -3y = 1

$3y = \frac{25}{19} -1\\\\3y = \frac{25-19}{19} \\\\3y = \frac{6}{19} \\\\y = \frac{2}{19}$

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3 years ago

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3 years ago

Please help me . it's simplifying expressions

Sergeu [11.5K]

Multiply in order
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4 years ago