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kondor19780726 [428]

3 years ago

15

Determine if the equation below is a function with independent variable x. If so, find the domain. If not, find a value of x to

which there corresponds more than one value of y.
x^{2} +y^{2} =25

1 answer:

Andre45 [30]3 years ago

8 0

Answer:

No because it contains points (3,4) and (3,-4). You cannot have a x assigned to more than one y-value if you want it to be a function.

Step-by-step explanation:

A function has one output per input.

If we are trying to determine if the given is a function of x, then x is the input.

However I can get two outputs from plugging in x=3.

$3^2+y^2=25$

$9+y^2=25$

Subtract 9 on both sides:

$y^2=25-9$

$y^2=16$

Take the square root of both sides:

$y=\pm \sqrt{16}$

$y=\pm 4$ .

So input x=3 yields y=4 and y=-4.

Since this input has more than one output then the given is not a function of x.

----Also!

If you graph the equation, it is a circle with radius 5 and center (0,0). So I could I plug in any number for x between -5 and 5 excluding -5 and 5 which would yield only one output each. Since plugging in either one gives:

$(\pm 5)^2+y^2=25$

$25+y^2=25$

Subtract 25 on both sides:

$y^2=25-25$

Simplify:

$y^2=0$

There is only one value y such that when you square it gives you 0. That is 0.

x=5 only gives y=0 and x=-5 only gives y=0.

There is no circle, unless it is a circle with radius 0 which means it really wouldn't be a circle, that is a function.

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Very buys a basket of mangoes that is priced $14 before tax. The sales tax is 6%. What is the total price Avery pays for t

igor_vitrenko [27]

Answer:

Avery needs to pay $14.84

Step-by-step explanation:

When there's a tax we need to sum the original value of the product with the tax's value. To find the amount of money Avery needs to pay in taxes we can apply a rule of three as shown below:

$\frac{14}{x} = \frac{100}{6} \frac{\%}{\%}$

Where "x" is the tax value, and $14 represents 100%, since it's the value used to calculate the tax. We have:

$x = \frac{14*6}{100}\\x = \frac{84}{100}\\x = 0.84$

The value to be paid is the product value plus the tax, therefore:

$\text{paid} = 14 + 0.84 = 14.84$

Avery needs to pay $14.84

6 0

3 years ago

If Tanisha has $nbsp 100 100 to invest at 66% per annum compounded semiannuallysemiannually, how long will it be before she h

Oxana [17]

Answer:

time is 6.76 years

Step-by-step explanation:

given data

amount = $150

payment = $100

rate r = 6% = 0.06

to find out

time period t

solution

we know it is compounding continuous

so we will apply here formula that is

amount = payment × $e^{rt}$ ..........1

put here all value we get

amount = payment × $e^{rt}$

150 = 100 × $e^{0.06t}$

take ln both side

ln 1.5 = $e^{0.06t}$

0.40546 = 0.06t

t = 0.40546 / 0.06

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so time is 6.76 years

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3 years ago

Divide using long division. Checky<br> (x3+ 3x2 + x - 9) = (x - 1)

Montano1993 [528]

Answer:

x squared plus 2x minus 1.

Step-by-step explanation:

x3+3x2+x-9 is in the division "house" and x-1 is on the outside. xsquare times x equals x cubed. and x square times negative 1 equals -x squsre. put x square on top of the roof. change the signs. the x cubed cancels out. and bring down 2x square from subtracting 3x square and -x square and bring down the x-9. Put 2x on top of the roof too and 2x times x equals 2x square and multiply by -1. U will have 2x square -2x square and -2x plus x which equals -1x cuz the 2x square cancels out. bring down the -9. Now i have -1x-9. Multiply by -1 and put -1 on the roof. -1x+1x cancels out. and -1 times -1 equals positive 1. So -9+1=8. U van do any further cause as soon as the last number is at the end of the roof and u cant go further, ur done dividing. so the answer is x square+2x-1/×-1 +8 as the remainder. hope i helped

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3 years ago

A ball is thrown upward with an initial velocity of 96 ft/sec from a height 640 ft. Its height h, in feet, after t seconds is

olchik [2.2K]

Check the picture below.

thus is at 0 = -16t² + 96t +640,

$\bf 0=-16t^2+96t+640\implies 0=-16(t^2-6t-40)
\\\\\\
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\begin{cases}
\boxed{10}\\
-4
\end{cases}$

well, clearly it can't be a negative value for the elapsed seconds, so it can't be -4.

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A bicycle rider increases his speed from 5 m/s to 15 m/s in 10 seconds

valentina_108 [34]

To find the acceleration of the bicycle rider, we are going to use the acceleration formula: $a= \frac{v_{f}-v_{i}}{t}$
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$t$ is the time

We know from our problem that increases his speed from 5 m/s to 15 m/s in 10 seconds, so his initial speed is 5 m/s and his final speed is 15 m/s; therefore, $v_{i}=5$ , $v_{f}=15$ , and $t=10$ . Lets replace those values in our formula:
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