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3 years ago

Is the following graph a function?

Mathematics

1 answer:

alekssr [168]3 years ago

7 0

Check the picture below.

notice that if we run the "vertical line test", the green vertical line there, touches the graph more than once, and for a function, it has to touch it only once, so no dice.

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What is the equation of the line that passes through the point (-7, 2) and has a slope of -1?

Morgarella [4.7K]

Answer:

y= -1x-5

Step-by-step explanation:

4 0

2 years ago

Between 0 degrees Celsius and 30 degrees Celsius, the volume V (in cubic centimeters) of 1 kg of water at a temperature T is giv

Ira Lisetskai [31]

Answer:

T = 3.967 C

Step-by-step explanation:

Density = mass / volume

Use the mass = 1kg and volume as the equation given V, we will come up with the following equation

D = 1 / 999.87−0.06426T+0.0085043T^2−0.0000679T^3

= (999.87−0.06426T+0.0085043T^2−0.0000679T^3)^-1

Find the first derivative of D with respect to temperature T

dD/dT = $\dfrac{70000000\left(291T^2-24298T+91800\right)}{\left(679T^3-85043T^2+642600T-9998700000\right)^2}$

Let dD/dT = 0 to find the critical value we will get

$\dfrac{70000000\left(291T^2-24298T+91800\right)}$ = 0

Using formula of quadratic, we get the roots:

T = 79.53 and T = 3.967

Since the temperature is only between 0 and 30, pick T = 3.967

Find 2nd derivative to check whether the equation will have maximum value:

$-\dfrac{140000000\left(395178T^4-65993368T^3+3286558821T^2+2886200857800T-121415215620000\right)}{\left(679T^3-85043T^2+642600T-9998700000\right)^3}$

Substituting the value with T=3.967,

d2D/dT2 = -1.54 x 10^(-8) a negative value. Hence It is a maximum value

Substitute T =3.967 into equation V, we get V = 0.001 i.e. the volume when the the density is the highest is at 0.001 m3 with density of

D = 1/0.001 = 1000 kg/m3

Therefore T = 3.967 C

3 0

3 years ago

Suppose you waited 10 years to invest in the same retirement fund and have the same $400,000 for retirement at the same 8% inter

Ierofanga [76]

Answer:

Step-by-step explanation:

Using the compound interest formula to fins the amount after 10years;

A = P(1+r)^n

Principal P = $400,000

Rate r = 8% = 0.08

Time t = 10 years

Substitute

A = 400,000(1+0.08)^10

A = 400,000(1.08)^10

A = 400,000(2.1589)

A = 863,569.99

A ≈ 863,570

Hence the amount after 10 years is $863,570

Monthly deposit = $863,570/120 (10 years is equivalent to 120months)

Monthly deposit = 7,196.42

<em>Therefore he will have to deposit $7,196.42 into his account monthly</em>

7 0

2 years ago

I need help please ..

mafiozo [28]

The answer is A hope this helped

3 0

3 years ago

Need help on this math problem

erik [133]

Answer:

$-5, 18, \sqrt{13}$

Step-by-step explanation:

We can solve the first equation, f of -3. The value of the function f is $\frac{1+x^2}{x+1}$ , and plugging in -3 gets us $\frac{1+9}{1-3}$ , this results in 10 divided by negative 2, which is negative 5.

Now, we must solve g of negative one third. The function g is defined as $|9x-15|$ . Plugging in negative one third into the question gets us $|9(-\frac{1}{3})-15|$

9 times negative one third is -3, and -3 minus 15 is -18. The absolute value of -18 is 18.

Now, we must solve h of negative 2, and h is defined as $\sqrt{-3-8x}$ . Plugging in negative 2, we have $\sqrt{-3-8(-2)}$ . Negative 8 times negative 2 is positive 16, and 16 minus 3 is 13. The answer is the square root of 13

7 0

2 years ago