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3 years ago

5 times a number is 6 less than the square of that number

Mathematics

1 answer:

Fed [463]3 years ago

3 0

Answer:

5x = x^2 - 6

Step-by-step explanation:

a number can be represented by x,

5 times a number can be represented as the product of 5 and x, 6 less than the square of that number tells us that this is equal to a number squared minus 6. is tells us that these two expressions are equal.

If you want a working number, just solve by completing the square once this is in standard form. This is then converted to vertex form.

x^2-5x-6 = (x-5/2)^2-49/4 = (x^2-5x+25/4) -49/4 = x^2-5x-6.

(x-5/2)^2-49/4=0

(x-5/2)^2=49/4

(x-5/2) = ±√49/4

(x-5/2) = ±7/2

x=5/2±7/2

x=(5±7)/2

x=12/2,-2/2

x=6,-1

Thus, the number can either be 6 or -1.

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Write the differential equation model that fits the given description. (a) The rate of change of the volume of a snowball (due t

miskamm [114]

Answer:

a) he rate of change of the volume of a snowball (due to melting) is proportional to the square of the volume at time t. Initially, the snowball has a volume of 900 cm3

$\frac{dV(t)}{dT} = A*V(t)^{2} \\$ and V(0) = 900 $cm^{3}$

where A is a real constant, it appears because it says that the change i volume (dV/dt) is "proportional" to $V(t)^{2}$ . Furthermore, we should assume that A is a negative number, because the volume of the snowball will decrease as the time pasese by.

(b) For an insect moving along some path, the velocity at time t is proportional to the square root of its position.

$\frac{dr(t)}{dt} = B*\sqrt{r(t)}$

Here again appears a constant B for the "proportional" part. And i wrote the velocity as $\frac{dr(t)}{dt}$ "the rate of change of the position with respect to te time".

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3 years ago

In a recent survey of college professors, it was found that the average amount of money spent on entertainment each week was nor

Alenkinab [10]

Answer:

0.0918

Step-by-step explanation:

We know that the average amount of money spent on entertainment is normally distributed with mean=μ=95.25 and standard deviation=σ=27.32.

The mean and standard deviation of average spending of sample size 25 are

μxbar=μ=95.25

σxbar=σ/√n=27.32/√25=27.32/5=5.464.

So, the average spending of a sample of 25 randomly-selected professors is normally distributed with mean=μ=95.25 and standard deviation=σ=27.32.

The z-score associated with average spending $102.5

Z=[Xbar-μxbar]/σxbar

Z=[102.5-95.25]/5.464

Z=7.25/5.464

Z=1.3269=1.33

We have to find P(Xbar>102.5).

P(Xbar>102.5)=P(Z>1.33)

P(Xbar>102.5)=P(0<Z<∞)-P(0<Z<1.33)

P(Xbar>102.5)=0.5-0.4082

P(Xbar>102.5)=0.0918.

Thus, the probability that the average spending of a sample of 25 randomly-selected professors will exceed $102.5 is 0.0918.

5 0

3 years ago

2x^2-3x-9 please help

Romashka-Z-Leto [24]

Im assuming you mean 2x^2-3x-9=0 ?
If so, you have to factorise the equation
(2x-3) (x+3) = 0

2x - 3 = 0
2x = 3
x = 1.5

x + 3 = 0
x = -3

x is either 1.5 or -3

8 0

3 years ago

Read 2 more answers

Find the zeros of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients

Anna [14]

Answer:

Zeros would be x= 0, -2

Step-by-step explanation:

hope this helps :)

6 0

2 years ago

The number of views on a viral video can be modeled by the function S(t)=9600(3)^t+2. Write an equivalent function of the form S

anyanavicka [17]

Answer:

The equivalent expression would be;

S(t) = 86,400•3^t

Step-by-step explanation:

Here, we want to make a transformation

From what we have;

S(t) = 9,600(3)^(t + 2)

From indices, we know that;

x^(a + b) = x^a•x^b

Thus, we have it that;

S(t) = 9600•3^t•3^2

S(t) = (9 * 9600) * 3^t

S(t) = 86,400•3^t

8 0

3 years ago