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3 years ago

What is the answer to this question? g(x)=2^x+7 for g(3)

Mathematics

2 answers:

Crazy boy [7]3 years ago

5 0

Answer:

Step-by-step explanation:

g(x)=2^x+7

g(3) =2^(3)+7 = 15

Viktor [21]3 years ago

4 0

ANSWER : -24

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A rock thrown vertically upward from the surface of the moon at a velocity of 36m/sec reaches a height of s = 36t - 0.8 t^2 met

Verdich [7]

Answer:

a. The rock's velocity is $v(t)=36-1.6t \:{(m/s)}$ and the acceleration is $a(t)=-1.6 \:{(m/s^2)}$

b. It takes 22.5 seconds to reach the highest point.

c. The rock goes up to 405 m.

d. It reach half its maximum height when time is 6.59 s or 38.41 s.

e. The rock is aloft for 45 seconds.

Step-by-step explanation:

Velocity is defined as the rate of change of position or the rate of displacement. $v(t)=\frac{ds}{dt}$
Acceleration is defined as the rate of change of velocity. $a(t)=\frac{dv}{dt}$

The rock's velocity is the derivative of the height function $s(t) = 36t - 0.8 t^2$

$v(t)=\frac{d}{dt}(36t - 0.8 t^2) \\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'\\\\v(t)=\frac{d}{dt}\left(36t\right)-\frac{d}{dt}\left(0.8t^2\right)\\\\v(t)=36-1.6t$

The rock's acceleration is the derivative of the velocity function $v(t)=36-1.6t$

$a(t)=\frac{d}{dt}(36-1.6t)\\\\a(t)=-1.6$

b. The rock will reach its highest point when the velocity becomes zero.

$v(t)=36-1.6t=0\\36\cdot \:10-1.6t\cdot \:10=0\cdot \:10\\360-16t=0\\360-16t-360=0-360\\-16t=-360\\t=\frac{45}{2}=22.5$

It takes 22.5 seconds to reach the highest point.

c. The rock reach its highest point when t = 22.5 s

Thus

$s(22.5) = 36(22.5) - 0.8 (22.5)^2\\s(22.5) =405$

So the rock goes up to 405 m.

d. The maximum height is 405 m. So the half of its maximum height = $\frac{405}{2} =202.5 \:m$

To find the time it reach half its maximum height, we need to solve

$36t - 0.8 t^2=202.5\\36t\cdot \:10-0.8t^2\cdot \:10=202.5\cdot \:10\\360t-8t^2=2025\\360t-8t^2-2025=2025-2025\\-8t^2+360t-2025=0$

For a quadratic equation of the form $ax^2+bx+c=0$ the solutions are

$x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\mathrm{For\:}\quad a=-8,\:b=360,\:c=-2025:\\\\t=\frac{-360+\sqrt{360^2-4\left(-8\right)\left(-2025\right)}}{2\left(-8\right)}=\frac{45\left(2-\sqrt{2}\right)}{4}\approx 6.59\\\\t=\frac{-360-\sqrt{360^2-4\left(-8\right)\left(-2025\right)}}{2\left(-8\right)}=\frac{45\left(2+\sqrt{2}\right)}{4}\approx 38.41$

It reach half its maximum height when time is 6.59 s or 38.41 s.

e. It is aloft until s(t) = 0 again

$36t - 0.8 t^2=0\\\\\mathrm{Factor\:}36t-0.8t^2\rightarrow -t\left(0.8t-36\right)\\\\\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}\\\\t=0,\:t=45$

The rock is aloft for 45 seconds.

5 0

3 years ago

What is a coterminal angles

navik [9.2K]

Answer: Coterminal Angles are angles who share the same initial side and terminal sides. Finding coterminal angles is as simple as adding or subtracting 360° or 2π to each angle, depending on whether the given angle is in degrees or radians.

6 0

3 years ago

The difference of twice a number and 4 is 16 .

german

Answer:

Let X be the number.

Twice the number would be 2x

The difference between the two, would be subtraction, so you would subtract 4 from 2x

The equation becomes 2x-4 = 16

Now solve for x:

2x-4 = 16

Add 4 to each side:

2x = 20

Divide both sides by 2:

x = 20/2

x = 10

The number is 10.

7 0

3 years ago

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Which graph shows the solution to the system of linear inequalities?

ICE Princess25 [194]

Answer:

x = 6 ; Rewritten: 2x-3y-12=0 ; y=-4

Step-by-step explanation:

2x-3 multiply 0=12

x=6 ( that's the function)

Rewritten steps: 2x-3y=12 then move constant to the left by adding its opposite to both sides which gives you 2x-3y-12=12-12. After the sum of two opposites equals 0 which is 2x-3y-12=0

Y Intercept :

2x-3y=12 and to find y intercept, sub x = 0 ; to 2 multiply 0 -3y=12 and then you solve for the equation which is your answer.

7 0

3 years ago

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a statistics professor finds that when he schedules an office hour at the 10:30a, time slot, an average of three students arrive

Veseljchak [2.6K]

Answer:

The probability that in a randomly selected office hour in the 10:30 am time slot exactly two students will arrive is 0.2241.

Step-by-step explanation:

Let X = number of students arriving at the 10:30 AM time slot.

The average number of students arriving at the 10:30 AM time slot is, λ = 3.

A random variable representing the occurrence of events in a fixed interval of time is known as Poisson random variables. For example, the number of customers visiting the bank in an hour or the number of typographical error is a book every 10 pages.

The random variable X is also a Poisson random variable because it represents the fixed number of students arriving at the 10:30 AM time slot.

The random variable X follows a Poisson distribution with parameter λ = 3.

The probability mass function of X is given by:

$P(X=x)=\frac{e^{-\lambda}\lambda^{x}}{x!};\ x=0,1,2,3...,\ \lambda>0$

Compute the probability of X = 2 as follows:

$P(X=2)=\frac{e^{-3}3^{2}}{2!}=\frac{0.0498\times 9}{2}=0.2241$

Thus, the probability that in a randomly selected office hour in the 10:30 am time slot exactly two students will arrive is 0.2241.

6 0

3 years ago

Read 2 more answers