F(x)=3x means the same thing as y=3x but is written in function notation. A. true B. false

Bashir works in a weather station and has launched a weather ballon. The height of the baloon is 4 kilometers and it is 1 kilome

andrew-mc [135]

Answer:

(c) 4.1 km

Explanation:

We are given that the height of the balloon is 4 km and that it is 1 km away from the station.

Setting up the diagram that describes the given scenario, we would end up with a right-angled triangle as the one shown in the attached image

where:

height of the balloon = 4 km represents one side of the triangle

distance between the base of the balloon and the station = 1 km represents the other side

distance between the balloon and the station is the length we want to find and it represents the hypotenuse of the triangle.

To get the length of the hypotenuse, we will use the Pythagorean theorem

$hypotenuse = +\sqrt{(side1)^2 + (side2)^2}$

Substitute with the givens:

$hypotenuse = +\sqrt{(4)^2 + (1)^2}$ = √17 ≈ 4.1 km

Hope this helps :)

3 0

2 years ago

Measurements of regular hexagon

TEA [102]

The regular hexagon has both reflection symmetry and rotation symmetry.

Reflection symmetry is present when a figure has one or more lines of symmetry. A regular hexagon has 6 lines of symmetry. It has a 6-fold rotation axis.

http://prntscr.com/96ow2n

Rotation symmetry is present when a figure can be rotated (less than 360°) and still look the same as before it was rotated. The center of rotation is a point a figure is rotated around such that the rotation symmetry holds. A regular hexagon can be rotated 6 times at an angle of 60°

http://prntscr.com/96oxjx

5 0

3 years ago

Can someone please help me with this question

Cerrena [4.2K]

Answer:

5x+3>23

Step-by-step explanation:

x $\geq$ 4

8 0

2 years ago

The function in Exercise represents the rate of flow of money in dollars per year. Assume a 10-year period at 8% compounded cont

anzhelika [568]

Answer:

a) The present value is 688.64 $

b) The accumulated amount is 1532.60 $

Step-by-step explanation:

a) The preset value equation is given by this formula:

$P=\int^{T}_{0}f(t)e^{-rt}dt$

where:

T is the period in years (T = 10 years)
r is the annual interest rate (r=0.08)

So we have:

$P=\int^{T}_{0}(0.01t+100)e^{-rt}dt$

Now we just need to solve this integral.

$P=\int^{T}_{0}0.01te^{-rt}dt+\int^{T}_{0}100e^{-rt}dt$

$P=e^{-0.08t}(-1.56-0.13t)|^{10}_{0}+1250e^{-0.08t}|^{10}_{0}$

$P=0.30+688.34=688.64 $$

The present value is 688.64 $

b) The accumulated amount of money flow formula is:

$A=e^{r\tau}\int^{T}_{0}f(t)e^{-rt}dt$

We have the same equation but whit a term that depends of τ, in our case it is 10.

So we have:

$A=e^{r\tau}\int^{T}_{0}(0.01t+100)e^{-rt}dt=e^{0.08\cdot 10}P$

$A=e^{0.08\cdot 10}688.64=1532.60 $$

The accumulated amount is 1532.60 $

Have a nice day!

6 0

2 years ago

A function has a constant halving time. What type of function does this represent?

Anna71 [15]

The function which has a constant halving time is in the following form

$A(t) = A_{0} ( \frac{1}{2} )^ \frac{t}{h}$
Where: A₀ is the initial amount
 h is the half life time or the halving time.
 t is the time
 A(t) the amount that remains at time t

The previous function represents an Exponential decay function.


so, The correct answer is option B. Exponential decay

8 0

3 years ago

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