If 8x = 48, then x = ___. (Only input whole number) Numerical Answers Expected! Answer for Blank 1:

A discuss moves from P1 (4,8) to P2 (15,17). What is the lincar displacement in the horizontal and vertical directions? What is

Yakvenalex [24]

Answer:

The horizontal displacement is 11 units, the vertical displacement is 9 units, and the projection angle is 39.3 degrees.

Step-by-step explanation:

We can start using the definition of displacement in one dimension between any 2 points which is the difference between them, so we have

$\Delta s = s_2-s_1$

And apply it to get the horizontal and vertical displacements.

Once we have found them, we can use trigonometric functions to find the projection angle with respect the horizontal.

Linear displacements.

Using the definition of displacement, we can write the horizontal displacement as

$\Delta x = x_2-x_1$

So we can use the given points $P1:(x_1,y_2) \text{ and } P_2: (x_2,y_2)$ on the displacement formula

$\Delta x = 15-4\\\Delta x = 11$

In the same manner we can look at the y components of those points to find the vertical displacement

$\Delta y = 17-8\\\Delta y =9$

Thus the horizontal displacement is 11 units and the vertical displacement is 9 units.

Projection angle.

The projection angle with respect the horizontal is the angle that is made between the line that connects the points P1 and P2 and the horizontal, so we can use the linear displacements previously found to write

$\tan(\theta) = \cfrac{\Delta y}{\Delta x}$

Solving for the angle we get

$\theta = \tan^{-1}\left(\cfrac{\Delta y}{\Delta x}\right)$

Replacing values

$\theta = \tan^{-1}\left(\cfrac{9}{11}\right)$

Which give us

$\theta = 39.3^\circ$

So the projection angle is 39.3 degrees.

7 0

3 years ago

The equation h=7sin(pi/21t)+28 can be used to model the height, h, in feet of the end of one blade of a windmill turning on an a

satela [25.4K]

Answer:

7 feet is the length of the blade of the windmill.

Step-by-step explanation:

We have the equation

h = 7 sin(pi/21t) + 28 ------ eq1

At time 't' = 0, the end of the blade is pointing to the right parallel to the ground meaning it is at the same height as the other end. (Ф = 0°)

So, by calculating the maximum height of this end at Ф = 90°. we can calculate the length of the blade.

Now, we know that a general model equation of a circular simple harmonic motion is represented as : y = A sinωt + k ----- eq2

Where A is the amplitude that is, maximum displacement from mean to maximum position.

ω is the angular frequency.

Comparing eq1 and eq2:

A = 7

so the difference in blades end height at Ф = 0° and Ф = 90° is 7 feet.

Hence, the length of the blade is 7 feet.

4 0

3 years ago

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Pls only do this if yk it because i’m giving correct answer brainliest! :))

Leno4ka [110]

Answer:

$x=2+\frac{1}{2}\sqrt[]{21}$

or

$x=2-\frac{1}{2}\sqrt{{21}$

Step-by-step explanation:

$4x^2-16x-26=-21$

Add 21 on both sides.

$4x^2-16x-26+21=-21+21$

$4x^2-16x-5=0$

a=4

b=-16

c=-5

$x=\frac{-b\frac{+}{}\sqrt[]{b^2-4ac} }{2a}$

$x=\frac{-(-16)\frac{+}{}\sqrt[]{(-16)^2-4(4)(-5)} }{2(4)}$

$x=\frac{16\frac{+}{}\sqrt[]{256+80} }{8}$

$x=\frac{16\frac{+}{}\sqrt[]{336} }{8}$

$x=\frac{16\frac{+}{}\sqrt[]{2^2*2^2*21} }{8}$

$x=\frac{16\frac{+}{}2*2\sqrt[]{21} }{8}$

$x=\frac{16\frac{+}{}4\sqrt[]{21} }{8}$

---------------------------------------------------------------------------

$x=\frac{16}{8}+\frac{4\sqrt[]{21}}{8}$

$x=2+\frac{1}{2}\sqrt[]{21}$

---------------------------------------------------------------------------

$x=\frac{16}{8}-\frac{4\sqrt[]{21}}{8}\\x=2-\frac{1}{2}\sqrt{{21}$

6 0

2 years ago

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if rounded to the nearest dime what is the greatest amount of money that rounds to $105.40? what is the least amount of money th

Kamila [148]

The greatest amount of money would be $105.40. The least amount would also be $105.40. Because the zero is less than five the dollar amount would stay the same.

4 0

3 years ago

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Which is bigger: 3/8 or 7/20

umka21 [38]

$\rm ^{20)}\frac{3}{8}= \frac{60}{160} \\ \\ ^{8)}\frac{7}{20}= \frac{56}{160} \\ \\ So~ \frac{3}{80}~is~bigger~because~60\ \textgreater \ 56.$

4 0

3 years ago

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