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2 years ago

15 points!

1 answer:

7 0

So this is a bit confusing. I don't know if you need me to solve them then simplify or just reduce them but I will try to write it anyways.

1. $(4^{3} )^5$
For this, you can just multiply 3 by 5 which is 15 then place it as an exponent as $4^{15}$

But if you need to solve it, you multiply 4 by itself 15 times which is107,3741,824 but I don't think thats what you are looking for but here it is anyways

I assume that it was the former that was the answer

Answer: $4^{15}$

2. $4^{-2}$

When dealing with negative exponents, you get one and divide by the base according to the exponent. It says -2⇒2 which means you divide 1 by 4, twice

1÷4÷4=.0625

Answer: .0625

3. $4^3$

Since its positive, you multiply by the base number (rather than divide if it was negative)

So it is 4×4×4=64

Answer: 64

4. $4^8$

Here, you just take what I did in step 3 and multiply by the base number according to the exponent

4×4×4×4×4×4×4×4=65,536

Answer: 65, 536

5. $4^{15}$

You do what you did in the previous steps but multiply the base 15 times

4×4×4×4×4×4×4×4×4×4×4×4×4×4×4=1,073,741,824

Answer: 1,073,741,824

If you don't know what to do, go and ask your teacher because he/she would know best on what to do :-)

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2 years ago

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The measure of the supplement of an angle is three times the measure of the

gtnhenbr [62]

<h2>Answer:</h2>

<h3><em>x=45degrees</em></h3>

<h2>Step-by-step explanation:</h2>

Let the angle to be solved be x

Let the supplement/compliment by y

x+y=90 Complimentary angles add up to 90 degrees.

x+3y=180 Supplementary angles add up to 180 degrees, the other angle is thrice the other compliment.

Evaluating this as a system:

x+y=90 Isolate x:

x=90−y Input into the other equation:

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3 years ago

This is a 3 part 1 question each part on how to locate the plane and a small explanation report working out the recovery details

sesenic [268]

Third leg.

The crew flies at a speed of 560 mi/h in direction N-20°-E.

The wind has a speed of 35 mi/h and a direction S-10°-E.

We then can draw this as:

We have to add the two vectors to find the actual speed and direction.

We will start by adding the x-coordinate (W-E axis):

$\begin{gathered} x=560\cdot\sin (20\degree)+35\cdot\sin (10\degree) \\ x\approx560\cdot0.342+35\cdot0.174 \\ x\approx191.53+6.08 \\ x\approx197.61 \end{gathered}$

and the y-coordinate (S-N axis) is:

$\begin{gathered} y=560\cdot\cos (20\degree)-35\cdot\cos (10\degree) \\ y\approx560\cdot0.940-35\cdot0.985 \\ y\approx526.23-34.47 \\ y\approx491.76 \end{gathered}$

Then, the actual speed vector is v3=(197.61, 491.76).

The starting location for the third leg is R2=(216.66, 167.67) [taken from the previous answer].

Then, we have to calculate the displacement in 20 minutes using the actual speed vector.

We can calculate the movement in each of the axis. For the x-axis:

$\begin{gathered} R_{3x}=R_{2x}+v_{3x}\cdot t \\ R_{3x}=216.66+197.61\cdot\frac{1}{3} \\ R_{3x}=216.66+65.87 \\ R_{3x}=282.53 \end{gathered}$

NOTE: 20 minutes represents 1/3 of an hour.

We can do the same with the y-coordinate:

$\begin{gathered} R_{3y}=R_{2y}+v_{3y}\cdot t \\ R_{3y}=167.67+491.76\cdot\frac{1}{3} \\ R_{3y}=167.67+163.92 \\ R_{3y}=331.59 \end{gathered}$

The final position is R3 = (282.53, 331.59).

To find the distance from the origin and direction, we transform the cartesian coordinates of R3 into polar coordinates:

The distance can be calculated as if it was a right triangle:

$\begin{gathered} d^2=x^2+y^2_{} \\ d^2=282.53^2+331.59^2 \\ d^2=79823.20+109951.93 \\ d^2=189775.13 \\ d=\sqrt[]{189775.13} \\ d\approx435.63 \end{gathered}$

The angle, from E to N, can be calculated as:

$\begin{gathered} \tan (\alpha)=\frac{y}{x} \\ \tan (\alpha)=\frac{331.59}{282.53} \\ \tan (\alpha)\approx1.1736 \\ \alpha=\arctan (1.1736) \\ \alpha=49.56\degree \end{gathered}$

If we want to express it from N to E, we substract the angle from 90°: