What is 4 to the z power

A boat is sighted from a 50-meter observation tower on the shoreline at an angle of depression of 4 degrees moving directly towa

MAXImum [283]

Answer:

5.76 km/h

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relationship between angles and sides of a right triangle. Here, we are given the side opposite the angle (angle of depression), and we want to find the adjacent side (distance from shore).

Tan = Opposite/Adjacent

tan(4°) = (height of tower)/(distance from shore)

tan(4°) = (50 m)/(distance from shore)

Then the distance from shore is ...

distance from shore = (50 m)/tan(4°) ≈ 715.03 m

__

At the second sighting, the distance from shore is ...

distance from shore = (50 m)/tan(12°) ≈ 235.23 m

So, the distance traveled in 1/12 hour is ...

715.03 m - 235.23 m = 479.80 m

and the speed in km per hour is ...

speed = 0.4798 km/(1/12 h) = 5.7576 km/h

The speed of the boat is about 5.76 km per hour.

4 0

3 years ago

Ellen saved $2000 and she spent 10% of it to buy a bike. Kim saved 8% more than that of Ellen's left savings. If Lisa saved 60%

enyata [817]

Answer: Lis saved $1166.4 .

Step-by-step explanation:

Given , Ellen saved $2000 and she spent 10% of it to buy a bike.

Then, Ellen's left saving = saved amount - 10% of (saved amount)

= $2000 - 0.10 x $2000 [We convert perecntage to decimal by diving it by 100]

= $2000 - $200

= $1800

So, Ellen's left saving= $1800

Also, Kim saved 8% more than that of Ellen's left savings.

Kim's Saving = Ellen's left saving + 8% of (Ellen's left saving)

= $1800 + (0.08) x ($1800) [We convert perecntage to decimal by diving it by 100]

= $1800 + $144

i.e. Kim's Saving= $1944

If Lisa saved 60% as much as Kim, then Lisa's saving = 60% of (Kim's Saving)

= (0.60) x ($1944) [We convert perecntage to decimal by diving it by 100]

i.e. Lisa's saving = $1166.4

4 0

2 years ago

Please help me solve this

iren [92.7K]

Answer:

The answer is D

Step-by-step explanation:

180(6-2)

180 times 4

720

7 0

3 years ago

As a result of a cyclone, the price of bananas rose 85% to $9.99 per kg. How much did bananas cost before the cyclone?

Karo-lina-s [1.5K]

The original price was $8.49 :)

7 0

3 years ago

Is (x-3) a factor of f(x) = x^2 - 32?

Leokris [45]

Answer:

$No$

Explanation:

Here, we want to use the factor theorem to check if the given linear expression is a factor of the binomial

Now, according to the factor theorem, a factor of a polynomial would leave no remainder when divided by it

Mathematically, it means when we substitute the factor value into the polynomial, it is expected that the remainder is zero is the substituted is a factor of the polynomial

We set x-2 to zero:

$\begin{gathered} \text{ x-2 = 0} \\ x\text{ = 2} \end{gathered}$

Now, we substitute 2 into the polynomial as follows:

$f(2)\text{ = }2^2-32\text{ = 4-32 = -28}$

There is a remainder of -28 and thus, the linear factor is not a factor of the binomial

3 0

1 year ago