At 2 PM there were 13 seagulls on the beach. At 5 PM there were 70 seagulls. What is the constant rate of change

Given that p=9i+12j and q=-6i-8j. Evaluate |p-q|-{|p|-|q|}

krok68 [10]

Answer:

$|p-q|-(|p|-|q|) = 20$

Step-by-step explanation:

First let's find the value of 'p-q':

$p - q = 9i + 12j - (-6i - 8j)\\p - q = 9i + 12j + 6i + 8j\\p - q = 15i + 20j\\$

To find |p-q| (module of 'p-q'), we can use the formula:

$|ai + bj| = \sqrt{a^{2}+b^{2}}$

Where 'a' is the coefficient of 'i' and 'b' is the coefficient of 'j'

So we have:

$|p - q| = |15i + 20j| = \sqrt{15^{2}+20^{2}} = 25$

Now, we need to find the module of p and the module of q: $|p| = |9i + 12j| = \sqrt{9^{2}+12^{2}} = 15$

$|q| = |-6i - 8j| = \sqrt{(-6)^{2}+(-8)^{2}} = 10$

Then, evaluating |p-q|-{|p|-|q|}, we have:

$|p-q|-(|p|-|q|) = 25 - (15 - 10) = 25 - 5 = 20$

7 0

3 years ago

Josiah invests $360 into an account that accrues 3% interest annually. Assuming no deposits or withdrawals are made, which equat

Natalka [10]

y = 360(1.03)x is the answer

6 0

3 years ago

Read 2 more answers

A gift shop owner bought fifty vases for $210. she sells seven vases for what she paid for ten originally. what profit does she

Slav-nsk [51]

The profit earned by the gift shop owner on fifty vases will be $ 91.07.

<h3>What is profit?</h3>

The amount of money earned by any seller on the cost price is called the profit. It is given that A gift shop owner bought fifty vases for $210. she sells seven vases for what she paid for ten originally.

The profit will be calculated as we will create the expressions for all the selling and purchasing given in the question.

The total cost price of vases:-

50 vases = $210

1 Vase = 210 / 50 = 4.25

So 10 vases will be purchased at the price of:-

10 Vase = 4.25 x 10 = 42.5

Now from the question of the amount he paid for 10 vases, he gained it by selling 7 vases.

7 Vase = 42.5

1 Vase = 42.5 / 7 = 6.07

So he sold one vase for $6.07 and purchased it at $4.25.

The profit will be = 6.07 - 4.25 = 1.821

So profit for selling 50 vases will be:-

Profit = 50 x 1.821 = $91.07

Therefore profit earned by the gift shop owner on fifty vases will be $ 91.07.

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6 0

2 years ago

Which of these equations represent functions where x is the input and y is the

Arisa [49]

Answer:

y=2x-A

Step-by-step explanation:

4 0

3 years ago

A bicycle wheel with diameter 16 inches rides over a screw in the street. the screw is on level ground before it punctures the b

weqwewe [10]

The height of the screw = 16 inches.

<h3>How do you determine the number of revolutions in a circle?</h3>

The total distance covered in one revolution will be equal to the perimeter of the wheel. Finally, to find the total number of revolutions, divide the total distance by distance covered in one revolution.

Given that,

Diameter of a bicycle = 16 inches

The distance the bike moves (forward) after the screw punctures the tire = 56π inches

We note that the circumference of the bicycle = π·D = π × 16 = 16π inches

Therefore,

$\frac{56\pi }{16\pi }$ = 3.5

Showing that the bicycle moves three and half complete turns (revolution) where after each complete turn, the screw starts from the bottom of the tire.

The height, h of the screw in the final half turn is given by the relation;

h = A cos(Bx - C) + D

Where

A = Amplitude of the motion = Diameter/2 = 16/2 = 8

P = The period of the motion 2π/B

Bx = The angle described by the motion = Half of one revolution = π = 180°

C = Phase shift = π

D = The mid line = Diameter/2 = 8 inches

Therefore;

h = 8×cos(π - π) + 8 = 16 inches

Hence, After the bike moves forward another 56π inches the height of the screw = 16 inches.

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8 0

2 years ago