Complete the point-slope equation of the line through (-5,4) and (1,6)

A grasshopper jumps straight up from the ground with an initial vertical velocity of 8 feet per second. After how many seconds w

vlabodo [156]

Answer:

Problem 1 : After 0.25 s

Problem 2 : The squirrel doesn't reach the ground before the nut

Step-by-step explanation:

Problem 1

This is a standard physics problem

The equation that defines the movement of the grasshopper given the initial velocity, and the acceleration is the following

Distance = Do + Vo*t + 0.5*a*t^2

Where

Do is the initial distance.

(Do = 0, because the grasshopper is on the ground and we choose the reference system there)

Vo is the initial velocity = 8 feet/sec

a is the acceleration that is exerted on the body (in this case a = g = -9.8 m/s^2 = - 32.174 feet per second per second.)

t is the time

We substitute in the equation, and solve for t (time)

Distance = Do + Vo*t + 0.5*a*t^2

(1 foot)= (0)+ (8 feet/s)*t + 0.5*(-32.174 feet/s^2)*t^2

Solving this equation, we get that

t = 0.25 s

Problem 2

This problem is similar to the previous one

We apply the same formula

D = Do + Vo*t + 0.5*a*t^2

But in this case, we are going in the opposite direction, and we have an initial distance.

Do = 27 feet

Vo is the initial velocity of the nut = -6 feet/s

D = 0 (Ground)

We substitute in the equation, and solve for t (time)

(0) = (27) + (-6 feet/s)*t + 0.5*(-32 feet/s^2)*t^2

t = 1.125 s < 2s

The nut reaches ground in 1.125 s, so the squirrel doesn't reach the ground before the nut

4 0

4 years ago

Shane is using pieces of square paper to cover a cube shaped gift with sides that are 9 inches long to find out the area of the

nordsb [41]

Answer:

The area of the cube is 486 inches^2

Step-by-step explanation:

In this question, we are tasked with calculating the area of cube with side 9 inch.

Mathematically, the area can be calculated using the formula A = 6s^2

Now, what we need to do is to substitute 9 inches for s

Thus, A = 6 * 9^2

A = 6 * 81

A = 486 inches^2

3 0

3 years ago

A theater group made appearances into cities the hotel charge before tax and the second city was 1500 higher than the first the

Svetlanka [38]

Answer:

The hotel charge in each city before tax was $5125 of the first city and $3625 of the second city.

Step-by-step explanation:

Given:

A theater group made appearances into cities the hotel charge before tax and the second city was 1500 higher than the first.

The tax of the first city was 6% and the tax of the second city was 10%.

Total hotel tax paid for two cities with $670.

Now, to find the hotel charge in each city before tax.

Let the hotel charge in first city before tax be $x.$

And the hotel charge in second city before tax be $y.$

So, as the hotel charge of the second city was 1500 higher than the first.

Thus,

$y=x-1500$ ........(1)

And as given, the tax of the first city was 6% and the tax of the second city was 10%, total hotel tax paid for two cities with $670.

6% of $x$ + 10% of $y$ = $670.

$\frac{6x}{100} +\frac{10y}{100} =670$

$0.06x+0.10y=670$

Substituting the value of $y$ from equation (1) we get:

$0.06x+0.10(x-1500)=670$

$0.06x+0.10x-150=670$

$0.16x-150=670$

Adding both sides by 150 we get:

$0.16x=820$

Dividing both sides by 0.16 we get:

$x=5125.$

The hotel charge in first city before tax = $5125.

Now, substituting the value of $x$ in equation (1) we get:

$y=x-1500$

$y=5125-1500$

$y=3625.$

The hotel charge in second city before tax = $3625.

Therefore, the hotel charge in each city before tax was $5125 of the first city and $3625 of the second city.

5 0

4 years ago

Find the value of x then classify the triangle by its angles

kupik [55]

X = 72 and it's a scalene triangle

5 0

3 years ago

Simplify the ratio 24:135

kap26 [50]

The answer is 8:45. Enjoy!

5 0

4 years ago

Read 2 more answers