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emmasim [6.3K]
2 years ago
15

Jodie ran at an average speed of 8 km/h for 45 minutes. How far did she run in km?

Mathematics
1 answer:
kenny6666 [7]2 years ago
5 0

Answer:

6 km.

Step-by-step explanation:

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A ball is thrown up in the air, and it's height (in feet) as a function of time (in seconds) can be written as h(t) = -16t2 + 32
olga2289 [7]

Answer:

1) Using properties of the quadratic equation:

Here the height equation is:

h(t) = -16t^2 + 32t + 6

We can see that the leading coefficient is negative, this means that the arms of the graph will open downwards.

Then, the vertex of the quadratic equation will be the maximum.

Remember that for a general quadratic equation:

a*x^2 + b*x + c = y

the x-value of the vertex is:

x = -b/2a

Then in our case, the vertex is at:

t = -32/(2*-16) = 1

The maximum height will be the height equation evaluated in this time:

h(1) = -16*1^2 + 32*1 + 6 = 22

The maximum height is 22ft

2) Second method, using physics.

We know that an object reaches its maximum height when the velocity is equal to zero (the velocity equal to zero means that, at this point, the object stops going upwards).

If the height equation is:

h(t) = -16*t^2 + 32*t + 6

the velocity equation is the first derivation of h(t)

Remember that for a function f(x) = a*x^n

we have that:

df(x)/dx = n*a*x^(n-1)

Then:

v(t) = dh(t)/dt = 2*(-16)*t + 32 + 0

v(t) = -32*t + 32

Now we need to find the value of t such that the velocity is equal to zero:

v(t) = 0 = -32*t + 32

       32*t = 32

            t = 32/32 = 1

So the maximum height is at t = 1

(same as before)

Now we just need to evaluate the height equation in t = 1:

h(1) = -16*1^2 + 32*1 + 6 = 22

The maximum height is 22ft

4 0
3 years ago
If a person making $47,000 receives a 3% raise, how much money do they make now?
Firlakuza [10]

Answer:its 5

Step-by-step explanation:

d

3 0
3 years ago
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please help me answer these 3 questions correctly . u will get 30 pints if you do and the brainlest. please do not answer if you
stira [4]

Answer:

1

1

3

Step-by-step explanation:

6 0
2 years ago
Determine the range of the function graphed below.<br> Answer choices are below as well
Softa [21]

Answer:

The range of the function will be (- ∞, 4].

Step-by-step explanation:

See the graph attached.

Here we have to get the range of the graphed function.

The value of y in the graphed function varies in the range of less than or equal to 4.

Because the graph of the function does not move beyond 4 towards +∞.

Therefore, the range of the function will be (- ∞, 4]. (Answer)

5 0
3 years ago
X² + 9x +22 = 0 anyone know what this is
Mrrafil [7]
-7 i’m not completely sure though
8 0
3 years ago
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