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-BARSIC- [3]
3 years ago
13

Heather finished the 12-kilometer race in 2 hours. If Heather kept her pace constant, what was her rate? A. 24 km/hr. B. 14 km/h

r. C. 10 km/hr. D. 6 km/hr.
Mathematics
1 answer:
andriy [413]3 years ago
7 0

Answer: D, 6km/hr.

Step-by-step explanation:

Heather can finish a 12-kilometer race in 2 hours, and now we have to find how many kilometers she can ride/run at in 1 hour.

How many hours can Heather run in 1 hour? To solve that, we can use the equation 12 ÷ 2.

12 ÷ 2 = 6.

Therefore, if Heather keeps her pace constant, then her rate will be 6km/hr, or D.

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EXAMPLE 5 If f(x, y, z) = x sin(yz), (a) find the gradient of f and (b) find the directional derivative of f at (1, 2, 0) in the
solong [7]

Answer:

<h2>a) f =  sin(yz)i + xzcos(yz)j + xycos(yz)k</h2><h2>b) -2</h2>

Step-by-step explanation:

Given f(x, y, z) = x sin(yz), the formula for calculating the gradient of the function is expressed as ∇f(x, y, z) = fx(x, y, z)i+ fy(x, y, z)j+fz(x, y, z)k where;

fx, fy and fz are the differential of the functions with respect to x, y and z respectively.

a) ∇f(x, y, z) = sin(yz)i + xzcos(yz)j + xycos(yz)k

The gradient of f =  sin(yz)i + xzcos(yz)j + xycos(yz)k

b) Directional derivative of f at (1,2,0) in the direction of v = i + 4j − k is expressed as ∇f(1, 2, 0)*v

∇f(1, 2, 0) = sin(2(0))i +1*0cos(2*0)j + 1*2cos(2*0)k

∇f(1, 2, 0) = sin0i +0cos(0)j + 2cos(0)k

∇f(1, 2, 0) = 0i +0j + 2k

Given v = i + 4j − k

∇f(1, 2, 0)*v (note that this is the dot product of the two vectors)

∇f(1, 2, 0)*v =  (0i +0j + 2k)*(i + 4j − k )

Given i.i = j.j = k.k =1 and i.j=j.i=j.k=k.j=i.k = 0

∇f(1, 2, 0)*v = 0(i.i)+4*0(j.j)+2(-1)k.k

∇f(1, 2, 0)*v = 0(1)+0(1)-2(1)

∇f(1, 2, 0)*v =0+0-2

∇f(1, 2, 0)*v= -2

 

Hence, the directional derivative of f at (1, 2, 0) in the direction of v = i + 4j − k is -2

7 0
3 years ago
Pine Bluff Middle School is having its annual Spring Fling dance, which will cost
Anon25 [30]
I think your asking  how much the school will have left over. If so:

125 ( not including the tickets)
It depends on how many kids are coming to the dance in order to fully solve this problem.

You didn't word this properly so that what I got with what I had:)

If you have anymore questions, ask me them on my profile so I'll be sure to get them:)

I hope this helps:)
3 0
3 years ago
A kitchen sink has a volume of 1800 cubic inches.What is the volume of a similar sink that is larger by a scale factor of 2
bonufazy [111]

Answer:

14400 cubic inches.

Step-by-step explanation:

Let l, b and h are length, breadth and height of a cuboid respectively, then

V=l\times b\times h

If another cuboid is larger by a scale factor of k, then kl, kb and kh are length, breadth and height of new cuboid respectively.

V_1=kl\times kb\times kh

V_1=k^3(l\times b\times h)

V_1=k^3V       ...(i)

It is given that a kitchen sink has a volume of 1800 cubic inches and a similar sink is larger by a scale factor of 2.

Substitute k=2 and V=1800 in equation (i).

V_1=2^3(1800)

V_1=14400

Therefore, the volume of required sink is 14400 cubic inches.

7 0
3 years ago
Help me with it plizz
Liono4ka [1.6K]
2x + 9 = -65
2x = -65 - 9
2x = -74
x = -74/2
x = -37

So, your final answer is -37

Hope this helps!

3 0
3 years ago
PLEASE HELP ASAP!! Will give brainliest!
Degger [83]
Hi there! 9.125 * 10^-3 is definitely less than 9.125 * 10^2, because when it comes to negative powers of 10, the numbers are decimals. 10^-3 equals 0.001 or one thousandths in word form. 10^2 is 100. When solving for the answers. 0.009125 is less than 912.5. When 912.5 is divided by 0.009125 912.5 is 100^5 or 100,000 times greater than 0.009125. The answer is that 9.125 * 10^-3 is 100,000 (100^5) times less than 9.125 * 10^2.
7 0
4 years ago
Read 2 more answers
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