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Sladkaya [172]
3 years ago
6

Jason and Nick were biking at a constant speed of 10 seconds, Jason biked 30 meters and Nick biked 45 meters. Who was biking at

a faster rate?
Mathematics
1 answer:
Contact [7]3 years ago
6 0

Answer:

Nick

Step-by-step explanation:

Find their rates by dividing the number of meters they biked by 10:

Jason:

30/10

= 3 meters/sec

Nick:

45/10

= 4.5 meters/sec

So, since 4.5 is bigger than 3, Nick was biking at a faster rate.

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A factory made 357,945 baseball bats over the last 2 years. During that time, the factory made 490,867 little league baseballs a
mojhsa [17]

Answer:

522,761 baseballs

Step-by-step explanation:

Number of baseball bats produced over the last 2 years = 357, 945

Number of little league baseballs produced over the last 2 years = 490,867

Number of major league baseballs produced over the last 2 years = 389,839

Total number of baseballs produced over the period = 490,867 + 389,839

                                                                                         = 880,706

Number of baseballs manufactured more than bats = 880,706 - 357945

                                                                                      = 522,761

There are 522,761 baseballs produced more than bats during the 2 years.

8 0
3 years ago
Let S be the surface defined by x 2 + 2y 3 + 3z 4 = 6. Let T be the surface defined parametrically by r(u, v) = (1+ln u, 2e v+u−
aleksandrvk [35]

The tangent to C through (1, 1, 1) must be perpendicular to the normal vectors to the surfaces S and T at that point.

Let f(x,y,z)=x^2+2y^3+3z^4. Then S is the level curve f(x,y,z)=6. Recall that the gradient vector is perpendicular to level curves; we have

\nabla f(x,y,z)=(2x,6y,12z^2)

so that the gradient of f at (1, 1, 1) is

\nabla f(1,1,1)=(2,6,12)

For the surface T, we have

\begin{cases}1+\ln u=1\\2e^v+u-2=1\\uv+1=1\end{cases}\implies u=1,v=0

so that \vec r(1,0)=(1,1,1). We can obtain a vector normal to T by taking the cross product of the partial derivatives of \vec r(u,v), and evaluating that product for u=1,v=0:

\dfrac{\partial\vec r}{\partial u}\times\dfrac{\partial\vec r}{\partial v}=\left(u-2ve^v,-1,\dfrac{2e^v}u\right)

\left(\dfrac{\partial\vec r}{\partial u}\times\dfrac{\partial\vec r}{\partial v}\right)(1,0)=(1,-1,2)

Now take the cross product of the two normal vectors to S and T:

(2,6,12)\times(1,-1,2)=(24,8,-8)

The direction of vector (24, 8, -8) is the direction of the tangent line to C at (1, 1, 1). We can capture all points on the line containing this vector by scaling it by t\in\Bbb R. Then adding (1, 1, 1) shifts this line to the point of tangency on C. So the tangent line has equation

\vec\ell(t)=(1,1,1)+t(24,8,-8)=(1+24t,1+8t,1-8t)

7 0
3 years ago
A circle has center O(−2, −4) and radius 10. Which of the following points is on the circle? V(8, −4) X(5, −2) Y(−6, 0) Z(5, 7)
vladimir2022 [97]
Imma go for V(8,-4) on the circle.
6 0
3 years ago
True or false <br> cos(65 degrees) = sqrt 1+cos(130 degrees)/2
Snezhnost [94]
False is the correct answer
5 0
3 years ago
Is 8 and 45 a domain of integers from 0 to 5
Thepotemich [5.8K]

Answer:

yes

Step-by-step explanation:

7 0
2 years ago
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