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mart [117]
3 years ago
5

If it takes Tim 20 minutes to bike 6 miles, how many minutes will it take him to bike 144 miles?​

Mathematics
2 answers:
gogolik [260]3 years ago
4 0

Answer:

80 MINS  to bike 144 miles

Step-by-step explanation:

20=6 miles

144 divided by 6 = 24  

24 more miles to go

6 times 4 = 24 miles

20+20+20+20= 80

kari74 [83]3 years ago
3 0

Answer:

144/6 = 24

24 x 20 = 480

480 is the answer

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Use the Chain Rule (Calculus 2)
atroni [7]

1. By the chain rule,

\dfrac{\mathrm dz}{\mathrm dt}=\dfrac{\partial z}{\partial x}\dfrac{\mathrm dx}{\mathrm dt}+\dfrac{\partial z}{\partial y}\dfrac{\mathrm dy}{\mathrm dt}

I'm going to switch up the notation to save space, so for example, z_x is shorthand for \frac{\partial z}{\partial x}.

z_t=z_xx_t+z_yy_t

We have

x=e^{-t}\implies x_t=-e^{-t}

y=e^t\implies y_t=e^t

z=\tan(xy)\implies\begin{cases}z_x=y\sec^2(xy)=e^t\sec^2(1)\\z_y=x\sec^2(xy)=e^{-t}\sec^2(1)\end{cases}

\implies z_t=e^t\sec^2(1)(-e^{-t})+e^{-t}\sec^2(1)e^t=0

Similarly,

w_t=w_xx_t+w_yy_t+w_zz_t

where

x=\cosh^2t\implies x_t=2\cosh t\sinh t

y=\sinh^2t\implies y_t=2\cosh t\sinh t

z=t\implies z_t=1

To capture all the partial derivatives of w, compute its gradient:

\nabla w=\langle w_x,w_y,w_z\rangle=\dfrac{\langle1,-1,1\rangle}{\sqrt{1-(x-y+z)^2}}}=\dfrac{\langle1,-1,1\rangle}{\sqrt{-2t-t^2}}

\implies w_t=\dfrac1{\sqrt{-2t-t^2}}

2. The problem is asking for \frac{\partial z}{\partial x} and \frac{\partial z}{\partial y}. But z is already a function of x,y, so the chain rule isn't needed here. I suspect it's supposed to say "find \frac{\partial z}{\partial s} and \frac{\partial z}{\partial t}" instead.

If that's the case, then

z_s=z_xx_s+z_yy_s

z_t=z_xx_t+z_yy_t

as the hint suggests. We have

z=\sin x\cos y\implies\begin{cases}z_x=\cos x\cos y=\cos(s+t)\cos(s^2t)\\z_y=-\sin x\sin y=-\sin(s+t)\sin(s^2t)\end{cases}

x=s+t\implies x_s=x_t=1

y=s^2t\implies\begin{cases}y_s=2st\\y_t=s^2\end{cases}

Putting everything together, we get

z_s=\cos(s+t)\cos(s^2t)-2st\sin(s+t)\sin(s^2t)

z_t=\cos(s+t)\cos(s^2t)-s^2\sin(s+t)\sin(s^2t)

8 0
3 years ago
A sum of money was to be shared among three friends,Albert,Micheal,Moses in the ratio 3:5:6.if Micheal receives $45,find the sum
kirza4 [7]

Answer:

The sum of the money shared is $1372

Step-by-step explanation:

The given ratio is

Albert:Michael:Moses=3:5:6

The total ratio is 3+5+6=14

Let the sum of money shared be $x.

Then Albert's share = 3/14 x x = 3x/ 14

Michal's Share   = 5x/14

If Michael received $196 more than Albert, then the difference between their share is the $196.

7 0
3 years ago
A is an m×n matrix.Check the true statements below:A. The kernel of a linear transformation is a vector space.B. If the equation
Bess [88]

Answer:

Results are (1) True. (2) False. (3) False. (4) True. (5) True. (6) True.

Step-by-step explanation:

Given A is an m\times n matrix.  Let T :U\to V  be the corresponding linear transformationover the field F and \theta be identity vector in V. Now if x\in Ker( T)\implies T(x)=\theta.

(1) The kernel of a linear transformation is a vector space : True.

Let x,y\in Ker( T), then,

T(x+y)=T(x)+T(y)=\theta+\theta=\theta\impies x+y\in Ker( T)

hence the kernel is closed under addition.

Let \lambda\in F, x\in Ker( T), then

T(\lambda x)=\lambda T(x)=\lambda\times \theta=\theta

\lambda x\in Ker(T) and thus Ket(T) is closed under multiplication

Finally, fore all vectors u\in U,

T(\theta)=T(\theta+(-\theta))=T(\theta)+T(-\theta)=T(\theta)-T(\theta)=\theta

\implies \theta\in Ker(T)

Thus Ker(T) is a subspace.

(2) If the equation Ax=b is consistent, then Col(A) is \mathbb R^m : False

if the equation Ax=b is consistent, then Col(A) must be consistent for all b.

(3) The null space of an mxn matrix is in \mathbb R^m

: False

The null space that is dimension of solution space of an m x n matrix is always in \mathbb R^n.

(4) The column space of A is the range of the mapping x\to Ax

: True.

(5) Col(A) is the set of all vectors that can be written as Ax for some x. : True.

Here Ax will give a linear combination of column of A as a weights of x.

(6) The null space of A is the solution set of the equation Ax=0.

: True

5 0
3 years ago
100 POINTS FOR BRAINLIEST! according to the image, whats the answer? Answer wisely for the full 100
lesantik [10]

Answer:

Step-by-step explanation:

To find the area of a semicircle the formula is

\frac{\pi r^2}{2} \\=\frac{\pi 1^2}{2} \\=6.283m^2

The square

A=a^2=2^2=4m^2\\6.283+4=10.283m^2

A=wl=7*9=63m^2 (rectangle)

A=\frac{ab}{2} =\frac{6*4.5}{2} =13.5m^2\\63+13.5=76.5m^2 (triangle)

5 0
3 years ago
Read 2 more answers
What is the simplified form of 15 x to the eighth power over 24 y to the fifth power divided by 4 x to the fourth power over 8 s
IRISSAK [1]
The exponent symbol when typing is ^. so I so rewrite this for you.
(15x^8 / 24y^5) / (4x^4 / 8y^2)

I assumed you meant 8y squared because you said 8 squared.

now when we divide by a fraction, we can actually multiply by it's reciprocal and get the same thing. The word reciprocal really just means flip it over. so:

(15x^8 / 24y^5) * (8y^2 / 4x^4)

let's reduce the coefficients ( the numbers in front of the x and y) to make it easier.

We have 15/24 which can be reduced to 5/8
and 8/4 which is 2/1

so:
(5x^8 / 8y^5) * (2y^2 / x^4)

multiply numerator and denominator
(10x^8y^2) / (8x^4y^5)

now reduce coeffient. 10/8 is 5/4
reduce x: x^8/x^4 is x^4
reduce y: y^2/y^5 is 1/y^3

now put together
5x^4 / 4y^3

so C
3 0
3 years ago
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