A group of 13 kids went for a hike by the river. The number of kids who fell into

Using n for the variable, write an algebraic expression that represents a number that is divisible by the given number. (Hint: A

iris [78.8K]

Answer:

'5n' is the correct answer.

Step-by-step explanation:

Let 'n' be any integer i.e. a number from the set {....., -3,-2,-1,0,1,2,3, ..... }

so 'n' can be termed as the variable here because its value can change and can be any value from the above set.

A number 'q' that can be divided by a a given number 'p' can be written as:

$n \times p$

When divided by 'p' :

$\dfrac{q}p = \dfrac{n \times p}{p}\\\dfrac{q}p = n$

So, The number 'q' is completely divisible by 'p' leaving 'n' as the quotient.

Using this concept, let us solve the questions:

a) Using 'n' as the variable, a number that is divisible by 5 can be written as:

$5n$

Read more on Brainly.com - brainly.com/question/16919676#readmore

7 0

3 years ago

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

The measurement, y, varies directly with regard to another value, x. If y = 9 and x = 24, find x for y = 25. 9.4 50 66.7

ale4655 [162]

Answer:

<u>The correct answer is C. 66.7</u>

Step-by-step explanation:

1. y varies directly with regard to x

y = 9 and x = 24

If y = 25, what is the value of x?

2. For finding that value of x, first of all, we should understand what happened to y.

If y moves from 9 to 25 it means that y has been multiplied by 2.77, using this simple division

25/9 = 2.777

3. And we should use that same number or value to calculate the new value of x

If x was 24, now the new value of x is 24 * 2.777

24 * 2.777 = 66. 67 or 66.7 (rounding to just one decimal)

<u>The correct answer is C. 66.7</u>

4 0

3 years ago

The interest rate r required to increase your investment p to the amount a in t years is found by mc075-1.jpg. Find the interest

kotegsom [21]

I hope this is the answer :)
45.67=r

6 0

3 years ago

Read 2 more answers

Stacy was born in 1996.When she was, her brother was 7. What year was her brother born

Tasya [4]

Answer:

Her brother was born in 1989

Step-by-step explanation:

Since the brother was 7 when Stacy was born in 1996, all you have to do is subtract 7 from 1996 to get 1989 because thats when the brother would be zero years of age.

4 0

3 years ago

Read 2 more answers