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3 years ago

If you multiplied the mystery number by 1000, the resulting number would have a 7 in the ones place.

Mathematics

1 answer:

ser-zykov [4K]3 years ago

8 0

The answer rounded to the nearest hundredth is 84.65.

Consider the number 84.647.

If we multiply this number by 1000, the result is 84647 which has 7 in its one's place.

Also, note that the value of the digit in the ones place is 4, which is half of 8, the value in the tenths place.

The remaining digit in the tenths place is 4.

Hence, the correct answer is 84.65 rounded to the nearest nundredth.

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Find dy/dx by implicit differentiation for ysin(y) = xcos(x)

tatyana61 [14]

Answer:

$\frac{dy}{dx}=\frac{\cos(x)-x\sin(x)}{\sin(y)+y\cos(y)}$

Step-by-step explanation:

So we have:

$y\sin(y)=x\cos(x)$

And we want to find dy/dx.

So, let's take the derivative of both sides with respect to x:

$\frac{d}{dx}[y\sin(y)]=\frac{d}{dx}[x\cos(x)]$

Let's do each side individually.

Left Side:

We have:

$\frac{d}{dx}[y\sin(y)]$

We can use the product rule:

$(uv)'=u'v+uv'$

So, our derivative is:

$=\frac{d}{dx}[y]\sin(y)+y\frac{d}{dx}[\sin(y)]$

We must implicitly differentiate for y. This gives us:

$=\frac{dy}{dx}\sin(y)+y\frac{d}{dx}[\sin(y)]$

For the sin(y), we need to use the chain rule:

$u(v(x))'=u'(v(x))\cdot v'(x)$

Our u(x) is sin(x) and our v(x) is y. So, u'(x) is cos(x) and v'(x) is dy/dx.

So, our derivative is:

$=\frac{dy}{dx}\sin(y)+y(\cos(y)\cdot\frac{dy}{dx}})$

Simplify:

$=\frac{dy}{dx}\sin(y)+y\cos(y)\cdot\frac{dy}{dx}}$

And we are done for the right.

Right Side:

We have:

$\frac{d}{dx}[x\cos(x)]$

This will be significantly easier since it's just x like normal.

Again, let's use the product rule:

$=\frac{d}{dx}[x]\cos(x)+x\frac{d}{dx}[\cos(x)]$

Differentiate:

$=\cos(x)-x\sin(x)$

So, our entire equation is:

$=\frac{dy}{dx}\sin(y)+y\cos(y)\cdot\frac{dy}{dx}}=\cos(x)-x\sin(x)$

To find our derivative, we need to solve for dy/dx. So, let's factor out a dy/dx from the left. This yields:

$\frac{dy}{dx}(\sin(y)+y\cos(y))=\cos(x)-x\sin(x)$

Finally, divide everything by the expression inside the parentheses to obtain our derivative:

$\frac{dy}{dx}=\frac{\cos(x)-x\sin(x)}{\sin(y)+y\cos(y)}$

And we're done!

5 0

3 years ago

Determine whether each statement is always sometimes or never true explain your reasoning

Aneli [31]

17) Sometimes true

Given only that a quadrilateral is a parallelogram, we can only conclude the opposite sides are congruent - not the adjacent sides

18) Always true

Adjacent angles of a parallelogram are supplementary.

19) Always true.

Opposite sides of a parallelogram are congruent.

20) Never true

Diagonals of a parallelogram bisect each other, meankng that MR = RP.

8 0

1 year ago

PLS HELP!!!!!!!!!!!!!!!!!!!!

docker41 [41]

Answer:

y = 2x

Step-by-step explanation:

plug in the x number of scooters to get cost y

multiply by two each time

hope this helps :)

6 0

3 years ago

Read 2 more answers

What is the surface area of the above composite object made out of two rectangular prisms?

aleksandrvk [35]

Answer:

550 mm^2

Step-by-step explanation:

A net can be drawn as shown in the first figure attached. Each square represents 5 mm by 5 mm, so is 25 mm^2. Altogether, there are 22 of them, so the total area is ...

(25 mm^2)·22 = 550 mm^2

The second attachment shows that net folded up to make the given figure.

_____

In the first attachment, the green shades represent the left- and right-side faces. (Darker green is left side.) The red and blue shades represent the front- and back-side faces. The white rectangles represent the top and bottom faces. The dark black lines are the cut lines. If you want to fold the figure up, the lighter lines are the fold lines.

The second attachment is just verification that all faces are accounted for and the net actually corresponds to the given figure.

4 0

3 years ago

Ippppppppppppppppppopkokhiufytedfliyhuigjboihlk.h

Lemur [1.5K]

Answer:

it b

Step-by-step explanation:

5 0

2 years ago