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3 years ago

Find the slope of a line that passes through the points (4, -2) and (6, -8).

Mathematics

1 answer:

zavuch27 [327]3 years ago

6 0

Answer:

-3

Step-by-step explanation:

slope=(y2-y1)/(x2-x1)

slope=(-8-(-2))/(6-4)=-3

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Please help asap 25 pts

Kazeer [188]

$s=12\sqrt{4t}+10$

$for\ x=0\to y=12\sqrt{4\cdot0}+10=12\sqrt0+10=10\\for\ x=1\to y=12\sqrt{4\cdot1}+10=12\sqrt4+10=12\cdot2+10=34\\for\ x=4\to y=12\sqrt{4\cdot4}+10=12\sqrt{16}+10=12\cdot4+10=58\\for\ x=6\to y=12\sqrt{4\cdot6}+10=12\cdot2\sqrt6+10=24\sqrt6+10\approx69\\for\ x=10\to y=12\sqrt{4\cdot10}+10=12\cdot2\sqrt{10}+10=24\sqrt{10}+10\approx86\\for\ x=12\to y=12\sqrt{4\cdot12}+10=12\cdot4\sqrt3+10=48\sqrt3+10\approx93$

$\underline{x|\ 0|\ 1\ |\ 4|\ 6\ |10|12|}\\y|10|34|58|69|86|93|$

$\text{The graph in attachment}$

$\boxed{Answer:\ about\ \$93,000}$

3 0

3 years ago

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

DONT SKIP PLZ

irinina [24]

Answer:

The first one: 3.2 units

3 0

3 years ago

Read 2 more answers

Angle Measurements

Naddik [55]

Answer:

X = 11

Complementary angles

Step-by-step explanation:

Complementary angles are when two angles add up to 90 degrees.

3x + 10 + 47 = 90

3x + 10 = 43

3x = 33

x = 11

4 0

3 years ago

Please help me it is an easy question

Ugo [173]

Answer:

200 yd²

Step-by-step explanation:

A = 17 yd

B = 15 yd

C = 2 yd

D = 8 yd

b) Area of rectangle = length * width

$\sf Area \ of \ 2 \ triangle = 2* \dfrac{1}{2}* base * height = base* height\\\\$

Area of right triangular prism = Areas of two triangle + area of the upper rectangle + area of middle rectangle + area of below rectangle

= 8 * 15 + 17 * 2 + 15 *2 + 8*2

= 120 + 34 + 30 + 16

= 200 yd²

5 0

2 years ago