All categories

3 years ago

Find the distance between points K and H.

Mathematics

1 answer:

Usimov [2.4K]3 years ago

6 0

Answer:

Step-by-step explanation:

K is the midpoint between 60 and 80.

Distance between 60 and 80 is,

80 - 60 = 20

Distance between K and H is,

20 / 2 = 10

You might be interested in

PLEASE HELP :D ( these are multi step equations )

AnnyKZ [126]

For the first problem the answer is -5/2

2x−7+10=−2

Step 1: Simplify both sides of the equation.
2x−7+10=−2
2x+−7+10=−2
(2x)+(−7+10)=−2

(Combine Like Terms)
2x+3=−2

Step 2: Subtract 3 from both sides.
2x+3−3=−2−3
2x=−5

Step 3: Divide both sides by 2.
2x/2=−5/2
x=−5/2

Answer:
x= -5/2

3 0

3 years ago

NO LINKS OR FILES!

Archy [21]

(a) If the particle's position (measured with some unit) at time t is given by s(t), where

$s(t) = \dfrac{5t}{t^2+11}\,\mathrm{units}$

then the velocity at time t, v(t), is given by the derivative of s(t),

$v(t) = \dfrac{\mathrm ds}{\mathrm dt} = \dfrac{5(t^2+11)-5t(2t)}{(t^2+11)^2} = \boxed{\dfrac{-5t^2+55}{(t^2+11)^2}\,\dfrac{\rm units}{\rm s}}$

(b) The velocity after 3 seconds is

$v(3) = \dfrac{-5\cdot3^2+55}{(3^2+11)^2} = \dfrac{1}{40}\dfrac{\rm units}{\rm s} = \boxed{0.025\dfrac{\rm units}{\rm s}}$

$\dfrac{-5t^2+55}{(t^2+11)^2} = 0 \implies -5t^2+55 = 0 \implies t^2 = 11 \implies t=\pm\sqrt{11}\,\mathrm s \imples t \approx \boxed{3.317\,\mathrm s}$

(d) The particle is moving in the positive direction when its position is increasing, or equivalently when its velocity is positive:

$\dfrac{-5t^2+55}{(t^2+11)^2} > 0 \implies -5t^2+55>0 \implies -5t^2>-55 \implies t^2 < 11 \implies |t|$

In interval notation, this happens for t in the interval (0, √11) or approximately (0, 3.317) s.

(e) The total distance traveled is given by the definite integral,

$\displaystyle \int_0^8 |v(t)|\,\mathrm dt$

By definition of absolute value, we have

$|v(t)| = \begin{cases}v(t) & \text{if }v(t)\ge0 \\ -v(t) & \text{if }v(t)$

In part (d), we've shown that v(t) > 0 when -√11 < t < √11, so we split up the integral at t = √11 as

$\displaystyle \int_0^8 |v(t)|\,\mathrm dt = \int_0^{\sqrt{11}}v(t)\,\mathrm dt - \int_{\sqrt{11}}^8 v(t)\,\mathrm dt$

and by the fundamental theorem of calculus, since we know v(t) is the derivative of s(t), this reduces to

$s(\sqrt{11})-s(0) - s(8) + s(\sqrt{11)) = 2s(\sqrt{11})-s(0)-s(8) = \dfrac5{\sqrt{11}}-0 - \dfrac8{15} \approx 0.974\,\mathrm{units}$

7 0

2 years ago

What is the exact distance from (-4, -2) to (4, 6)? (4 points)

ziro4ka [17]

Answer:

the answer is 12 points

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

How to do composition of functions

KengaRu [80]

<h2>If you rather have the link to get this info lmk!!</h2>

Example: f(x) = 2x+3 and g(x) = x2

"x" is just a placeholder. To avoid confusion let's just call it "input":

f(input) = 2(input)+3

g(input) = (input)2

Let's start:

(g º f)(x) = g(f(x))

First we apply f, then apply g to that result:

Function Composition - (g º f)(x) = (2x+3)2

What if we reverse the order of f and g?

(f º g)(x) = f(g(x))

First we apply g, then apply f to that result:

Function Composition - (f º g)(x) = 2x2+3

We get a different result! When we reverse the order the result is rarely the same. So be careful which function comes first.

<h2 />

5 0

3 years ago

Some one help ts also says explain ur thinking

AysviL [449]

Answer:

Step-by-step explanation:

Start off by explaining that u know this(don't use these exact word though :A composite number is a positive integer that can be formed by multiplying two smaller positive integers Equivalently. A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers.... I couldn't really see the whole page so this is what i could get for u.... Good luck

7 0

2 years ago