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3 years ago

Can someone help me with this question

Mathematics

1 answer:

Talja [164]3 years ago

7 0

Answer:

Step-by-step explanation:

from the attached diagram, we can see that

LN = MP

3x + 1 = 8x -4

8x-3x = 1 + 4

5x = 5

x = 1

hence

LN = 3x+ 1 = 3(1) + 1 = 4

NM = 4x-1 = 4(1) - 1= 3

hence by Pythagorean formula,

diagonal NP = diagonal LM = √( 3² + 4²) = √25 = 5

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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

22+n=−12 pls help me im kinda confused

Ede4ka [16]

Answer:

-34

Step-by-step explanation:

22+n=-12

n=-12-22

n=-34

When you bring a positive constant to the other side of the equal sign it goes negative and vise versa. Then you combine like terms.

Please follow me!!!! Hope this helps!!! Have a wonderful day :)

3 0

3 years ago

On a fruit farm 1/3 of the trees are apple trees and 1/5 are lemon trees. The rest are fig trees. There are 90 trees in all.

Vaselesa [24]

Answer:

I'm not sure what the question was but I've worked out all the three types of trees

Step-by-step explanation:

⅓ + ⅕ = 8/15 because:

×5 ×3

5/15 + 3/15 = 8/15

therefore 7/15 is fig trees

90÷15 =6

6×5 = 30 apple trees

6×3 = 18 lemon trees

6×7 = 42 fig trees

7 0

3 years ago

PLEASE HELP!! WILL GIVE BRAINLIEST!!

schepotkina [342]

Answer:

Please find attached pdf

Step-by-step explanation:

Download pdf

6 0

3 years ago

How long have the nashville predators been a team?

olganol [36]

This is the Internet. It's really easy to look up.

3 0

4 years ago