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Ivanshal [37]
3 years ago
8

In a scale drawing, the width of a sofa is 15 cm. The actual width of the sofa is 150 cm. What is the scale of drawing?

Mathematics
2 answers:
melisa1 [442]3 years ago
6 0

Answer:

10 is the scale drawing.

Step-by-step explanation:

sesenic [268]3 years ago
4 0

Answer:

1 cm : 10 cm

Step-by-step explanation:

If you put this into fraction form (15/150) and divide the numerator and denominator by 15, you will get 1/10. This means that for every 1cm on the paper, the couch is actually 10cm long (in that place) in real life.

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Archy [21]

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

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

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

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}}

(c) The particle is at rest when its velocity is zero:

\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 <em>t</em> 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 <em>v(t)</em> > 0 when -√11 < <em>t</em> < √11, so we split up the integral at <em>t</em> = √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 <em>v(t)</em> is the derivative of <em>s(t)</em>, 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's the answer<br>what's the answer ​
Jet001 [13]

Answer:

a

Step-by-step explanation:

a

6 0
2 years ago
Read 2 more answers
Find 3 consecutive odd integers whose sum is 225, explain please
aleksklad [387]
3 odd integers have a property that they average up to the middle large one. Let's say we have 3, 5, and 7. 3 is 2 less than 5 and 7 is 2 more than 5. so when you add them it equals 2 times 5. 
After we know that, the sum of 3 odd integers is just 3 times the middle number. ex. 3+5+7 = 3 times 5 = 15
Then we know the some number times three = 225. we find out that the middle number is 75, so the other two are 73 and 77
5 0
3 years ago
I need help with this question, please answer
dimaraw [331]
The answer is 12 a this is how to solve it:
5a+3a+14+4(a-6)+10
5a+3a+14+4a-24+10
8a+14+4a-24+10
12a+14-24+10
12a-10+10
12a
7 0
3 years ago
3. Factor the following trinomial. x^2 - 15x + 56.
makkiz [27]

Answer:

(x-7) (x-8)

Step-by-step explanation:

Break the expression into groups:

= x(x-7) -8(x-7)

Factor out x from:

x^2-7x     x(x-7)

Factor out -8 from -8x+56:

-8(x-7)

=x\left(x-7\right)-8\left(x-7\right)

8 0
2 years ago
Read 2 more answers
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