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defon
2 years ago
5

(Please help, quickly if possible.)

Mathematics
1 answer:
Step2247 [10]2 years ago
8 0

A scale factor is a contracting scale such that x < 1, where x is the scale factor.

For example, if the scale factor x is less than 1, then it must be decreasing in size, and thus be contracting in size.

But, if the scale factor is greater than 1, then it is expanding in size and increasing.

1) -5 is expanding. It is greater than one.

2) -1/4 is contracting. It is less than one.

3) 3.5 is expanding. It is greater than one.

4) 6/7 is contracting. It is less than one.

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Solve the area formula for h
White raven [17]

The answer is C: h = \frac{2A}{b}

Starting with the given formula for the area, A = 1/2hb, the first step is to isolate h by using the multiplicative inverse of b, which is \frac{1}{b} on both sides of the equation:

A(\frac{1}{b})  =  \frac{1}{2}hb* (\frac{1}{b})

The result will be:

\frac{A}{b} = \frac{1}{2}h

The last step is to use the multiplicative inverse of \frac{1}{2}, which is 2 or \frac{2}{1} to further isolate the variable <em>h </em>:

\frac{A}{b} (\frac{2}{1}) = (\frac{2}{1}) \frac{1}{2} h

The formula for h will be:

h = \frac{2A}{b}  which is the option C in your question.

4 0
3 years ago
A rock thrown vertically upward from the surface of the moon at a velocity of 36​m/sec reaches a height of s = 36t - 0.8 t^2 met
Verdich [7]

Answer:

a. The rock's velocity is v(t)=36-1.6t \:{(m/s)}  and the acceleration is a(t)=-1.6  \:{(m/s^2)}

b. It takes 22.5 seconds to reach the highest point.

c. The rock goes up to 405 m.

d. It reach half its maximum height when time is 6.59 s or 38.41 s.

e. The rock is aloft for 45 seconds.

Step-by-step explanation:

  • Velocity is defined as the rate of change of position or the rate of displacement. v(t)=\frac{ds}{dt}
  • Acceleration is defined as the rate of change of velocity. a(t)=\frac{dv}{dt}

a.

The rock's velocity is the derivative of the height function s(t) = 36t - 0.8 t^2

v(t)=\frac{d}{dt}(36t - 0.8 t^2) \\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'\\\\v(t)=\frac{d}{dt}\left(36t\right)-\frac{d}{dt}\left(0.8t^2\right)\\\\v(t)=36-1.6t

The rock's acceleration is the derivative of the velocity function v(t)=36-1.6t

a(t)=\frac{d}{dt}(36-1.6t)\\\\a(t)=-1.6

b. The rock will reach its highest point when the velocity becomes zero.

v(t)=36-1.6t=0\\36\cdot \:10-1.6t\cdot \:10=0\cdot \:10\\360-16t=0\\360-16t-360=0-360\\-16t=-360\\t=\frac{45}{2}=22.5

It takes 22.5 seconds to reach the highest point.

c. The rock reach its highest point when t = 22.5 s

Thus

s(22.5) = 36(22.5) - 0.8 (22.5)^2\\s(22.5) =405

So the rock goes up to 405 m.

d. The maximum height is 405 m. So the half of its maximum height = \frac{405}{2} =202.5 \:m

To find the time it reach half its maximum height, we need to solve

36t - 0.8 t^2=202.5\\36t\cdot \:10-0.8t^2\cdot \:10=202.5\cdot \:10\\360t-8t^2=2025\\360t-8t^2-2025=2025-2025\\-8t^2+360t-2025=0

For a quadratic equation of the form ax^2+bx+c=0 the solutions are

x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}

\mathrm{For\:}\quad a=-8,\:b=360,\:c=-2025:\\\\t=\frac{-360+\sqrt{360^2-4\left(-8\right)\left(-2025\right)}}{2\left(-8\right)}=\frac{45\left(2-\sqrt{2}\right)}{4}\approx 6.59\\\\t=\frac{-360-\sqrt{360^2-4\left(-8\right)\left(-2025\right)}}{2\left(-8\right)}=\frac{45\left(2+\sqrt{2}\right)}{4}\approx 38.41

It reach half its maximum height when time is 6.59 s or 38.41 s.

e. It is aloft until s(t) = 0 again

36t - 0.8 t^2=0\\\\\mathrm{Factor\:}36t-0.8t^2\rightarrow -t\left(0.8t-36\right)\\\\\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}\\\\t=0,\:t=45

The rock is aloft for 45 seconds.

5 0
3 years ago
Find the x - intercept of the graph of the equation
Alborosie

Answer:

ugh should i drop out

Step-by-step explanation:

5 0
3 years ago
85 points, please answer ASAP question below, my brain is hating me today, I feel like this is easy but I just can't get it
san4es73 [151]

Answer:

25

Step-by-step explanation:

420 - 45 = 375

375 / 15 = 25

5 0
3 years ago
Read 2 more answers
Please help me solve this and its about dot plots
Lubov Fominskaja [6]

Answer:

20

Step-by-step explanation:

Number of blue cars = 28

Number of dots in blue cars = 7

one dot  = 28÷ 7 = 4

One dot equals 4cars

Number of tan cars = 5*4 = 20

7 0
2 years ago
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