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lesya [120]
3 years ago
10

A rectangle is 8 feet long. It’s width is represented by “seven plus x feet.” Which expression represents the area, in square fe

et, of the rectangle?

Mathematics
1 answer:
elena-s [515]3 years ago
3 0
A=8•(7+x)'

a=area

You multiply 7+x by 8 to get the area. This is the equation you need.

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Consider an object moving along a line with the given velocity v. Assume t is time measured in seconds and velocities have units
Yakvenalex [24]

Answer:

a) positive direction: t < 2s & t>6s   ; negative direction: 2s < t < 6s

b) 7 m

c) 71 m

Step-by-step explanation:

Given:

v(t) = 3t^2 -24t +36   [0 , 7]

Find:

a) The value of time when particle is moving in positive direction:

The change in direction of the particle can be determined by v(t) > 0

Hence,

                                    0 < 3t^2 -24t +36

                                    0 < t^2 - 8t + 12

                                    0 < (t - 2)*(t - 6)

                                    t < 2s  , t  > 6s  

The particle travels in positive direction in the interval t < 2s and t > 6s , While it travels in negative direction when 2s < t < 6s.

b) The displacement ds over the given interval [ 0 , 7 ]

                                  ds = integral (v(t)).dt

                                  ds = t^3 -12t^2 +36t

                                  ds = 7^3 -12*7^2 +36*7

                                  ds = 7 m

c) Total distance traveled in the interval:

                                 Total distance= ds(0-2) + ds(2-6) + ds(6-7)

                                 D = 2*(2^3 -12*2^2 +36*2) - 2*(6^3 -12*6^2 +36*6) + 7

                                 D = 2*32 - 2*0 + 7

                                 D = 71 m          

     

6 0
3 years ago
A bank account starts off with 2000 dollars in it and each week 100 dollars are added​
wariber [46]

Answer:

= 2100 is your answer

4 0
2 years ago
Read 2 more answers
Find the x-coordinates of the two points on the curve
scZoUnD [109]

Answer: x = {-2, 2}

<u>Step-by-step explanation:</u>

Tangent means it is touching. Find the intersection of the two equations.

Solve the linear equation for y, then set the two equations equal to each other.

4y=x+8\qquad \rightarrow \qquad y=\dfrac{x+8}{4}

\dfrac{x-1}{x}=\dfrac{x+8}{4}\\\\\\\text{Cross multiply and solve for x:}\\4(x-1)=x(x+8)\\4x-4=x^2+8x\\.\qquad 0=x^2+4x+4\\.\qquad 0=(x+2)^2\\.\qquad 0=x+2\\.\qquad x=-2

To find the next point that is parallel to the linear equation and tangent to the curve, we need to use the linear equation with slope (m) = \dfrac{1}{4} and unknown b.

Let's try b = 0, then the equation of the linear equation is: y=\dfrac{1}{4}x

Set the equations equal to each other and solve for x:

\dfrac{x-1}{x}=\dfrac{x}{4}\\\\\\4(x-1)=x^2\\4x-4=x^2\\.\qquad 0=x^2-4x+4\\.\qquad 0=(x-2)^2\\.\qquad 0=x-2\\.\qquad x=2

This works!!!  If it didn't work, we would have tried other values for b until we arrived at a solution.

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What is the volume of a right cylinder with a base diameter of 6 cm and a height of 5 cm?
miskamm [114]
It’s about 141.37. Here’s the equation: V=πr2h=π·32·5≈141.37167
7 0
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In the year 2001, a total of 7.2 million passengers took a cruise vacation. The global cruise industry has been growing at 9% pe
g100num [7]
<span>To find the number of passengers for the next year (2002), take the prior value (7.2 million) and multiply it by 1.09. This will give the predicted value for 2002. In this case, it would be (7,200,000 * 1.09 = 7.848 million). This would show that there is a predicted rise of 0.648 million passengers for the year 2002.</span>
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