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Pachacha [2.7K]
3 years ago
13

Line m passes through the points (-4.3) and (4.7). What is the slope of the line that is parallel to line m?

Mathematics
1 answer:
Savatey [412]3 years ago
4 0

Step-by-step explanation:

slope equals to change in y/change in x

slope=7-3/4+4

=4/8=1/2

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Solve in one variable<br> 2/3x + 5 = 3/2x
Montano1993 [528]
First, we group together the terms with variables in one side by subtracting 3/2 x and 5 from both sides of the equation.
                   (2/3)x - (3/2)x + 5 - 5 = (3/2)x - (3/2)x - 5
                         (-5/6)x = -5
The value of x from the equation is 6. 
5 0
3 years ago
Jamie is riding a Ferris wheel that takes fifteen seconds for each complete revolution. The diameter of the wheel is 10 meters a
Agata [3.3K]

Answer:

The answers to the question is

(a) Jamie is gaining altitude at 1.676 m/s

(b) Jamie rising most rapidly at t = 15 s

At a rate of 2.094 m/s.

Step-by-step explanation:

(a) The time to make one complete revolution = period T = 15 seconds

Here will be required to develop the periodic motion equation thus

One complete revolution = 2π,

therefore the  we have T = 2π/k = 15

Therefore k = 2π/15

The diameter = radius of the wheel = (diameter of wheel)/2 = 5

also we note that the center of the wheel is 6 m above ground

We write our equation in the form

y = 5*sin(\frac{2*\pi*t}{15} )+6

When Jamie is 9 meters above the ground and rising we have

9 = 5*sin(\frac{2*\pi*t}{15} )+6 or 3/5 = sin(\frac{2*\pi*t}{15} ) = 0.6

which gives sin⁻¹(0.6) = 0.643 =\frac{2*\pi*t}{15}

from where t = 1.536 s

Therefore Jamie is gaining altitude at

\frac{dy}{dt} = 5*\frac{\pi *2}{15} *cos(\frac{2\pi t}{15}) = 1.676 m/s.

(b) Jamie is rising most rapidly when   the velocity curve is at the highest point, that is where the slope is zero

Therefore we differentiate the equation for the velocity again to get

\frac{d^2y}{dx^2} = -5*(\frac{\pi *2}{15} )^2*sin(\frac{2\pi t}{15}) =0, π, 2π

Therefore -sin(\frac{2\pi t}{15} ) = 0 whereby t = 0 or

\frac{2\pi t}{15} = π and t =  7.5 s, at 2·π t = 15 s

Plugging the value of t into the velocity equation we have

\frac{dy}{dt} = 5*\frac{\pi *2}{15} *cos(\frac{2\pi t}{15}) = - 2/3π m/s which is decreasing

so we try at t = 15 s and we have \frac{dy}{dt} = 5*\frac{\pi *2}{15} *cos(\frac{2\pi *15}{15}) = \frac{2}{3} \pim/s

Hence Jamie is rising most rapidly at t = 15 s

The maximum rate of Jamie's rise is 2/3π m/s or 2.094 m/s.

7 0
3 years ago
Please solve B, C, D, E, and F and I will give Brainliest!
kykrilka [37]

Answer:

a. 125

b. 25/64

c. 0.25

d. 343

e. 49/4

f. 0.81

Step-by-step explanation:

multiply by the same number by the amount of times the power tells you

b. 5*5 = 25         8*8= 64

c. 5*5 = 25         0.5*0.5 = 0.25

d. 7*7*7 = 343

e. 7*7 = 49         2*2= 4

f. 9*9 = 81        0.9*0.9= 0.81

5 0
2 years ago
The perimeter of a rectangular field is 320320 yd. the length is 2020 yd longer than the width. find the dimensions.
hichkok12 [17]
The sum of length and width is half the perimeter, 160 yd. The length is the average of the sum and difference of dimensions:
.. (160 +20)/2 = 90
Then the width is 160 -90 = 70

The rectangular field is 70 yd by 90 yd.
6 0
3 years ago
What is the circumference of the circle use 3.24 for pi
never [62]

Step-by-step explanation:

Formula:

d×3.14=C

or

r×3.14×2=C

d=diameter

r=radius

5 0
3 years ago
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