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qwelly [4]
3 years ago
11

Find the equation of a line that is perpendicular to y=−12x−1 and passes through the point (3,2).

Mathematics
1 answer:
Afina-wow [57]3 years ago
4 0

Answer:

y = (1/12)*x + 7/4

Step-by-step explanation:

y=−12x−1

Perpendicular line:

y = a*x + b

y = (1/12)*x + b

2 = (1/12) * 3 + b

2 = (3/12) + b

2 = 1/4 + b

2 - 1/4 = b

7/4 = b

Perpendicular line:

y = (1/12)*x + 7/4

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Emily is observing the velocity of a cyclist at different times. After four hours, the velocity of the cyclist is 14 km/h. After
lina2011 [118]
Assume that Emily starts from rest so that the velocity is zero at 0 hours.

Define the function v(t) for velocity in km/h, and t in hours.

Part A
From t=0 to t=4, v changes from 0 to 14.
Let v(t) = mt + b
The slope is
  m = 14/4 = 3.5, and the y-intercept is
  b = 0.
Therefore
v(t) = 3.5t,  for 0 ≤ t ≤ 4

Fromt=4 to t=9,  changes from 14 to 4.
Let v(t) = mt + b
The slope is
  m = (4 - 14)/(9 - 4) = -2
Therefore
  v = -2t + b
When t=4, v=14, therefore
 14 = -2*4 + b = -8 + b
 22 = b
v(t) = -2t + 22, for 4 < t ≤ 9.

Answer:
The equation for the velocity is
v(t) = 3.5t,  0 ≤ t ≤ 4
      = -2t + 22,  4 < t ≤ 9

Part B
The equation for velocity is a piecewise function that is graphed as shown below. If we assume that the second part of the equation is valid at t=10, then
v(10) = -2*10 + 22 = 2 km/h

3 0
3 years ago
Mario has a box of blocks 8 inches long, 6 inches wide, and 7 inches high.
Aleksandr [31]

Answer:

Volume = length× width× height

v=lwh

v=8×6×7

v=48×7

v= 336inches

3 0
3 years ago
Find the area of an equilateral triangle with apothem 7 cm.
lbvjy [14]
So hmm check the picture below

using the 30-60-90 rule, we get that much.. .bear in mind, an equilateral triangle has all equal sides, and therefore, all equal angles, so each angle is 60°, run a median through it from the center, and you split it in half

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8 0
3 years ago
Find the value of x for which m ll n
Nikitich [7]
Set the expressions equal to each other to get 17
3 0
3 years ago
Applying Properties of Exponents In Exercise,use the properties of exponents to simplify the expression.
vitfil [10]

Answer:

(A) e^2

(b) e^{-3}

(c) e^2

(d) e^3

Step-by-step explanation:

We have given expression and we have to simplify the expression using exponent property

(A) (\frac{1}{e})^{-2}

So (\frac{1}{e})^{-2}=\frac{1}{e^{-2}}=e^2

(b) (\frac{e^5}{e^2})^{-1}

So (\frac{e^5}{e^2})^{-1}=(e^{3})^{-1}=e^{-3}

(c) \frac{e^5}{e^3}

So \frac{e^5}{e^3}=e^2

(d) \frac{1}{e^{-3}}=e^3

7 0
3 years ago
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