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Alexeev081 [22]
3 years ago
10

The graph of 4x+12y=8 and y=Mx+5 are perpendicular. What is the value of m

Mathematics
1 answer:
Komok [63]3 years ago
8 0

Answer:

m=3

Step-by-step explanation:

we know that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

step 1

Find the slope of the given line

we have

4x+12y=8

isolate the variable y

12y=8-4x

y=\frac{2}{3}-\frac{1}{3}x

the slope of the given line is

m=-\frac{1}{3}

step 2

Find the slope m_2 of the perpendicular line to the given line

m_1*m_2=-1

m_1=-\frac{1}{3} ---> slope of the given line

(-\frac{1}{3})*m_2=-1

m_2=3

therefore

The value of m is

m=3

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Point A is located at negative 5 over 8 and point B is located at negative 2 over 8. What is the distance between points A and B
ki77a [65]
<h2>Answer:</h2>

Option: A is the correct answer.

A.  negative 5 over 8 minus negative 2 over 8 = negative 3 over 8; therefore, the distance from A to B is absolute value of negative 3 over 8 equals 3 over 8 units.

<h2>Step-by-step explanation:</h2>

The location of Point A is : A(-5/8)

and Point B is located at : B(-2/8)

We know that when two points lie over a number line then the distance between the two points is the absolute difference between the two points.

If A is located at a.

and B is located at b.

Then the distance between A and B is given by:

             |a-b|

Hence, here the distance between A and B is given by:

|\dfrac{-5}{8}-(\dfrac{-2}{8})|=|\dfrac{-5}{8}+\dfrac{2}{8}|=|\dfrac{-3}{8}|=\dfrac{3}{8}\\\\i.e.\\\\\text{Distance between A and B is}=\dfrac{3}{8}\ \text{units}

8 0
3 years ago
Read 2 more answers
How many mL of medication are needed to last 10 days if the dose of medication is 2.5 tsp TID (three times a day)?
rjkz [21]

Answer:

369.7 mL of medication

Step-by-step explanation:

How many mL of medication are needed to last 10 days if the dose of medication is 2.5 tsp TID (three times a day)?

From the above question,

The dosage of the medication =

2.5 tsp 3 times a day

= 2.5 × 3 = 7.5 tsp per day.

Since

1 day = 7.5 tsp

10 days = x tsp

Cross Multiply

x = 10 × 7.5 tsp

x = 75 tsp of medication for 10 days.

Step 2

It is important to note that:

1 tsp = 4.929 mL

75 tsp = x mL

Cross Multiply

x = 75 × 4.929 mL

x = 369.669 mL of medication

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7 0
2 years ago
Find, correct to four decimal places, the length of the curve of intersection of the cylinder 4x2 1 y2 − 4 and the plane x 1 y 1
charle [14.2K]

<u>Answer-</u> Length of the curve of intersection is 13.5191 sq.units

<u>Solution-</u>

As the equation of the cylinder is in rectangular for, so we have to convert it into parametric form with

x = cos t, y = 2 sin t   (∵ 4x² + y² = 4 ⇒ 4cos²t + 4sin²t = 4, then it will satisfy the equation)

Then, substituting these values in the plane equation to get the z parameter,

cos t + 2sin t + z = 2

⇒ z = 2 - cos t - 2sin t

∴ \frac{dx}{dt} = -\sin t

  \frac{dy}{dt} = 2 \cos t

  \frac{dz}{dt} = \sin t-2cos t

As it is a full revolution around the original cylinder is from 0 to 2π, so we have to integrate from 0 to 2π

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= \int_{0}^{2\pi}\sqrt{(\frac{dx}{dt})^{2}+(\frac{dy}{dt})^{2}+(\frac{dz}{dt})^{2}

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Now evaluating the integral using calculator,

=\int_{0}^{2\pi}\sqrt{(2\sin t)^{2}+(8\cos t)^{2}-(4\sin t\cos t) = 13.5191




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