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prisoha [69]
2 years ago
6

What is the equation of a line that contains the point (2,1) and is perpendicular to the line: y = 3x – 4?

Mathematics
1 answer:
jeka57 [31]2 years ago
8 0
Y = 3x - 4.....the slope here is 3. A perpendicular line will have a negative reciprocal slope. To find the negative reciprocal, u flip the slope and change the sign. So we will need a slope of -1/3...see how I flipped the slope of 3/1 and made it 1/3...and then changed the sign, making it -1/3.

y = mx + b
slope(m) = -1/3
(2,1)...x = 2 and y = 1
now we sub and find b, the y int
1 = -1/3(2) + b
1 = -2/3 + b
1 + 2/3 = b
3/3 + 2/3 = b
5/3 = b

so ur perpendicular equation is : y = -1/3x + 5/3
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Step-by-step explanation:

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3 years ago
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If a cup of coffee has temperature 97°C in a room where the ambient air temperature is 25°C, then, according to Newton's Law o
FinnZ [79.3K]

Answer:

The  average temperature  is T_{a} = 81.95^oC

Step-by-step explanation:

From the question we are told that

    The temperature of the coffee after time t is   T(t) =  25 + 72 e^{[-\frac{t}{45} ]}

Now the average temperature during the first 22 minutes i.e fro 0 \to  22minutes is mathematically evaluated as

              T_{a} =  \frac{1}{22-0}  \int\limits^{22}_{0} {25 +72 e^{[-\frac{t}{45} ]}} \, dx

               T_{a} = \frac{1}{22} [25 t  +  72 [\frac{e^{[-\frac{t}{45} ]}}{-\frac{1}{45} } ] ] \left| 22} \atop {0}} \right.

             T_{a} = \frac{1}{22} [25 t  - 3240e^{[-\frac{t}{45} ]} ] \left | 45} \atop {{0}} \right.

              T_{a} = \frac{1}{22} [25 (22)  - 3240e^{[-\frac{22}{45} ]}   - (- 3240e^{0} )]

            T_{a} = \frac{1}{22} [550  - 1987.12  +  3240]

          T_{a} = 81.95^oC

       

8 0
2 years ago
Omae wa sinderou nani (questions in the image btw)
Korvikt [17]

Let a be the number of hours worked at Job A and b the number of hours at Job B. Then

a+b=30

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7.5a+8b=234.50

From the first equation,

b=30-a

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7.5a+8(30-a)=234.50\implies-0.5a+240=234.50

\implies0.5a=5.50

\implies\boxed{a=11}

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3 years ago
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Anarel [89]

Answer:

y°= 51.30°

Step-by-step explanation:

Apply the formula for tangent of an angle

Tan Ф = opposite side length/adjacent side length

Tan y= 10/8

Tan y= 1.25

y° = tan⁻(1.25) = 51.34°

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gulaghasi [49]

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