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Lilit [14]
3 years ago
14

5x-y=7

Mathematics
1 answer:
seropon [69]3 years ago
3 0

Answer:

see graph of y = 5x - 7

Step-by-step explanation:

If graphing is the task, you should rewrite the equation in a y = ax + b form. All straight lines can be described in this form, only the a and b determine which line it is.

Your equation 5x-y=7 has the 5x on the left side, so lets move it to the right. It will get a negative sign (this is the same as subtracting 5x like you did in your picture)

5x - y = 7

-y = 7 - 5x

Now we still have the -y which should be a +y. So we multiply left and right with -1 and get:

y = -7 + 5x

If we swap the -y and 5x (we can, because they are just an addition), we get:

y = 5x - 7

Now the equation is in its "normal" form. It's like the y = ax + b with a and b chosen as a=5 and b=-7.

The normal form is handy because you can immediately see the slope is 5 and the intersection with the y-axis is at y=-7.

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Two sides of a triangle are 8 m and 9 m in length and the angle between them is increasing at a rate of 0.06 rad/s. Find the rat
Lelechka [254]
<h2>Rate at which area is increasing is 1.08 m²/s.</h2>

Step-by-step explanation:

Area of triangle is with side a and b and angle C between them is given by

                             A = 0.5 ab SinC

Here we need to find how area changes with  a and b fixed and C is changing,

                       \frac{dA}{dt}=\frac{d}{dt}\left (0.5 absinC\right )\\\\\frac{dA}{dt}=0.5ab\frac{d}{dt}\left (sinC\right )\\\\\frac{dA}{dt}=0.5abcosC\frac{dC}{dt}

We have

                 a = 8 m

                 b = 9 m

                 C=\frac{\pi}{3}rad\\\\\frac{dC}{dt}=0.06rad/s

Substituting

                 \frac{dA}{dt}=0.5\times 8\times 9\times cos\left ( \frac{\pi}{3}\right )\times 0.06\\\\\frac{dA}{dt}=1.08m^2/s

Rate at which area is increasing is 1.08 m²/s.

4 0
3 years ago
How much energy in joules can the solar panel produce each day if solar cells were 100% efficient and generate 1000 watts of pow
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Answer:

The solar panel produce 6.48 × 10⁶ J of energy each day.

Step-by-step explanation:

If the solar cells were 100% efficient and generate 1000 watts of power per square meter

The power generated per square meter will be

\frac{100}{100} \times 1000 watts/m^{2}

= 1000 watts/m²

This is the power that would be generated per square meter if the solar cells were 100% efficient.

Now, for a 1 square meter panel of solar cells with an efficiency of 30%, the power generated will be

\frac{30}{100} \times 1000 watts/m^{2} \times 1m^{2}

= 300 watts

This is the power that would be generated by a 1 square meter panel of solar cells with an efficiency of 30%

Now, to determine the energy in joules (J) that the solar panel produce each day

We can determine the energy from the formula

Energy = Power × time

From the question, the solar cells receives the equivalent of 6 hours of direct sunlight per day, that is

Time = (6 × 60 × 60) secs = 21600 secs

Hence,

Energy = 300 watts × 21600 secs

Energy = 6480000 Joules

Energy = 6.48 × 10⁶ J

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