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3 years ago

Which of the following is the equation of a line parallel to the line y = 3x + 2,

Mathematics

1 answer:

earnstyle [38]3 years ago

3 0

Answer:

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 3x + 2 is in this form with slope m = 3

• Parallel lines have equal slopes, hence

y = 3x + c ← is the partial equation of the parallel line

To find c substitute (10, 1) into the partial equation

1 = 30 + c ⇒ c = 1 - 30 = - 29

y = 3x - 29 ← in slope- intercept form

Subtract y from both sides

0 = 3x - y - 29 ( add 29 to both sides )

29 = 3x - y, thus

3x - y = 29 ← in standard form → B

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3 years ago

cylinder shaped can needs to be constructed to hold 200 cubic centimeters of soup. The material for the sides of the can costs 0

Dafna11 [192]

Answer:

Radius=2.09 cm

Height,h=14.57 cm

Step-by-step explanation:

We are given that

Volume of cylinderical shaped can=200 cubic cm.

Cost of sides of can=0.02 cents per square cm

Cost of top and bottom of the can =0.07 cents per square cm

Curved surface area of cylinder= $2\pi rh$

Area of circular base=Area of circular top= $\pi r^2$

Total cost,C(r)= $0.02\times 2\pi rh+2\pi r^2\times 0.07$

Volume of cylinder, $V=\pi r^2 h$

$200=\pi r^2 h$

$h=\frac{200}{\pi r^2}$

Substitute the value of h

$C(r)=0.02\times 2\pi r\times \frac{200}{\pi r^2}+2\pi r^2\times 0.07$

$C(r)=\frac{8}{r}+0.14\pi r^2$

Differentiate w.r.t r

$C'(r)=-\frac{8}{r^2}+0.28\pi r$

$C'(r)=0$

$-\frac{8}{r^2}+0.28\pi r=0$

$0.28\pi r=\frac{8}{r^2}$

$r^3=\frac{8}{0.28\pi}=9.095$

$r=(9.095)^{\frac{1}{3}}=2.09$

Again, differentiate w.r.t r

$C''(r)=\frac{16}{r^3}+0.28\pi$

Substitute the value of r

$C''(2.09)=\frac{16}{(2.09)^3}+0.28\pi=2.63>0$

Therefore,the product cost is minimum at r=2.09

h= $\frac{200}{\pi (2.09)^2}=14.57$

Radius of can,r=2.09 cm

Height of cone,h=14.57 cm

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3 years ago

The weights, in pounds, for 15 horses in a stable were

sweet-ann [11.9K]

The median value remains unchanged if the four values are reported using the corrected weight.

The correct answer is an option (B)

We know that the mean is calculated by finding the sum of all the weights of the horses and then dividing by the number of horses.

Decreasing one of the weights would decrease the sum and therefore decrease the mean.

So, the choice A is incorrect.

We know that the range is the difference between the highest and lowest weights, so decreasing the lowest weight would increase the range.

So, the choice C is incorrect.

We know that the Standard deviation is calculated based on the mean weight of the horses.

And decreasing one of the weights decreases the mean and therefore would affect the standard deviation.

So, the choice D is incorrect.

Now, as we know the median the middle value in a sorted, ascending or descending list of values.

So, the median weight is found by ordering the horses’ weights from least to greatest and then determining the middle value from this list of weights.

Decreasing the value for the horse with the lowest weight doesn’t affect the median since it’s still the lowest value.

Therefore, the median value remains unchanged if the four values are reported using the corrected weight.

The correct answer is an option (B)

Learn more about the median here:

brainly.com/question/28060453

#SPJ4

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