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3 years ago

Identify an equation in point slope form for the line parallel to y=1/2x-7 that passes through (-3,-2)

Mathematics

1 answer:

ANTONII [103]3 years ago

4 0

Answer:

Step-by-step explanation:

The point slope form of a straight line is expressed as

y - y1 = m(x - x1)

Where

m represents slope of the line

y1 represents the initial value of y

x1 represents the initial value of x

If two lines are parallel, it means that they have the same slope. From the equation of the given line, slope = 1/2

Therefore,

m = 1/2

x1 = - 3

y1 = - 2

Substituting into the point slope equation, it becomes

y - - 2 = 1/2(x - - 3)

y + 2 = 1/2(x + 3)

The equation is

y + 2 = 1/2(x + 3)

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3 years ago

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A potential energy function is given by U = A x3 + B x2 − C x + D . For positive parameters A, B, C, D this potential has two eq

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Answer:

7.8655

Step-by-step explanation:

Given the functionl

$U=Ax^3+Bx^2-cx+D$

Where,

$A=1.45J/m^3\\B=2.85J/m^2\\c= 1.7J/m\\D=0.6J$

We have, replacing,

$U=1.45x^3+2.85x^2-1.7x+0.6$

We need to derivate and verify for stable equilibrum that,

$\frac{d^2 U}{dx^2}>0$

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$U'(x) = 4.32x^2+5.7x-1.7$

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$x_1=-1.57008\\x_2=0.250636$

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$\frac{d^2U}{dx}=8.64x+5.7$

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3 years ago

Mr. Whitman gave a test to his 32 math students. He felt the results were low, so he retested them one week later. The results o

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The number of student more passed the retake, when the students need a 65 in order to pass the test is 8.

<h3>What is box and whiskers plot?</h3>

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A.The difference in the median grade-

The median of first test is 60 while the second test is 80. Thus, the difference is,

$d=80-60\\d=20$

B. Compare the percent of students who got at least a 60 on the original test to those that got at least a 60 on the retake.

The student, who got at least 60 in first test, falls in the second half of the plot. Thus, the 50% of students got atleast 60% marks. In the retake test, all 100% student got at least 60 on test.

C. If the students need a 65 in order to pass the test, how many more passed the retake?

In the first test 1/4 are passed while in second test 3/4 students are passed and got the marks 65 or more than this, Thus the number of student pass more in this test,

$n=(\dfrac{3}{4}-\dfrac{1}{2})\times 32\\n=8$