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sweet-ann [11.9K]
3 years ago
6

Please help me with this!!!

Mathematics
1 answer:
RSB [31]3 years ago
4 0
The answer that you have is most likely right, since the grouping did not change.
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Daniel wants to predict how far he can hike based on the time he spends on the hike. He collected some data on the time (in hour
blagie [28]

Linear equation is equation in which each term has at max one degree. The function that can represent the given graph is y=2.0769x + 1.5.

<h3>What is linear equation?</h3>

Linear equation is equation in which each term has at max one degree. Linear equation in variable x and y can be written in the form y = mx + c

Linear equation with two variables, when graphed on Cartesian plane with axes of those variables, give a straight line.

For the given graph the equation can be written as, y = mx+c, this is because the graph is a line which means the relationship is linear. Therefore, the equation can be written as,

y = mx + c

Now, there are two points that are on the line and the coordinates of this points are,

A = (4, 9.5)

B = (7.25, 16)

Further the slope of the equation is,

m = (16-9.5) / (7.25 - 4) = 2.0769

Since c is the y-intercept of the graph, therefore, the value of c is 1.5.

Thus, the function that can represent the given graph is y=2.0769x + 1.5.

Learn more about Linear equations:

brainly.com/question/27465710

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5 0
2 years ago
there are 90 girls in third year, 25 of whom Study biology what percentage of third year girls study biology
Shtirlitz [24]

Answer:

27.7% of third year girls study biology

5 0
2 years ago
Find the function y1 of t which is the solution of 121y′′+110y′−24y=0 with initial conditions y1(0)=1,y′1(0)=0. y1= Note: y1 is
strojnjashka [21]

Answer:

Step-by-step explanation:

The original equation is 121y''+110y'-24y=0. We propose that the solution of this equations is of the form y = Ae^{rt}. Then, by replacing the derivatives we get the following

121r^2Ae^{rt}+110rAe^{rt}-24Ae^{rt}=0= Ae^{rt}(121r^2+110r-24)

Since we want a non trival solution, it must happen that A is different from zero. Also, the exponential function is always positive, then it must happen that

121r^2+110r-24=0

Recall that the roots of a polynomial of the form ax^2+bx+c are given by the formula

x = \frac{-b \pm \sqrt[]{b^2-4ac}}{2a}

In our case a = 121, b = 110 and c = -24. Using the formula we get the solutions

r_1 = -\frac{12}{11}

r_2 = \frac{2}{11}

So, in this case, the general solution is y = c_1 e^{\frac{-12t}{11}} + c_2 e^{\frac{2t}{11}}

a) In the first case, we are given that y(0) = 1 and y'(0) = 0. By differentiating the general solution and replacing t by 0 we get the equations

c_1 + c_2 = 1

c_1\frac{-12}{11} + c_2\frac{2}{11} = 0(or equivalently c_2 = 6c_1

By replacing the second equation in the first one, we get 7c_1 = 1 which implies that c_1 = \frac{1}{7}, c_2 = \frac{6}{7}.

So y_1 = \frac{1}{7}e^{\frac{-12t}{11}} + \frac{6}{7}e^{\frac{2t}{11}}

b) By using y(0) =0 and y'(0)=1 we get the equations

c_1+c_2 =0

c_1\frac{-12}{11} + c_2\frac{2}{11} = 1(or equivalently -12c_1+2c_2 = 11

By solving this system, the solution is c_1 = \frac{-11}{14}, c_2 = \frac{11}{14}

Then y_2 = \frac{-11}{14}e^{\frac{-12t}{11}} + \frac{11}{14} e^{\frac{2t}{11}}

c)

The Wronskian of the solutions is calculated as the determinant of the following matrix

\left| \begin{matrix}y_1 & y_2 \\ y_1' & y_2'\end{matrix}\right|= W(t) = y_1\cdot y_2'-y_1'y_2

By plugging the values of y_1 and

We can check this by using Abel's theorem. Given a second degree differential equation of the form y''+p(x)y'+q(x)y the wronskian is given by

e^{\int -p(x) dx}

In this case, by dividing the equation by 121 we get that p(x) = 10/11. So the wronskian is

e^{\int -\frac{10}{11} dx} = e^{\frac{-10x}{11}}

Note that this function is always positive, and thus, never zero. So y_1, y_2 is a fundamental set of solutions.

8 0
3 years ago
Is it true that if one of the factors is 0, the product is 1?​
kaheart [24]

Answer:

The Principle of Zero Products states that if the product of two numbers is 0, then at least one of the factors is 0. (This is not really new.) If ab = 0, then either a = 0 or b = 0, or both a and b are 0.

hope it helped

5 0
2 years ago
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timama [110]
There are 86 laptops
7 0
3 years ago
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