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Orlov [11]
3 years ago
12

Find the x and y intercepts. Write your answer as x = y = 2x + 5y = 10

Mathematics
1 answer:
Ann [662]3 years ago
6 0
The x-intercept is present where y = 0

2x + 5y - 10 = 0
2x - 10 = -5y
2x - 10 = -5(0)
2x = 10
x = 5

The y-intercept is present where x = 0

2x + 5y = 10
2x + 5y - 10 = 0
5y - 10 = -2(0)
5y = 10
y = 2
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15 POINTS!!!!!!! What is the equation of the line in slope-intercept form? Line on a coordinate plane. Line runs through points
suter [353]

Answer:

y=\frac{4}{3}x+4 is the equation of line in slope intercept form.

Step-by-step explanation:

Line runs through points begin ordered pair negative 3 comma 0 end ordered pair and begin ordered pair 0 comma 4.

First ordered pair: (-3,0)

Second ordered pair: (0,4)

We have two points and need to find equation of line in slope intercept form

\text{Slope (m)}=\dfrac{y_2-y_1}{x_2-x_1}

\text{Slope (m)}=\dfrac{4-0}{0-(-3)}=\dfrac{4}{3}

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Equation of line in slope intercept form:

y=mx+b

where, m=\frac{4}{3} and b=4

Required equation:

y=\frac{4}{3}x+4

Thus, y=\frac{4}{3}x+4 is the equation of line in slope intercept form.

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Find the general solution of the following ODE: y' + 1/t y = 3 cos(2t), t > 0.
Margarita [4]

Answer:

y = 3sin2t/2 - 3cos2t/4t + C/t

Step-by-step explanation:

The differential equation y' + 1/t y = 3 cos(2t) is a first order differential equation in the form y'+p(t)y = q(t) with integrating factor I = e^∫p(t)dt

Comparing the standard form with the given differential equation.

p(t) = 1/t and q(t) = 3cos(2t)

I = e^∫1/tdt

I = e^ln(t)

I = t

The general solution for first a first order DE is expressed as;

y×I = ∫q(t)Idt + C where I is the integrating factor and C is the constant of integration.

yt = ∫t(3cos2t)dt

yt = 3∫t(cos2t)dt ...... 1

Integrating ∫t(cos2t)dt using integration by part.

Let u = t, dv = cos2tdt

du/dt = 1; du = dt

v = ∫(cos2t)dt

v = sin2t/2

∫t(cos2t)dt = t(sin2t/2) + ∫(sin2t)/2dt

= tsin2t/2 - cos2t/4 ..... 2

Substituting equation 2 into 1

yt = 3(tsin2t/2 - cos2t/4) + C

Divide through by t

y = 3sin2t/2 - 3cos2t/4t + C/t

Hence the general solution to the ODE is y = 3sin2t/2 - 3cos2t/4t + C/t

3 0
3 years ago
The temperature inside a certain industrial machine at time t seconds after startup, for 0 < t < 10, is given by h(t) = 42
frutty [35]

Answer:

t= \frac{125}{38} s

Step-by-step explanation:

We are given the temperature inside the machine from startup until 10 seconds later, the formula is:

h(t)= 42 \cdot t +1 - 4\cdot t +2  (degrees \, C)

We want to know at what time t the temperature inside the machine will be equal to 128 °C.

So we set:

h(t)=128

42\cdot t+1-4\cdot t+2=128

Now, we rearrange the equation to keep terms with t on the left hand side and terms without t on the right hand side

42\cdot t-4\cdot t=128-1-2

and we simplify:

(42-4)\cdot t= 128-2-1= 125

38 \cdot t = 125

now it's easy to solve for t:

t=\frac{125}{38}

And thus we arrive to the solution.

5 0
3 years ago
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