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Citrus2011 [14]
4 years ago
5

Plot the points a (-2,-3), b (-3,0), c (3,2), and d (4,-1). What type of quadrilateral is ABCD? Justify your answer using slope

formula.
Mathematics
1 answer:
jenyasd209 [6]4 years ago
6 0
<span>Plot the points a (-2,-3), b (-3,0), c (3,2), and d (4,-1). What type of quadrilateral is ABCD? Justify your answer using slope formula 

 the shape is a parellelogram, not a trapezoid all are parellel, but how to distinguish rhombus, rectangle, and square?</span> 
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3 years ago
Find f. f ″(x) = x^−2, x &gt; 0, f(1) = 0, f(6) = 0
marin [14]

If you do in fact mean f(1)=f(6)=0 (as opposed to one of these being the derivative of f at some point), then integrating twice gives

f''(x) = -\dfrac1{x^2}

f'(x) = \displaystyle -\int \frac{dx}{x^2} = \frac1x + C_1

f(x) = \displaystyle \int \left(\frac1x + C_1\right) \, dx = \ln|x| + C_1x + C_2

From the initial conditions, we find

f(1) = \ln|1| + C_1 + C_2 = 0 \implies C_1 + C_2 = 0

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Eliminating C_2, we get

(C_1 + C_2) - (6C_1 + C_2) = 0 - (-\ln(6))

-5C_1 = \ln(6)

C_1 = -\dfrac{\ln(6)}5 = -\ln\left(\sqrt[5]{6}\right) \implies C_2 = \ln\left(\sqrt[5]{6}\right)

Then

\boxed{f(x) = \ln|x| - \ln\left(\sqrt[5]{6}\right)\,x + \ln\left(\sqrt[5]{6}\right)}

3 0
2 years ago
An airplane travels at 150 miles per hour. The total distance traveled is 637.5 miles. Which equation should be solved to determ
OverLord2011 [107]
The distance (d) traveled by the airplane is the product of multiplying the speed (s) and the trip took (h). The equation is shown below, 
                                           d = s x h
Substitute the known values to the equation, 
                                       637.5 miles = (150 mile/ hour) x h
Manipulating the equation,
                                       h = (637.5 miles) / (150 mile/ hr) 
h is equal to 4.25 hours. 
8 0
3 years ago
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