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3 years ago

Use the graph of the function f(x) = x3 - 7x2 + 10x to identify its relative maximum and minimum.

Mathematics

1 answer:

Hoochie [10]3 years ago

6 0

Answer:

Step-by-step explanation:

hello :

f(x) = x3 - 7x2 + 10x

the derivate of f is : f'(x) =3x²-14x+10

sign of f'(x) : delta = b² - 4ac

a=3 b= -14 c=10

delta = (-14)² - 4(3)(10) = 176

you have two solution so its relative maximum and minimum.

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Solve y′′=sin(x) if y(0)=0 and y′(0)=5.<br><br> y(x)=?

Ksenya-84 [330]

Answer:

$y(x)=6x-sin(x)$

Step-by-step explanation:

Rewrite the differential equation as:

$\frac{d^{2} y }{dx^{2} } =sin(x)$

Integrate both sides with respect to x:

$\int\ \frac{d^{2} y }{dx^{2} } dx = \int\ sin(x) dx$

$\frac{dy}{dx} =-cos(x)+C_1$

Integrate one more time both sides with respect to x:

$\int\ \frac{dy}{dx} = \int\ -cos(x)+C_1 dx$

$y(x)=-sin(x)+C_1x+C_2$

Now that we find the solution, let's find its derivate:

$y'(x)=C_1-cos(x)$

Evaluating the initial conditions:

$y(0)=C_1(0)+C_2-sin(0)=0\\C_2=0$

$y'(0)=C_1-cos(0)=5\\C_1=5+1=6$

Replacing the value of the constants that we found in the differential equation solution:

$y(x)=6x-sin(x)$

6 0

3 years ago

How far up a wall will an 11 meter ladder reach, if the foot of the ladder must be 4 meters from the base of the wall? Round to

seraphim [82]

Use pythagorean theorem. 11m is the hypotenuse, while 4m is one of the legs. the wall should create a right angle with the ground which will allow for the pythagorean theorem. The height of where the ladder reaches will be named x.
x=<span>√11^2-4^2=10.25m.</span>

3 0

3 years ago

Read 2 more answers

Please fill in the final row (x)

Nata [24]

Answer:

x = 11

Step-by-step explanation:

The Frequency column has to total 50 ( number of rolls on dice )

Thus total the given frequencies and equate to 50, that is

12 + 8 + 7 + 3 + 9 + x = 50

39 + x = 50 ( subtract 39 from both sides )