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3 years ago

If f'(x) = cos(3^x), then the smallest value of x for which f has a relative maximum is:

Mathematics

1 answer:

anastassius [24]3 years ago

8 0

Answer:

A 0.411

Step-by-step explanation:

A graph of f'(x) is negative-going at its first zero-crossing of about x=0.411. Thus, this point where the derivative is zero corresponds to a local maximum.

_____

There are no zero crossings for negative values of x. The curve asymptotically approaches y=1.

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What is the rate of change for the function f(x)=2x-3

Stolb23 [73]

Answer:

Step-by-step explanation:

f(x) = 2x - 3 is a linear function

The rate of change of a linear function is the measure of the slope.

The equation is in slope- intercept form, that is

y = mx + c ( m is the slope and c the y- intercept )

y = 2x - 3 has slope m = 2

Thus rate of change = 2

4 0

3 years ago

A bridge in the shape of an arch connects two cities separated by a river. The two ends of the bridge are located at (–7, –13) a

sdas [7]

Answer:

$y=-\dfrac{13}{49}x^2$

Step-by-step explanation:

The shape of an arch corresponds to a parabola.

the general equation for a parabola is:

$y=ax^2+bx+c$

we're given three coordinates: (-7,-13),(7,-13) and (0,0)

so we can plug these values in the general equation to make 3 separate equations:

(x,y) = (-7,-13)

$-13=a(-7)^2+b(-7)+c$

$49a-7b+c=-13$

(x,y) = (7,-13)

$-13=a(7)^2+b(7)+c$

$49a+7b+c=-13$

(x,y) = (0,0)

$0=a(0)^2+b(7)+c$

$c=0$

so we have three equations. and we can solve them simultaneously to find the values of a,b, and c.

we've already found c = 0, let's use substitute it to other equations.

$49a-7b+c=-13\quad\Rightarrow\quad49a-7b=-13$

$49a+7b+c=-13\quad\Rightarrow\quad49a+7b=-13$

we can solve these two equation using the elimination method, by simply adding the two equations

$\quad\quad49a-7b=-13\\+\quad49a+7b=-13$

------------------------------

$\quad\quad 98a=-26$

$\quad\quad a=-\dfrac{13}{49}$

Now we can plug this value of a in any of the two equations.

$49a-7b=-13$

$49\left(-\dfrac{13}{49}\right)-7b=-13$

$-13-7b=-13$

$-7b=0$

$b=0$

We have the values of a,b, and c. We can plug them in the general equation to find the equation of the arch.

$y=\left(-\dfrac{13}{49}\right)x^2+0x+0$

$y=-\dfrac{13}{49}x^2$

$49y=-13x^2$

This our equation of the arch!

5 0

3 years ago

The length between the bases on a baseball field is 90 feet. A scale drawing shows the distance between the bases are 2 1/5 inch

kakasveta [241]

Answer:

So the distance from home plate to 2nd base is 127.279 ft

Step-by-step explanation:

I think it is right hope it helps :)

4 0

3 years ago

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Solve the inequality -9 ≤ 7-8v cmon bro

Lady bird [3.3K]

Answer:

v ≤ 2

Step-by-step explanation:

6 0

3 years ago

HELLO CAN SOMEONE HELP ME IM FAILING MATH NO FAKE ANSWERS PLS TY :)

mixer [17]

Answer:

Area of rectangle = 10 units²

Area of triangle = 10 units²

Area of figure = 20 units²

Step-by-step explanation:

7 0

2 years ago