How much does a 200kg object weight on earth

What is the range of y = sinx in the interval - π ≤ x ≤ 0?

Kaylis [27]

Answer:

$-1 \le y \le 1$

Step-by-step explanation:

Let be $y = \sin x$ , the range of the function corresponds to the set of values of $y$ . The sine function is a bounded function between -1 and 1. Hence, the range of the function is:

$-1 \le y \le 1$

6 0

2 years ago

Two sides of a triangle have measures of 6 inches and 12 inches. Which measure could be the length of the third side?

kondaur [170]

Answer: Yes an isosceles triangle has at least two sides that have equal measures.

3 0

3 years ago

patty is building a rope ladder for a tree house. she need two 5-foot pieces of rope the sides of the ladder.she needs 7 pieces

klio [65]

The answer is 136 because 7 x 18 is 126 then + 10 is 136

5 0

3 years ago

Square of which numbers are equal to 4?

shusha [124]

The answer would be 2 because a square root has to be the same 2 numbers which is 2 for this example. 2x2=4. Hope this helps! If you have anymore questions please ask me. Stay Safe! And have a good day!

6 0

3 years ago

I am having trouble with this relative minimum of this equation.<br>

Norma-Jean [14]

Answer:

So the approximate relative minimum is (0.4,-58.5).

Step-by-step explanation:

Ok this is a calculus approach. You have to let me know if you want this done another way.

Here are some rules I'm going to use:

$(f+g)'=f'+g'$ (Sum rule)

$(cf)'=c(f)'$ (Constant multiple rule)

$(x^n)'=nx^{n-1}$ (Power rule)

$(c)'=0$ (Constant rule)

$(x)'=1$ (Slope of y=x is 1)

$y=4x^3+13x^2-12x-56$

$y'=(4x^3+13x^2-12x-56)'$

$y'=(4x^3)'+(13x^2)'-(12x)'-(56)'$

$y'=4(x^3)'+13(x^2)'-12(x)'-0$

$y'=4(3x^2)+13(2x^1)-12(1)$

$y'=12x^2+26x-12$

Now we set y' equal to 0 and solve for the critical numbers.

$12x^2+26x-12=0$

Divide both sides by 2:

$6x^2+13x-6=0$

Compaer $6x^2+13x-6=0$ to $ax^2+bx+c=0$ to determine the values for $a=6,b=13,c=-6$ .

$a=6$

$b=13$

$c=-6$

We are going to use the quadratic formula to solve for our critical numbers, x.

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

$x=\frac{-13 \pm \sqrt{13^2-4(6)(-6)}}{2(6)}$

$x=\frac{-13 \pm \sqrt{169+144}}{12}$

$x=\frac{-13 \pm \sqrt{313}}{12}$

Let's separate the choices:

$x=\frac{-13+\sqrt{313}}{12} \text{ or } \frac{-13-\sqrt{313}}{12}$

Let's approximate both of these:

$x=0.3909838 \text{ or } -2.5576505$ .

This is a cubic function with leading coefficient 4 and 4 is positive so we know the left and right behavior of the function. The left hand side goes to negative infinity while the right hand side goes to positive infinity. So the maximum is going to occur at the earlier x while the minimum will occur at the later x.

The relative maximum is at approximately -2.5576505.

So the relative minimum is at approximate 0.3909838.

We could also verify this with more calculus of course.

Let's find the second derivative.

$f(x)=4x^3+13x^2-12x-56$