Evaluate the expressions when x = 3; y = 4 & z = -2

svet-max [94.6K]

Answer:

1.98

Step-by-step explanation:

Find the number in the hundredth place 8 and look one place to the right for the rounding digit 3. Round up if this number is greater than or equal to 5 and round down if it is less than 5.

4 0

3 years ago

Evaluate Dx / ^ 9-8x - x2^

Solnce55 [7]

It depends on what you mean by the delimiting carats "^"...

Since you use parentheses appropriately in the answer choices, I'm going to go out on a limb here and assume something like "^x^" stands for $\sqrt x$ .

In that case, you want to find the antiderivative,

$\displaystyle\int\frac{\mathrm dx}{\sqrt{9-8x-x^2}}$

Complete the square in the denominator:

$9-8x-x^2=25-(16+8x+x^2)=5^2-(x+4)^2$

Now substitute $x+4=5\sin y$ , so that $\mathrm dx=5\cos y\,\mathrm dy$ . Then

$\displaystyle\int\frac{\mathrm dx}{\sqrt{9-8x-x^2}}=\int\frac{5\cos y}{\sqrt{5^2-(5\sin y)^2}}\,\mathrm dy$

which simplifies to

$\displaystyle\int\frac{5\cos 
y}{5\sqrt{1-\sin^2y}}\,\mathrm dy=\int\frac{\cos y}{\sqrt{\cos^2y}}\,\mathrm dy$

Now, recall that $\sqrt{x^2}=|x|$ . But we want the substitution we made to be reversible, so that

$x+4=5\sin y\iff y=\sin^{-1}\left(\dfrac{x+4}5\right)$

which implies that $-\dfrac\pi2\le y\le\dfrac\pi2$ . (This is the range of the inverse sine function.)

Under these conditions, we have $\cos y\ge0$ , which lets us reduce $\sqrt{\cos^2y}=|\cos y|=\cos y$ . Finally,

$\displaystyle\int\frac{\cos y}{\cos y}\,\mathrm dy=\int\mathrm dy=y+C$

and back-substituting to get this in terms of $x$ yields

$\displaystyle\int\frac{\mathrm dx}{\sqrt{9-8x-x^2}}=\sin^{-1}\left(\frac{x+4}5\right)+C$

4 0

3 years ago

Simplify the expression to a polynomial in standard form. (x-2)(x2 +7x +4)

goldenfox [79]

Answer:

Step-by-step explanation:

(x - 2)(x² + 7x + 4) = x(x² + 7x + 4) - 2*(x² + 7x + 4)

= x*x² + x*7x + 4*x - 2*x² -2* 7x -2* 4

= x³ + 7x² + 4x - 2x² -14x -8

= x³ + 7x² - 2x² + 4x - 14x - 8

= x³ + 5x² - 10x - 8

5 0

2 years ago

ISTEP IS COMING UP AND IM NOT READY!!!

AlekseyPX

> and < with the lines under it mean that they can also be equal to the constant on the other side (greater/less than or equal to)

So x <= 3 can be anything less than 3 and 3.

*the = in this inequality is the equivalent of a line

Now vice versa.

x => 3 can be anything greater than 3 and 3.

Now for the dots.

The open dots in signs are (< and >).

Basically they start at that point they are on but don't include it.

So an open dot at 3 pointing to the left means that the value is greater than 3 but does not include 3.

The closed dots in signs are (<= and =>).

They start at the point and include it.

So a closed dot a 3 pointing to the left means that the value is greater than 3 and includes 3.

Arrows.

Arrows pointing to the left mean that the values are getting bigger.

Arrows pointing to the right mean that the values are getting smaller.

ie : An arrow pointing to the left with a starting point at 3 = 3 and anything bigger, such as 4.

ie : An arrow pointing to the right with a starting point at 3 = 3 and anything smaller, such as 2.

Solve for problems.

The main concept is isolate the variable.

This basically means make the variable be lonely ^^

Use +, -, *, and /

Ex : 6x + 2 > 3

First, we would subtract 2 from both sides.

6x > 1

Then, we would divide each side by 6, leaving the x alone.

x > 1/6

And voila! x is anything greater than 1/6 but it does not include 1/6.

Hope this helps! ^^

8 0

3 years ago

Read 2 more answers

You are choosing between two health clubs. Club A offers membership for a fee of $12 plus a monthly fee of $28. Club B offers me

EleoNora [17]

A has fixed one time fee of $12 and if you go to it say "m" months you pay $28 for each month, so your total cost at A is really 12 + 28m.

B has a fixed one time fee of $20 and if you go to it "m" months you pay $26 for each month, so you total cost at B is 20 + 26m.

how many months for the cost to be the same?

$\stackrel{A}{12+28m}=\stackrel{B}{20+26m}\implies 12+2m=20\implies 2m=8\implies m=\cfrac{8}{2}\implies m=4$

well, since the cost for both is the same, we can just get A's, knowing that B is the same

$12+28(4)\implies 12+112\implies 124$

5 0

2 years ago