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2 years ago

Four students simplified the expression.

Mathematics

2 answers:

Viktor [21]2 years ago

6 0

Answer:

camilaaaaaaaaaaaaaaa

scoray [572]2 years ago

5 0

Answer:

<em>Regan </em>subtracted the exponents: 410 − 5 = 45

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If f(x) =<br> **, what is fa+ 2)?

Alex777 [14]

Answer:

Step-by-step explanation:

fhjs

6 0

2 years ago

The surface area of a melting snowball decreases at a rate of3.8cm2/min. Find the rate at which its diameter decreases when the

Scorpion4ik [409]

Answer:

Step-by-step explanation:

This is a pretty basic related rates problem. I'm going to go through this just like I do in class when I'm teaching it to my students.

We see we have a snowball, which is a sphere. We are talking about the surface area of this sphere which has a formula of

$S=4\pi r^2$

In the problem we are given diameter, not radius. What we know about the relationship between a radius and a diameter is that

d = 2r so

$\frac{d}{2}=r$ Now we can have the equation in terms of diameter instead of radius. Rewriting:

$S=4\pi(\frac{d}{2})^2$ which simplifies to

$S=4\pi(\frac{d^2}{4})$ and a bit more to

$S=\pi d^2$ (the 4's cancel out by division). Now that is a simple equation for which we have to find the derivative with respect to time.

$\frac{dS}{dt}=\pi*2d\frac{dD}{dt}$ Now let's look at the problem and see what we are given as far as information.

The rate at which the surface area changes is -3.8, and we are looking for $\frac{dD}{dt}$ , the rate at which the diameter is changing, when the diameter is 13. Filling in:

$-3.8=\pi(2)(13)\frac{dD}{dt}$ and solving for the rate at which the diameter is changing:

$-\frac{3.8}{26\pi}=\frac{dD}{dt}$ and divide to get

$\frac{dD}{dt}=-.459\frac{cm}{min}$ Obviously, the negative means that the diameter is decreasing.

7 0

2 years ago

Which of the following is not a function?

rusak2 [61]

Answer: B

Number on the left: x-value
Number on the right: y-value

If there are 2 y-values for one x-value it is NOT considered a function.

For instance in the answer:

(2,3), (2,4), (3,3), (3,4)

You can clearly see that the x-values (2 & 3) repeat more than once; therefore, it is NOT a function.

On the other hand if you have 2 DIFFERENT x-values for the same y-value it IS A FUNCTION.

For ex D: (2,4), (3,4), (5,4), (6,4)

As you can see there are 4 DIFFERENT x-values with same y-value; therefore it is A FUNCTION

To make it easier:

If x-values appear more than once = NOT A FUNCTION

If x-values appear only ONCE = FUNCTION

Remember: y-values are ALLOWED to repeat

I hope this helps. If you have any questions please let me know in the comments.

4 0

2 years ago

Derive this with respect to x<br><img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7B%281%20%2B%20%20secx%29%20%7D%20" id="Tex

Elenna [48]

$~~~~\dfrac{d}{dx} \left(\dfrac{3}{1 + \sec x} \right)\\\\\\=3 \dfrac{d}{dx} \left( \dfrac 1{ 1+ \sec x} \right)\\\\\\=3 \dfrac{d}{dx} (1+ \sec x)^{-1}\\\\\\=3 (-1) (1 + \sec x )^{-1 -1} \dfrac{d}{dx}( 1 + \sec x)\\\\\\=-3(1 + \sec x)^{-2} ( 0 + \sec x \tan x)\\\\\\=-\dfrac{3\sec x \tan x}{(1 + \sec x)^2}$

8 0

1 year ago

10% of 65 pls help and explain the steps to get total answer

sergij07 [2.7K]

10% of 65
Of means multiply
=0.1 x 65
=6.5

Or you can use another way which is (part/whole) *(percent/100)

Whole=65
Percent=10
And part(part of 65)=unknown

(X/65)* (10/100)
Cross multiply
x= 6.5

So 10% of 65 is 6.5

5 0

2 years ago