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Diano4ka-milaya [45]
3 years ago
12

Write this number in standard notation. 4.702 x 10^–4

Mathematics
2 answers:
Rzqust [24]3 years ago
4 0
0.0004702 I always learnt to do this by moving the the decimal point across (left in the case of a minus power) as many steps as the power
NemiM [27]3 years ago
4 0

<u>Answer:</u> The number in standard notation will be 0.0004702

<u>Step-by-step explanation:</u>

Standard notation is defined as the notation in which number is written in the simplest way.

If the number written in scientific notation has positive exponent on 10 as 10^n, the decimal point will move 'n' times to the right.

If the number written in scientific notation has negative exponent on 10 as 10^{-n}, the decimal point will move 'n' times to the left.

We are given a number which is 4.702\times 10^{-4}

So, its value in standard notation will be 0.0004702

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Need help with AP CAL
anzhelika [568]

Answer: Choice C

\displaystyle \frac{1}{2}\left(1 - \frac{1}{e^2}\right)

============================================================

Explanation:

The graph is shown below. The base of the 3D solid is the blue region. It spans from x = 0 to x = 1. It's also above the x axis, and below the curve y = e^{-x}

Think of the blue region as the floor of this weirdly shaped 3D room.

We're told that the cross sections are perpendicular to the x axis and each cross section is a square. The side length of each square is e^{-x} where 0 < x < 1

Let's compute the area of each general cross section.

\text{area} = (\text{side})^2\\\\\text{area} = (e^{-x})^2\\\\\text{area} = e^{-2x}\\\\

We'll be integrating infinitely many of these infinitely thin square slabs to find the volume of the 3D shape. Think of it like stacking concrete blocks together, except the blocks are side by side (instead of on top of each other). Or you can think of it like a row of square books of varying sizes. The books are very very thin.

This is what we want to compute

\displaystyle \int_{0}^{1}e^{-2x}dx\\\\

Apply a u-substitution

u = -2x

du/dx = -2

du = -2dx

dx = du/(-2)

dx = -0.5du

Also, don't forget to change the limits of integration

  • If x = 0, then u = -2x = -2(0) = 0
  • If x = 1, then u = -2x = -2(1) = -2

This means,

\displaystyle \int_{0}^{1}e^{-2x}dx = \int_{0}^{-2}e^{u}(-0.5du) = 0.5\int_{-2}^{0}e^{u}du\\\\\\

I used the rule that \displaystyle \int_{a}^{b}f(x)dx = -\int_{b}^{a}f(x)dx which says swapping the limits of integration will have us swap the sign out front.

--------

Furthermore,

\displaystyle 0.5\int_{-2}^{0}e^{u}du = \frac{1}{2}\left[e^u+C\right]_{-2}^{0}\\\\\\= \frac{1}{2}\left[(e^0+C)-(e^{-2}+C)\right]\\\\\\= \frac{1}{2}\left[1 - \frac{1}{e^2}\right]

In short,

\displaystyle \int_{0}^{1}e^{-2x}dx = \frac{1}{2}\left[1 - \frac{1}{e^2}\right]

This points us to choice C as the final answer.

5 0
2 years ago
Which of the following inequalities matches the graph? (1 point)
Lilit [14]
Y is less than or equal to 0
8 0
3 years ago
Write an equation in point slope form for the line through the given point with the given slope (5,-6) m= -0.38
tester [92]
Heeelllllloooooo! :D

Okay this is a very similar question to the one I answered earlier....

I'll show you step by step so you will be able to do this in the future on your own

(y - y₁) = m(x - x₁)     -----> point-slope form
(y + 6) = (-0.38)(x - 5)
y + 6 = -0.38x + 1.9
<u>y = -0.38x - 4.1</u><u />

There you go!

<u>Please vote me for Brainliest if there is a second answer!!!</u> ^__^
4 0
3 years ago
20. what us the area of the figure:
Varvara68 [4.7K]
If the angle in B is 45º, that means the angle in A is also going to be 45º, considering it's a right triangle, so AC and BC are they have the same length.
Then using Pythagoras, you'll get that AC^{2} + BC^{2} equals AB^{2} .
Now, you know that AC=BC and that AB=24.
So you'll get 2AC^{2} =24^2 . You do the square root in both sides and you get that 2AC=24 and AC=12.

Now that you know that both AC and BC equal 12, you can find the area by just multiplying them and then diving them by 2. (The formula for the area of a triangle is half base multiplied by height, and in a right triangle, if a cathetus is the base, the other cathetus<span> will be the height)

And so the area is equal to 72.</span>
8 0
3 years ago
Someone can help?? ​
oee [108]

Answer:

Step-by-step explanation:

let  cos^{-1}x=t

cos t=x

when x=1,cos t=1=cos 0

t \rightarrow 0

\lim_{x \to 1} \frac{1-\sqrt{x}}{(cos ^{-1}x)^2 } \\= \lim_{t \to 0} \frac{1-\sqrt{cos~t}}{t^2} \times \frac{1+\sqrt{cos~t}}{1+\sqrt{cos ~t}} \\= \lim_{t \to 0} \frac{1-cos~t}{t^2(1+\sqrt{cos~t})}}  \\= \lim_{t \to 0 }\frac{2 sin^2~\frac{t}{2}}{t^2(1+\sqrt{cos~t})}} \\= 2\lim_{t \to 0 }(\frac{sin~t/2}{\frac{t}{2} })^2 \times \frac{1}{4} \times  \lim_{t \to 0 }\frac{1}{1+\sqrt{cos~t}} \\=\frac{2}4} \times 1^2 \times \frac{1}{1+\sqrt{cos~0}} \\=\frac{1}{2} \times \frac{1}{1+1} \\=\frac{1}{4}

4 0
3 years ago
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