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3 years ago

10 POINTS!!! FULL ANSWER IN STEP BY STEP FORMAT!!

Mathematics

1 answer:

Lilit [14]3 years ago

4 0

After a little manipulation, the given diff'l equation will look like this:

e^y * dy = (2x + 1) * dx.
x^2
Integrating both sides, we get e^y = 2------- + x + c, or e^y = x^2 + x + c
2

Now let x=0 and y = 1, o find c:

e^1 = 0^2 + 0 + c. So, c = e, and the solution is e^y = x^2 + x + e.

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5. Given the following triangle side lengths, identify the triangle as acute, right or obtuse. Show your work. a. 3in, 4in, 5 in

Keith_Richards [23]

The answer to the question is D

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Algebra help (last one lol)

katovenus [111]

B. Isolate the y term

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the exit to garrett's house is after exit 51 but before exit 62. the number on the exit sing is not a prime nunber. the number i

Alex Ar [27]

52
- is prime? No
- is multiple of 3? No
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53
- is prime? Yes
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54
- is prime? No
- is multiple of 3? Yes
- is multiple of 4? No
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55
- is prime? No
- is multiple of 3? No
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56
- is prime? No
- is multiple of 3? No
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57
- is prime? No
- is multiple of 3? Yes
- is multiple of 4? No
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58
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- is multiple of 3? No
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59
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60
- is prime? No
- is multiple of 3? Yes
- is multiple of 4? Yes

Therefore 60 is the answer, as it fits all the conditions

Simple trial and error.

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3 years ago

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Factor completely 4x^5-20x^3

nikdorinn [45]

Answer:

Step-by-step explanation:

First, try to factor a common factor.

GCF of 4 and -20 is 4.

GCF of x^5 and x^3 is x^3.

Factor out 4x^3.

4x^5 - 20x^3 =

= 4x^3(x^2 - 5)

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Assume that the flask shown in the diagram can be modeled as a combination of a sphere and a cylinder. Based on this assumption,

kompoz [17]

If the flask shown in the diagram can be modeled as a combination of a sphere and a cylinder, then its volume is

$V_{flask}=V_{sphere}+V_{cylinder}.$

Use following formulas to determine volumes of sphere and cylinder:

$V_{sphere}=\dfrac{4}{3}\pi R^3,\\ \\V_{cylinder}=\pi r^2h,$

wher R is sphere's radius, r - radius of cylinder's base and h - height of cylinder.

Then

$V_{sphere}=\dfrac{4}{3}\pi R^3=\dfrac{4}{3}\pi \left(\dfrac{4.5}{2}\right)^3=\dfrac{4}{3}\pi \left(\dfrac{9}{4}\right)^3=\dfrac{243\pi}{16}\approx 47.71;$
$V_{cylinder}=\pi r^2h=\pi \cdot \left(\dfrac{1}{2}\right)^2\cdot 3=\dfrac{3\pi}{4}\approx 2.36;$
$V_{flask}=V_{sphere}+V_{cylinder}\approx 47.71+2.36=50.07.$

Answer 1: correct choice is C.

If both the sphere and the cylinder are dilated by a scale factor of 2, then all dimensions of the sphere and the cylinder are dilated by a scale factor of 2. So

R'=2R, r'=2r, h'=2h.

Write the new fask volume:

$V_{\text{new flask}}=V_{\text{new sphere}}+V_{\text{new cylinder}}=\dfrac{4}{3}\pi R'^3+\pi r'^2h'=\dfrac{4}{3}\pi (2R)^3+\pi (2r)^2\cdot 2h=\dfrac{4}{3}\pi 8R^3+\pi \cdot 4r^2\cdot 2h=8\left(\dfrac{4}{3}\pi R^3+\pi r^2h\right)=8V_{flask}.$

Then

$\dfrac{V_{\text{new flask}}}{V_{\text{flask}}} =\dfrac{8}{1}=8.$

Answer 2: correct choice is D.

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