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3 years ago

Questions number 1

Mathematics

1 answer:

Brut [27]3 years ago

8 0

9514 1404 393

Answer:

145.3 square inches

Step-by-step explanation:

The lateral area of the cylinder is given by ...

LA = 2πrh

LA = 2π(2.5 in)(9.25 in) = 46.25π in²

LA ≈ 145.3 in²

About 145.3 square inches of paper is used for the label.

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Please help me solve this problem

Alex

The answer for this is X+2g= 0

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3 years ago

Find the general solution to each of the following ODEs. Then, decide whether or not the set of solutions form a vector space. E

Ipatiy [6.2K]

Answer:

(A) $y=ke^{2t}$ with $k\in\mathbb{R}$ .

(B) $y=ke^{2t}/2-1/2$ with $k\in\mathbb{R}$

(D) $y=k_1e^{2t}+k_2e^{-2t}+e^{3t}/5$ with $k_1,k_2\in\mathbb{R}$ ,

Step-by-step explanation

(A) We can see this as separation of variables or just a linear ODE of first grade, then $0=y'-2y=\frac{dy}{dt}-2y\Rightarrow \frac{dy}{dt}=2y \Rightarrow \frac{1}{2y}dy=dt \ \Rightarrow \int \frac{1}{2y}dy=\int dt \Rightarrow \ln |y|^{1/2}=t+C \Rightarrow |y|^{1/2}=e^{\ln |y|^{1/2}}=e^{t+C}=e^{C}e^t} \Rightarrow y=ke^{2t}$ . With this answer we see that the set of solutions of the ODE form a vector space over, where vectors are of the form $e^{2t}$ with $t$ real.

(B) Proceeding and the previous item, we obtain $1=y'-2y=\frac{dy}{dt}-2y\Rightarrow \frac{dy}{dt}=2y+1 \Rightarrow \frac{1}{2y+1}dy=dt \ \Rightarrow \int \frac{1}{2y+1}dy=\int dt \Rightarrow 1/2\ln |2y+1|=t+C \Rightarrow |2y+1|^{1/2}=e^{\ln |2y+1|^{1/2}}=e^{t+C}=e^{C}e^t \Rightarrow y=ke^{2t}/2-1/2$ . Which is not a vector space with the usual operations (this is because $-1/2$ ), in other words, if you sum two solutions you don't obtain a solution.

(C) This is a linear ODE of second grade, then if we set $y=e^{mt} \Rightarrow y''=m^2e^{mt}$ and we obtain the characteristic equation $0=y''-4y=m^2e^{mt}-4e^{mt}=(m^2-4)e^{mt}\Rightarrow m^{2}-4=0\Rightarrow m=\pm 2$ and then the general solution is $y=k_1e^{2t}+k_2e^{-2t}$ with $k_1,k_2\in\mathbb{R}$ , and as in the first items the set of solutions form a vector space.

(D) Using C, let be $y=me^{3t}$ we obtain that it must satisfies $3^2m-4m=1\Rightarrow m=1/5$ and then the general solution is $y=k_1e^{2t}+k_2e^{-2t}+e^{3t}/5$ with $k_1,k_2\in\mathbb{R}$ , and as in (B) the set of solutions does not form a vector space (same reason! as in (B)).

4 0

3 years ago

Mrs. Lin is sewing costumes for her grandchildren. She is making three lion costumes, one zebra costume, and two bear costumes.

stepladder [879]

Answer:

$12\frac{1}{8}\ yd$

Step-by-step explanation:

we know that

The total fabric that Mrs. Lin needs is equal to

$3(1\frac{2}{3})+2\frac{5}{8}+2(2\frac{1}{4})$

Convert mixed number to an improper fraction

$1\frac{2}{3}=1+\frac{2}{3}=\frac{5}{3}$

$2\frac{5}{8}=2+\frac{5}{8}=\frac{21}{8}$

$2\frac{1}{4}=2+\frac{1}{4}=\frac{9}{4}$

substitute

$3(\frac{5}{3})+\frac{21}{8}+2(\frac{9}{4})$

$5+\frac{21}{8}+\frac{9}{2}$

$\frac{40+21+36}{8}=\frac{97}{8}\ yd$

Convert to mixed number

$\frac{97}{8}\ yd= \frac{96}{8}+\frac{1}{8}=12\frac{1}{8}\ yd$

4 0

4 years ago

I need help on this question can someone help.

leva [86]

Answer:

G. (8,6)

Step-by-step explanation:

remember that EF is four times the length of DE

so the distance between E and D multiplied by 4 should equal F

4 0

2 years ago

SomeOne Do This Thank You If u had because if u answered my question u get.................................................... i

jonny [76]

Answer:

Step-by-step explanation:

By gradient, if you mean the "slope" of the linear function, then you have to find two points of the graph and use the "rise over run strategy". Given two coordinates, (x1, y1) and (x2, y2) of a linear function in the form y=mx+b, the slope of the line is (y2-y1)/(x2-x1). This shows the amount of "rise", or the vertical change, and the amount of "run", which is the horizontal change. Rise/Run gives the steepness of the line. The slope can also be modeled by Δy/Δx, which is the change in y over the change in x

Plugging in the given points (0,5) and (-5,0):

(y2-y1)/(x2-x1)= (5-0)/(0-(-5)) = 5/5 = 1

7 0

3 years ago