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2 years ago

Simplify and write the answer in exponential form 3x^4 × y^4 x^4

Mathematics

1 answer:

RideAnS [48]2 years ago

6 0

Answer:

The simplified expression in the exponential form will be: $3x^8y^4$

Step-by-step explanation:

Given the expression

$3x^4\times \:y^4x^4$

simplifying the expression and writing the answer in exponential form

$\mathrm{Apply\:exponent\:rule}:\quad \:a^b\times \:a^c=a^{b+c}$

$x^4x^4=x^{4+4}$

so the expression becomes

$3x^4\times \:y^4x^4=3x^{4+4}y^4$

$=3x^8y^4$ ∵ $\mathrm{Add\:the\:numbers:}\:4+4=8$

Therefore, the simplified expression in the exponential form will be: $3x^8y^4$

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Find the general solution to 3y′′+12y=0. Give your answer as y=... . In your answer, use c1 and c2 to denote arbitrary constants

lozanna [386]

Answer:

$y(x)=c_1e^{2ix}+c_2e^{-2ix}$

Step-by-step explanation:

You have the following differential equation:

$3y''+12y=0$ (1)

In order to find the solution to the equation, you can use the method of the characteristic polynomial.

The characteristic polynomial of the given differential equation is:

$3m^2+12=0\\\\m^2=-\frac{12}{3}=-4\\\\m_{1,2}=\pm2\sqrt{-1}=\pm2i$

The solution of the differential equation is:

$y(x)=c_1e^{m_1x}+c_2e^{m_2x}$ (2)

where m1 and m2 are the roots of the characteristic polynomial.

You replace the values obtained for m1 and m2 in the equation (2). Then, the solution to the differential equation is:

$y(x)=c_1e^{2ix}+c_2e^{-2ix}$

4 0

3 years ago

Brian likes to go bird watching along the Harvest Park Trail in a nearby forest preserve. He wants to calculate the area enclose

QveST [7]

The question has missing details

The missing options are:

A. 188,000 square yards

B. 138,000 square yards

C. 600 square yards

D. 300 square yards

See attachment 1 for the missing diagram

Answer:

B. 138,000 square yards

Step-by-step explanation:

The figure can be divided into two shapes (see attachment 2)

From attachment 2,

The dimension of the big rectangle is 1300ft by 800ft

The dimension of the small rectangle is 500ft by 400ft

So, the area is:

Area of the big rectangle added to the area of the small rectangle

i.e.

$Area = 1300 * 800 + 500 * 400$

$Area = 1040000 + 200000$

$Area = 1240000ft^2$

Convert to $yd^2$ by dividing by 9

$Area = 1240000yd^2 /9$

$Area = 137777.777778\ yd^2$

From the list of given options, the closest to the area of the diagram is

B. 138,000 square yards

8 0

3 years ago

Find the sum of the first 17 terms of the arithmetic sequence 10, 14, 18, 22, 26...

kari74 [83]

10, 14, 18 ....

notice, we get the next term by simply adding 4 to the current term, thus "4" is the "common difference, and we know that 10 is the first term.

$\bf n^{th}\textit{ term of an arithmetic sequence}
\\\\
a_n=a_1+(n-1)d\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
d=\textit{common difference}\\
----------\\
a_1=10\\
d=4\\
n=17
\end{cases}
\\\\\\
a_{17}=10+(17-1)(4)\implies a_{17}=10+(16)(4)
\\\\\\
a_{17}=10+64\implies a_{17}=74\\\\
-------------------------------$

$\bf \textit{ sum of a finite arithmetic sequence}
\\\\
S_n=\cfrac{n(a_1+a_n)}{2}\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
----------\\
a_1=10\\
a_{17}=74\\
n=17
\end{cases}
\\\\\\
S_{17}=\cfrac{17(10+74)}{2}\implies S_{17}=\cfrac{17(84)}{2}\implies S_{17}=714$

6 0

2 years ago

Read 2 more answers

Jess is in art club and they have two leadership positions (President and Vice President) there are 15 members. How many members

kari74 [83]

Only 2 members can take a spot because there are only 2 positiot

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3 years ago

a jug contains 2.45 liters of cranberry juice. A bottle contains 2 wholes 13/25 liters of grape juice. which container holds les

IgorLugansk [536]

The cranberry juice contains less fruit juice

5 0