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2 years ago

How can I simplify/rewrite the 1st(top) equation into the 2nd(Botton),please show a step by step solution.

Mathematics

1 answer:

Vaselesa [24]2 years ago

4 0

Answer:

see below

Step-by-step explanation:

$-2(4 - \frac{x}{2} )^{5} + C$

Think of the above as:

$-\frac{2}{1}$ * $(\frac{8}{2} - \frac{x}{2} )^{5} + C$

= $-\frac{2}{1}$ * $\frac{(8 - x)^{5}}{2^{5}} + C$

= $-\frac{2}{1}$ * $\frac{(8 - x)^{5}}{32} + C$

= $-\frac{1}{1}$ * $\frac{(8 - x)^{5}}{16} + C$

= $\frac{-1(8 - x)^{5}}{16} + C$

= $\frac{(-8 + x)^{5}}{16} + C$

Can flip it around to be...

$\frac{(x - 8)^{5}}{16} + C$

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3 years ago

A person that is 5 feet tall casts a shadow 25 feet long. How long is the shadow of a tree that is 15 feet tall?

fiasKO [112]

The person and his shadow make a right triangle as well as the tree and it's shadow. they will be similar right triangles containing angles that are equal. I'm in similar triangles the angles are proportional so a ratio could be used to determine the shadow length. this ratio is:
25/5 = x/15
(Notice that both the height of the person and
the height of the tree height of the tree are on
the bottom because these would be similar
sides and the same for the shadows with both
on top. this could easily have been switched
with the shadows on bottom and heights on
top like:
5/25 = 15/x
however I noticed the 25/5 could easily be
reduced. this eliminated the need for cross
multiplication.)

The 25/5 can be reduced to 5:
5 = x/15
and then multiply both sides by 15 and you get:
x = 75
so the answer is 75 feet long.

this can be checked various ways. using trigonometry we have the opposite and adjacent sides so tangent could be used to find the angle between the shadow and the hypotenuse. this is:
tan (x) = opposite/adjacent
opposite = height
adjacent = shadow
so:
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3 years ago

I WILL MARK BRAINLIEST !!! Harper is going to invest $6,900 and leave it in an account for 12 years. Assuming the

Komok [63]

Answer:

4.4%

Step-by-step explanation:

A=P\left(1+\frac{r}{n}\right)^{nt}

A=P(1+

)

Compound interest formula

A=11700\hspace{35px}P=6900\hspace{35px}t=12\hspace{35px}n=365

A=11700P=6900t=12n=365

Given values

11700=

\,\,6900\left(1+\frac{r}{365}\right)^{365(12)}

6900(1+

365

)

365(12)

Plug in values

11700=

\,\,6900\left(1+\frac{r}{365}\right)^{4380}

6900(1+

365

)

4380

Multiply

\frac{11700}{6900}=

6900

11700

\,\,\frac{6900\left(1+\frac{r}{365}\right)^{4380}}{6900}

6900

6900(1+

365

)

4380

Divide by 6900

1.695652174=

\,\,\left(1+\frac{r}{365}\right)^{4380}

(1+

365

)

4380

\left(1.695652174\right)^{1/4380}=

(1.695652174)

1/4380

\,\,\left[\left(1+\frac{r}{365}\right)^{4380}\right]^{1/4380}

[(1+

365

)

4380

]

1/4380

Raise both sides to 1/4380 power

1.000120571=

\,\,1+\frac{r}{365}

365

-1\phantom{=}

−1=

\,\,-1

−1

Subtract 1

0.000120571=

\,\,\frac{r}{365}

365

365\left(0.0001206\right)=

365(0.0001206)=

\,\,\left(\frac{r}{365}\right)365

(

365

)365

Multiply by 365

0.044008415=

\,\,r

4.4008415\%=

4.4008415%=

\,\,r

7 0

2 years ago

Read 2 more answers

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ruslelena [56]

Parameterize the path $\mathcal C$ by

$\mathbf r(t)=x(t)\,\mathbf i+y(t)\,\mathbf j$

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and $0\le t\le\pi$ . Then

$\displaystyle\int_{\mathcal C}\mathbf f(x,y)\cdot\mathrm d\mathbf r=\int_{t=0}^{t=\pi}\mathbf f(x(t),y(t))\cdot\dfrac{\mathrm d\mathbf r}{\mathrm dt}\,\mathrm dt$
$=\displaystyle\int_0^\pi(9\cos^2t\,\mathbf i+9\sin^2t\,\mathbf j)\cdot(-3\sin t\,\mathbf i+3\cos t\,\mathbf j)\,\mathrm dt$
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3 years ago

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In this case: the sample mean is 70 and the margin of error is approximately 1.95

So to calculate the confidence interval, do the following:
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Looks like that would be the last choice. hope this helps.. it's been awhile since my work with statistics :-)

4 0

3 years ago

Read 2 more answers

How can I simplify/rewrite the 1st(top) equation into the 2nd(Botton),please show a step by step solution.​

How can I simplify/rewrite the 1st(top) equation into the 2nd(Botton),please show a step by step solution.