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3 years ago

What is 25.0996 rounded to the nearest thousandth

Mathematics

1 answer:

madreJ [45]3 years ago

4 0

Answer:

25.100

Step-by-step explanation:

The thousandth place is the third digit to the right of the decimal point - tenths is the first, hundredths is the second, thousandths is the third. Since six rounds up and both nines round up, one must round up all of the way from the fourth decimal place to the tenth decimal place.

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The width of the ochoa community pool is 20 feet. The length is twice as long as it's width . what is the perimeter of the pool?

guapka [62]

Width = 20 feet
length = 2(20) = 40 feet
then the perimeter equals 2width+ 2length = 2(20)+ 2(40) = 40+80 = 120 feet

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4 years ago

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Vadim26 [7]

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3 years ago

Given that QR¯∥ST¯, identify the length of PT¯.

wariber [46]

Answer:

PT = 16.3 units

Step-by-step explanation:

From the picture attached,

From ΔPQR and ΔPST,

QR ║ST [Given]

PQ is a transversal line.

Therefore, ∠PST ≅ ∠PQR [Corresponding angles]

∠P ≅ ∠P [Common angle]

ΔPQR ~ ΔPST [By AA property of similarity of two triangles]

Therefore, by the property of similarity, corresponding sides of the similar triangles will be proportional.

$\frac{PQ}{PS}=\frac{PR}{PT}$

$\frac{12+28}{28}= \frac{PT+7}{PT}$

$\frac{40}{28}=1+\frac{7}{PT}$

$\frac{10}{7}-1=\frac{7}{PT}$

$\frac{10-7}{7}=\frac{7}{PT}$

PT = $\frac{49}{3}$

PT = 16.3 units

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3 years ago

Find the sum of an 8-term geometric sequence when the first term is 7 and the last term is 114,688 and select the correct answer

vladimir1956 [14]

A.152,915 is the answer

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3 years ago

A man starts walking north at 5 ft/s from a point P. Five minutes later a woman starts walking south at 6 ft/s from a point 500

aev [14]

Check the picture below.

the man is going North, and he has a rate of 5 f/s, she's going south, 500 miles from P, the green distance, and she's going 6 f/s.

by the time she started walking, he already had been walking for 5 minutes, or 300 seconds, since he's going 5 f/s, then he had already covered 1500 feet by then.

after that, they both walked for 15 minutes more or 900 seconds, and for her that means 5400 feet, whilst for him going slower means 4500 feet, as you see in the picture.

since he's going North and she's going South, dy/dt is the combined rates, as you see there.

now, let's use the pythagorean theorem, bearing in mind that the green 500 feet are constant all the while, that matters because the derivative of a constant is 0.

$\bf r^2=x^2+y^2\stackrel{chain~rule}{2r\cfrac{dr}{dt}}=0+\stackrel{chain~rule}{2y\cfrac{dy}{dt}}\implies \cfrac{dr}{dt}=\cfrac{2y}{2r}\cdot \cfrac{dy}{dt}
\\\\\\
\cfrac{dr}{dt}=\cfrac{y}{r}\cdot \cfrac{dy}{dt}$

so, what is "r" value 15 minutes later anyway?

$\bf r=\sqrt{(1500+4500+5400)^2+500^2}\implies r=\sqrt{11400^2+500^2}
\\\\\\
r=\sqrt{130210000}\implies r=100\sqrt{13021}$

then we just plug those folks in the derivative,

$\bf \cfrac{dr}{dt}=\cfrac{y}{r}\cdot \cfrac{dy}{dt}\qquad 
\begin{cases}
r=100\sqrt{13021}\\
\frac{dy}{dt}=11\\
y=11400
\end{cases}\implies \cfrac{dr}{dt}=\cfrac{11400}{100\sqrt{13021}}\cdot 11
\\\\\\
 \cfrac{dr}{dt}=\cfrac{114\cdot 11}{\sqrt{13021}}\implies \cfrac{dr}{dt}=\cfrac{1254}{\sqrt{13021}}\implies \cfrac{dr}{dt}\approx 10.99~\frac{f}{s}$

7 0

4 years ago