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Over [174]
3 years ago
9

Find the width of a rectangular prism if the volume is 546cm, the height is 7cm and the length is 13cm.

Mathematics
1 answer:
Margaret [11]3 years ago
7 0

7x w x 13=546

(7x13)*w= 546

91w=546

91w/91= 546/91

w= 6

the width is 6cm

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The point that is the reflection of D across the x-axis and the y-axis is point ___ , and the coordinates of this point are ___
Ainat [17]

Answer:

lol it is 7 90 3

Step-by-step explanation:

6 0
3 years ago
Two certificates of deposit pay interest that differ by 3%. Money invested for one year in the first CD earns $240 interest. The
Soloha48 [4]

a = interest rate of first CD

b = interest rate of second CD

and again, let's say the principal invested in each is $X.

\bf a-b=3\qquad \implies \qquad \boxed{b}=3+a~\hfill \begin{cases} \left( \frac{a}{100} \right)X=240\\\\ \left( \frac{b}{100} \right)X=360 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \left( \cfrac{a}{100} \right)X=240\implies X=\cfrac{240}{~~\frac{a}{100}~~}\implies X=\cfrac{24000}{a} \\\\\\ \left( \cfrac{b}{100} \right)X=360\implies X=\cfrac{360}{~~\frac{b}{100}~~}\implies X=\cfrac{36000}{b} \\\\[-0.35em] ~\dotfill\\\\

\bf X=X\qquad thus\qquad \implies \cfrac{24000}{a}=\cfrac{36000}{b}\implies \cfrac{24000}{a}=\cfrac{36000}{\boxed{3+a}} \\\\\\ (3+a)24000=36000a\implies \cfrac{3+a}{a}=\cfrac{36000}{24000}\implies \cfrac{3-a}{a}=\cfrac{3}{2} \\\\\\ 6-2a=3a\implies 6=5a\implies \cfrac{6}{5}=a\implies 1\frac{1}{5}=a\implies \blacktriangleright 1.2 = x\blacktriangleleft

\bf \stackrel{\textit{since we know that}}{b=3+a}\implies b=3+\cfrac{6}{5}\implies b=\cfrac{21}{5}\implies b=4\frac{1}{5}\implies \blacktriangleright b=4.2 \blacktriangleleft

3 0
3 years ago
How do you find the parameterization of a helix?
Marina CMI [18]

Answer:

\left\{\begin{array}{l}x=r\cos t\\ \\ y=r\sin t\\ \\z=at\end{array}\right.

Step-by-step explanation:

A <u>helix</u> is a curve for which the tangent makes a constant angle with a fixed line. The shortest path between two points on a cylinder (one not directly above the other) is a fractional turn of a helix, as can be seen by cutting the cylinder along one of its sides, flattening it out, and noting that a straight line connecting the points becomes helical upon re-wrapping (see attached diagram for helix).

The parametrization for the helix is

\left\{\begin{array}{l}x=r\cos t\\ \\ y=r\sin t\\ \\z=at\end{array}\right.,

where r is the radius of the helix, a is the constant, and t\in [0,2\pi ) is the parameter

7 0
3 years ago
What is the rate of change
LenKa [72]
The rate of change is -4
5 0
3 years ago
Read 2 more answers
Determine if the sequence is geometric. If it is, find the common ratio, the 8th term, and the explicit formula. -2, 6, -18, 54,
aleksandrvk [35]

Answer:

Step-by-step explanation:

In a geometric sequence, the consecutive terms differ by a common ratio,r. Considering the given sequence,

r = 6/- 2 = - 18/6 = - 3

Therefore, the sequence is geometric.

The formula for determining the nth term of a geometric progression is expressed as

Tn = ar^(n - 1)

Where

a represents the first term of the sequence.

r represents the common ratio.

n represents the number of terms.

From the information given,

a = - 2

r = - 3

The explicit formula is

Tn = - 2 × (- 3)^(n - 1)

To find the 8th term, T8,

T8 = - 2 × (- 3)^(8 - 1)

T8 = - 2 × (- 3)^7

T8 = - 2 × - 2187

T8 = 4374

3 0
3 years ago
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