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3 years ago

What is the nth term of the arithmetic sequence 7,5,3,1?

Mathematics

1 answer:

Minchanka [31]3 years ago

3 0

Answer:

tn = 7 + (n - 1)*(-2) or

tn = 9 - 2n

Step-by-step explanation:

You are (beginning with 7) subtracting 2 from the term to the left.

a = 7

d = -2

tn = a1 + (n - 1)*d

tn = 7 + (n - 1)*(-2)

Try this out on n = 4

t4 = 7 + (4 - 1)*-2

t4 = 7 + (3) (-2)

t4 = 7 - 6

t4 = 1 just as it says.

More generally

tn = 7 + (n - 1)*-2

tn = 7 + (-2n) + 2

tn = 9 - 2n

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if it would take billy an hour to race over to his girlfriends house and two hours if he went 20 miles per hour slower how far a

mel-nik [20]

Recall your d = rt, distance = rate * time.

now, let's say she lives "d" miles away, and so if Billy goes say at "r" mph fast to her house, he gets there in 1hr.

now, if he goes 20 mph slower, namely " r - 20 " mph, he gets there in 2 hours, same "d" miles.

$\bf \begin{array}{lccclll}
&\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\
&------&------&------\\
\textit{Billy}&d&r&1\\
\textit{slower Billy}&d&r-20&2
\end{array}
\\\\\\
\begin{cases}
d=r(1)\implies d=\boxed{r}\\
d=2(r-20)\\
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d=2d-40\implies 40=d$

5 0

3 years ago

A cylinder has a a radius of 18in and a<br> height of 21in. Find its volume.

IgorLugansk [536]

Answer:

Just Multiply them together

Step-by-step explanation:

4 0

2 years ago

A gumball has a diameter that is 66 mm. The diameter of the gumball's spherical hollow core is 58 mm. What is the volume of the

grigory [225]

Answer:

Volume of gumball without including its hollow core is 48347.6 cubic mm.

Step-by-step explanation:

Given:

Diameter of Gumball = 66 mm

Since radius is half of diameter.

Radius of gumball = $\frac{diameter}{2}=\frac{66}{2} =33 \ mm$

Now We will first find the Volume of Gumball.

To find the Volume of Gumball we will use volume of sphere which is given as;

Volume of Sphere = $\frac{4}{3}\pi r^3$

Now Volume of Gumball = $\frac{4}{3}\times3.14 \times (33)^3 = 150456.24 \ mm^3$

Also Given

Diameter of gumball's spherical hollow core = 58 mm

Since radius is half of diameter.

Radius of gumball's spherical hollow core = $\frac{diameter}{2}=\frac{58}{2} =29 \ mm$

Now We will find the Volume of gumball's spherical hollow core.

Volume of Sphere = $\frac{4}{3}\pi r^3$

So Volume of gumball's spherical hollow core = $\frac{4}{3}\times3.14 \times (29)^3 = 102108.61 \ mm^3$

Now We need to find volume of the gumball without including its hollow core.

So, To find volume of the gumball without including its hollow core we would Subtract Volume of gumball spherical hollow core from Volume of Gumball.

volume of the gumball without including its hollow core = Volume of Gumball - Volume of gumball's spherical hollow core = $150456.24\ mm^3 - 102108.61\ mm^3 = 48347.63\ mm^3$

Rounding to nearest tenth we get;

volume of the gumball without including its hollow core = $48347.6\ mm^3$

Hence Volume of gumball without including its hollow core is 48347.6 cubic mm.

8 0

3 years ago

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IgorC [24]

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To do this we need to move right 6 as the x-coordinate goes from -4 to 2. We also need to move down 4 as the y-coordinate goes from 5 to 1. So we add 6 to the x-coordinate and subtract 4 from the y-coordinate. The transformation rule is (x+6, y-4).

Once you do this the circles have the same center. Next you wish to dilate circle 1 so it ends up being the same size at circle 2. That means you stretch it out in such a way that it keeps its shape. Circle 1 has a radius of 2 centimeters and circle 2 has a radius of 6 centimeters. That is 3x bigger. So we dilate by a factor of 3.

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The value of x is? What is the value of x in this problem?

snow_lady [41]

Answer:

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