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babymother [125]

2 years ago

13

The volume of a stack of identical circular drink coasters, each 1 centimeter thick, can be found using the function v(r)=8(3.14

)(r)^2, where r is the radius of a coaster. What does the constant 8 in the function represent?

2 answers:

Vladimir79 [104]2 years ago

8 0

The volume of a stack of identical circular drink coasters, each 1 centimeter thick, can be found using the function v(r)=8(3.14)(r)^2, where r is the radius of a coaster. What does the constant 8 in the function represent?

The constant 8 represents the height of the stack and hence the number of coasters.

Gnesinka [82]2 years ago

5 0

Answer:

It represents the number of coasters.

Step-by-step explanation:

The formula for finding the volume of a cylinder is

V = πr²h

If you we take π =3.14 and h = 1 cm, as given in the question, then we can rewrite the formula for the volume of one coaster as

V = 3.14 * r²

But the formula in this question is

V(r) = 8*3.14 * r² so this means that there are 8 coasters here hence the formula for one coaster being multiplied by 8.

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LK is tangent to circle J at point K. Circle J is shown. Line segment J K is a radius. Line segment K L is a tangent that inters

Evgen [1.6K]

Answer:

$(B)r=\dfrac{85}{12}$

Step-by-step explanation:

Given a circle centre J

Let the radius of the circle =r

LK is tangent to circle J at point K

From the diagram attached

LX=6
Radius, XJ=JK=r
LK=11

Theorem: The angle between a tangent and a radius is 90 degrees.

By the theorem above, Triangle JLK forms a right triangle with LJ as the hypotenuse.

Using Pythagoras Theorem:

$(6+r)^2=r^2+11^2\\(6+r)(6+r)=r^2+121\\36+6r+6r+r^2=r^2+121\\12r=121-36\\12r=85\\r=\dfrac{85}{12}$

The length of the radius, $r=\dfrac{85}{12}$

8 0

2 years ago

Read 2 more answers

Suppose that demand in period 1 was 7 units and the demand in period 2 was 9 units. Assume that the forecast for period 1 was fo

Zepler [3.9K]

Answer:

Step-by-step explanation:

Forecast for period 1 is 5

Demand For Period 1 is 7

Demand for Period 2 is 9

Forecast can be given by

$F_{t+1}=F_t+\alpha (D_t-F_t)$

where

$F_{t+1}=Future Forecast$

$F_t=Present\ Period\ Forecast$

$D_t=Present\ Period\ Demand$

$\alpha =smoothing\ constant$

$F_{t+1}=5+0.2(7-5)$

$F_{t+1}=5.4$

Forecast for Period 3

$F_{t+2}=F_{t+1}+\alpha (D_{t+1}-F_{t+1})$

$F_{t+2}=5.4+0.2\cdot (9-5.4)$

$F_{t+2}=6.12$

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2 years ago

Colin invests £2350 into a savings account. The bank gives 4.2% compound interest for the first 4 years and 4.9% thereafter. How

mixer [17]

To solve this, we are going to use the compound interest formula: $A=P(1+ \frac{r}{n} )^{nt}$
where
$A$ is the final amount after $t$ years
$P$ is the initial investment
$r$ is the interest rate in decimal form
$n$ is the number of times the interest is compounded per year

For the first 4 years we know that: $P=2350$ , $r= \frac{4.2}{100} =0.042$ , $t=4$ , and since the problem is not specifying how often the interest is communed, we are going to assume it is compounded annually; therefore, $n=1$ . Lest replace those values in our formula:
$A=P(1+ \frac{r}{n} )^{nt}$
$A=2350(1+ \frac{0.042}{1} )^{(1)(4)}$
$A=2350(1+0.042)^{4}$
$A=2770.38$

Now, for the next 6 years the intial investment will be the final amount from our previous step, so $P=2770.38$ . We also know that: $r= \frac{4.9}{100} =0.049$ , $t=6$ , and $n=1$ . Lets replace those values in our formula one more time:
$A=P(1+ \frac{r}{n} )^{nt}$
$A=2770.38(1+ \frac{0.049}{1})^{(1)(6)$
$A=2770.38(1+0.049)^6$
$A=3691.41$

We can conclude that Collin will have <span>£3691.41 in his account after 10 years.</span>

4 0

2 years ago

A quadratic pattern has a second term equal to 1,a third term equal to -16 and a fifth term equal to -14

chubhunter [2.5K]

Given are several terms in a quadratic pattern:

a1 = ?
a2 = 1
a3 = -16
a4 = ?
a5 = -14

let:

x y
1 ?
2 1
3 -16
4 ?
5 -14

considering the 2nd term and 3rd term, we can determine a quadratic function:

y = -17x + 35

therefore,

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7 0

2 years ago

You have heard that customers will try a new caterer if the price is 20% below their existing caterer. Your competitor prices a

Evgesh-ka [11]

Answer:

b) $640

Step-by-step explanation:

Competitor's price = $800

<u>Price, 20% below of competitor's:</u>

$800 - 20% =
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Correct answer choice is b) $640

3 0

2 years ago