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ella [17]
2 years ago
10

Rob is making a scale model of the Solar System on the school field. He wants the distance from the Sun to Jupiter to be 8 metre

s on his scale model. The real distance from the Sun to Jupiter is 7.8 × 10 8 kilometres. Find the scale of the model. Give your answer in the form 1 : n , where n is written in standard form.
Mathematics
1 answer:
ANEK [815]2 years ago
3 0

Answer:

1 : 9.75 * 10⁷

Step-by-step explanation:

To find n, we have to divide the real distance by the scale distance. This is 7.8 * 10⁸ / 8 = 0.975 * 10⁸ = 9.75 * 10⁷ which means that the ratio is 1 : 9.75 * 10⁷.

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The Colossus Ferris wheel debuted at the 1984 New Orleans World’s Fair. The ride is 180 ft tall, and passengers board the ride a
Makovka662 [10]

Answer:

T=\frac{2}{3}

Interpretation:

It means that Passenger will reach to same height after each 2/3 minutes

Step-by-step explanation:

We are given height function as

h=82.5sin(3\pi(t+0.5))+97.5

where

h is the height above the ground

t is the time

we can compare it with standard equation

y=Asin(B(t+C))+D

Period formula is

T=\frac{2\pi}{B}

now, we can compare and find B

B=3\pi

we can find period

T=\frac{2\pi}{3\pi}

T=\frac{2}{3}

Interpretation:

It means that Passenger will reach to same height after each 2/3 minutes

5 0
2 years ago
Three friends are playing catch. Zoe is in a straight path 12 feet to the west of alex. Jin is in a straight path 9feet to the n
Tanzania [10]

Answer:

15 ft

Step-by-step explanation:

This problem can be represented by a right angle triangle, shown in the diagram below.

The distance between Jin and Zoe is the hypotenuse of the triangle, x.

According to Pythagoras theorem,

hyp² = opp² + adj²

Where opp is the opposite side and adjacent is the adjacent side to any angle of consideration (which is not important in this case)

Hence:

x² = 12² + 9²

x² = 144 + 81

x² = 225

Finding the square root:

x = 15 ft

Jin and Zoe are 15 ft apart.

4 0
2 years ago
The radius of a right circular cone is increasing at a rate of 1.4 in/s while its height is decreasing at a rate of 2.1 in/s. At
kow [346]

Given:

\dfrac{dr}{dt}=1.4\text{ in/s}

\dfrac{dh}{dt}=-2.1\text{ in/s}

To find:

The rate of change in volume at r=120\text{ in. and }175\text{ in.}

Solution:

We know that, volume of a cone is

V=\dfrac{1}{3}\pi r^2h

Differentiate with respect to t.

\dfrac{dV}{dt}=\dfrac{1}{3}\pi\times \left[(r^2\dfrac{dh}{dt}) + h(2r\dfrac{dr}{dt})\right]

Substitute the given values.

\dfrac{dV}{dt}=\dfrac{1}{3}\times \dfrac{22}{7}\times \left[(120)^2(-2.1) +175(2)(120)(1.4)\right]

\dfrac{dV}{dt}=\dfrac{22}{21}\times \left[-30240+58800\right]

\dfrac{dV}{dt}=\dfrac{22}{21}\times 28560

\dfrac{dV}{dt}=29920

Therefore, the volume of decreased by 29920 cubic inches per second.

6 0
2 years ago
The value of good wine increases with age. Thus, if you are a wine dealer, you have the problem of deciding whether to sell your
Katyanochek1 [597]

Answer: 64 years

Step-by-step explanation:

Let assume the dealer sold the bottle now for $P, then invested that money at 5% interest. The return would be:

R1 = P(1.05)^t,

This means that after t years, the dealer would have the total amount of:

$P×1.05^t.

If the dealer prefer to wait for t years from now to sell the bottle of wine, then he will get the return of:

R2 = $P(1 + 20).

The value of t which will make both returns equal, will be;

R1 = R2.

P×1.05^t = P(1+20)

P will cancel out

1.05^t = 21

Log both sides

Log1.05^t = Log21

tLog1.05 = Log21

t = Log21/Log1.05

t = 64 years

The best time to sell the wine is therefore 64years from now.

7 0
2 years ago
The solution to the given system of linear equations lies in which quadrant?
Rina8888 [55]
X-3y=6
x+y=2
this is an substitution problem
so first you can do is rewrite the problem by subjection one variable
x=3y+6
then substitute this in the other proble
x+y=2
(3y+6)+y=2
4y+6=2
4y=2-6
4y=-4
y=-1
then substitute the no. in the original equation. 
x=3y+6
x=3(-1)+6
x=-3+6
x=3
now you got the intercepts and you draw the line and check.
it's in the IV quadrant
5 0
1 year ago
Read 2 more answers
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