Answer:
The ship is located at (3,5)
Explanation:
In the first test, the equation of the position was:
5x² - y² = 20 ...........> equation I
In the second test, the equation of the position was:
y² - 2x² = 7 ..............> equation II
This equation can be rewritten as:
y² = 2x² + 7 ............> equation III
Since the ship did not move in the duration between the two tests, therefore, the position of the ship is the same in the two tests which means that:
equation I = equation II
To get the position of the ship, we will simply need to solve equation I and equation II simultaneously and get their solution.
Substitute with equation III in equation I to solve for x as follows:
5x²-y² = 20
5x² - (2x²+7) = 20
5x² - 2y² - 7 = 20
3x² = 27
x² = 9
x = <span>± </span>√9
We are given that the ship lies in the first quadrant. This means that both its x and y coordinates are positive. This means that:
x = √9 = 3
Substitute with x in equation III to get y as follows:
y² = 2x² + 7
y² = 2(3)² + 7
y = 18 + 7
y = 25
y = +√25
y = 5
Based on the above, the position of the ship is (3,5).
Hope this helps :)
Answer:
100 meters per hour.
Step-by-step explanation:
7,200 seconds / 60 = 120 minutes
120 minutes / 60 = 2 hours
200 meters / 2 hours = 100 meters
Since the squirrel moved 200 meters in 2 hours, the squirrel moved 100 metres per hour.
After 7 years fund balance will be $2152336.05 if the philanthropist pledges to donate 10% of a fund each year.
<h3>What is an exponential function?</h3>
It is defined as the function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent. 
where a is a constant and a>1
We have:
A philanthropist pledges to donate 10% of a fund each year.
We can find the amount left after 7 years as follows:
A = 450000(1 - 0.1)⁷
10% of a fund each year.
Rate r = 10% = 0.1
A = 450000(0.9)⁷
A = $2152336.05
Thus, after 7 years fund balance will be $2152336.05 if the philanthropist pledges to donate 10% of a fund each year.
Learn more about the exponential function here:
brainly.com/question/11487261
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Answer:
Step-by-step explanation:
from the graph of f(x)
when x=1,f(x)=0
or f(1)=0
when f(x)=2,x=2
for g(x)
when x=6,g(x)=16
or g(6)=16
when g(x)=18,x=32
for h(x)
when x=14
h(x)=27x-7
h(14)=27×14-7=7(27×2-1)=7(54-1)=7×53=371
h(x)=-493
27x-7=-493
27 x=-493+7=-486
3 x=-54
x=-18
for p(t)
when t=94
p(t)=24
p(94)=24
p(t)=67
t=31
