Answer:
[tex]\dfrac{800 \pi}{7} \ miles/min[/tex]
Step-by-step explanation:
From the given information:
We learned that the light rotates 8 revolutions per minute.
Therefore;
[tex]\dfrac{d \theta}{d t}= \dfrac{8 * 2 \pi}{1 \ min}[/tex]
[tex]\dfrac{d \theta}{d t}= 16\pi \ rads/min\\[/tex]
From the trigonometry formula, the tanget of the lighthouse in relation to the closest point on a straight shoreline can be expressed as:
[tex]tan \theta = \dfrac{x}{7}[/tex]
By differentiation with respect to t; we have:
[tex]\dfrac{d(tan \theta)}{dt} = \dfrac{1}{7} * \dfrac{dx}{dt}[/tex]
[tex]\dfrac{d(tan \theta)}{d \theta}* \dfrac{d \theta}{dt} = \dfrac{1}{7} * \dfrac{dx}{dt}[/tex]
By applying the chain rule:
[tex]sec^2 * \dfrac{d \theta }{d t} = \dfrac{1}{7} * \dfrac{dx}{dt}[/tex]
[tex](1 + tan ^2 \theta) \dfrac{d \theta }{dt} = \dfrac{1}{7} * \dfrac{dx}{dt}[/tex]
When x = 3 ; we have [tex]tan \theta = \dfrac{1}{7}[/tex]
[tex]\bigg (1 + \dfrac{1}{49} \bigg ) \dfrac{d \theta }{dt} = \dfrac{1}{7} * \dfrac{dx}{dt}[/tex]
Also;
[tex]\dfrac{d \theta}{d t}= 16\pi \ rads/min\\[/tex]
[tex]\bigg (1 + \dfrac{1}{49} \bigg ) 16 \pi = \dfrac{1}{7} * \dfrac{dx}{dt}[/tex]
[tex]\bigg ( \dfrac{50}{7} \bigg ) 16 \pi = \dfrac{dx}{dt}[/tex]
[tex]\dfrac{dx}{dt} = \dfrac{800 \pi}{7} \ miles/min[/tex]
If the average gas price was 3.85 per gallon how much did you spend on gas and if you used 25 gallons of gas?
Answer:
Step-by-step explanation:
96.25 for 25 gallons
3.85 times 25 and that's your answer
Laila bought 20 strawberries. She ate 1 strawberry. What percentage of the strawberries did Laila eat?
Answer: 5%
Step-by-step explanation: 100%÷20=5%
is 0 a natural number?
Answer:
No 0 is not a natrual number but it is a whole number.
Step-by-step explanation:
the image of the point (-8, -5) under a reflection across the x-axis is (8, -5)
True or false
Select the correct scientific notation form of this numeral. Can someone help me with this
541
5.0 × 10 2
5 × 10 2
5.41 × 10 2
5.4 × 10 2
Answer:
it would be 5.41 x 10^2
Step-by-step explanation:
the reason it would be this is because when you have it ^2 you love the decimal that many places the same goes for the number was negative then you would move it backwards.
Answer:
The answer is 5.41 × 10^2
Step-by-step explanation:
To make sure the answer is right, picture a decimal on the right of the 1 in the numeral. Then, picture it going to the left until it's next to the 5. Since it moved twice, the exponent is 2 and the decimal is 5.41. Hope this helps!
Determine if the ordered pair (−2,1) is a solution of 2x−y=−3.
yes or no
Answer:
no, it is not a solution
Step-by-step explanation:
2x−y=−3.
insert the x value and y value ---> x= -2 y= 1
2(-2) -(1)= -3
simplify
-4-1=-3
-5= -3
NO
brainliest will be givenChristine has a summer job cutting grass.
She earns $400 every 2 weeks. How much
will she earn over the summer holidays,
which are 12 weeks long?
Answer:
$2400 in 12 weeks is your answer
4 (2+6)+4-3 (9-7))))))
Answer:
the answer is 10
Step-by-step explanation:
i hope it helped you!
Are y = -5x + 2 and y = 5x – 3 parallel, perpendicular or neither?
A.Parallel
B.Perpendicular
C.Neither
Answer:
parallel is the answer
Please help me quickly! 3.5.2 Practice for income tax
Answer:
$15,475
Step-by-step explanation:
Mr. and Mrs. Jones make a combined $92,400 in taxable income. Looking at the table, their income is over $67,900 but not over $137,050.
So, the tax is $9,350. But, it also includes 25% of the amount over $67,900.
So,
$92,400 - $67,900 = $24,500
0.25 × $24,500 = $6,125
$9,350 + $6,125 = $15,475
Hope that helps.
Solve the equation. Then check your solution.
A-1/2=3/5
Answer:
B: 1 1/10
Step-by-step explanation:
Step 1:
a - 1/2 = 3/5 Equation
Step 2:
a - 5/10 = 6/10 Find the common denominator
Step 3:
a = 4/10 + 6/10 Add 5/10 on both sides
Answer:
a = 11/10 or 1 1/10
Hope This Helps :)
Jose scored 80% on Part A of a math test and 92% on part B of the math test. His total mark on the test was 63. The total possible marks for the test was 75. Which system of equations represents this situation?
a (0.80A + 0.92B = 63 A + B = 75
ь (80A + 92B = 63 A + B = 75
с 0.80A + 0.92B = 75 A+B=63
d (80A + 92B = 75 A+B=63
Answer:
A
Step-by-step explanation:
3,397 is 13.7 percent of what number
3397% of 13.7 = 465.389
12x-15?simplify or expand the expression
Answer:
3 (4x - 5) You would expand the expression, by factoring 3 out of each of the numbers.
An amusement park has two roller coasters. One is 628 feet long, and the other is 485 feet long if you ride both roller coasters, about how many feet will you travel in all
Answer:
1113
Step-by-step explanation:
628ft+485ft=1113ft
I’m lost. Can you help me?
Answer:
yes i can ❤ help you you. just say.!
How many grams are in 1.204 x 10 24 atoms lithium
Answer:
We have:
1.204x10^24 atoms of lithium.
The weight of one atom of lithium is: 6.941 atomic mass units.
And we know that:
1 atomic mass unit = 1.661x10^(-24)g
Then the mass of one atom is 6.941 times 1.661x10^(-24)g
m = 6.941*1.661x10^(-24)g = 1.153x10^(-23)g
Then the mass of 1.204x10^24 atoms is 1.204x10^24 times 1.153x10^(-23)g
M = 1.204x10^24 *1.153x10^(-23)g = 1.388x10^(24 - 23) g
M = 1.388x10^1g = 13.88 g
Then 1.204x10^24 atoms of lithium wieght 13.88 grams.
] Find the vector form of the general solution to the given linear system Ax = b. Then use that result to find the vector form of the general solution to Ax = 0.
This question is incomplete, the complete question is;
Find the vector form of the general solution to the given linear system Ax = b; Then use that result to find the vector form of the general solution to Ax = 0.
x1 + x2 + 2x3 = 5
x1 + x3 = -2
2x1 + x2 + 3x3 = 3
Answer:
the vector form of the general solution to the given linear system Ax = b
x1 -2 -1
x2 = 7 +s -1
x3 0 1
find the vector form of the general solution to Ax = 0.
x1 -1
x2 = s -1
x3 1
Step-by-step explanation:
Given that;
x1 + x2 + 2x3 = 5
x1 + x3 = -2
2x1 + x2 + 3x3 = 3
Augmented matrix is expressed as;
1 1 2 5
1 0 3 -2
2 1 3 3
R2 ← R2 - R1
1 1 2 5
0 -1 -1 -7
2 1 3 3
R3 ← R3 - 2R1
1 1 2 5
0 -1 -1 -7
0 -1 -1 -7
R3 ← R3 - R2
1 1 2 5
0 -1 -1 -7
0 0 0 0
R1 ← R1 + R2
1 0 1 -2
0 -1 -1 -7
0 0 0 0
R2 ← - R2
1 0 1 -2
0 1 1 7
0 0 0 0
SO from the above reduced matrix, we get
x1 = -2 - x3
x2 = 7 - x3
x3 = x3
now we introduce parameter "s" for free variable x3
x1 = -2 - s
x2 = 7 - s
x3 = s
x1 -2 -1
x2 = 7 +s -1
x3 0 1
General solution of Ax = 0 will be
x1 -1
x2 = s -1
x3 1
Which of the following values is the slope of any line parallel to 5x + 7y = 6?
A. 7
B. 5
C. -7/5
D. -5/7
Answer:
D
Step-by-step explanation:
Someone help please
What is the slope of the following equation?
Answer:
-5
Step-by-step explanation:
the slope is the one conected to the x
A box with 3 pounds of chocolate costs $54.
what is the unit rate per pound
HELP ME PLEASE ASAP
Answer:
$18 per pound
Step-by-step explanation:
3 pounds/3 = 1 pound
54/3=18
Find the measure of the angle indicated in bold.
Answer:
35º
Step-by-step explanation:
20x + 5 = 24x - 1
x = 1.5
Ben drank 2/5.of a pitcher lemonade.Tonya drank 1/4 of the Lemonade.what is the fraction of the lemonade did they drink together?step step explanation who work with plz
Answer: 13/20
Step-by-step explanation:
Find the lowest common denominator (20)
Multiply the numerators by the other denominators
(2 * 4)
--------
20
&
(1 * 5)
--------
20
8/20 + 5/20 = 13/20
A. Similar - AA
B. Similar - SSS
C. Similar - SAS
D. Cannot be determined
Write the equation that describes the line in slope
intercept form:
slope 8, y intercept = 2
Answer:
y = 8x + 2
Step-by-step explanation:
Step-by-step explanation:
please mark me as brainlest
what is 33 devided by 78
Question:
What is 33/78
What is 78/33
Step-by-step explanation:
Well if you think about it 33/78=0.42307692307
Well if you think about it 78/33=2.36363636364
Answer:
Those big numbers :p
Solve 2x + 6y = 11, solve for y
Answer:
y= 11-2x / 6
Step-by-step explanation:
Darius filled up his gas tank with 24 gallons of gas. For each mile that he drives, he uses 0.06 gallons of gas. How may gallons of gas are left in the tank after driving 240 miles?
Answer:
9.6 gallonsStep-by-step explanation:
Step one:
Given that the capacity of the gas tank is 24 gallons.
we know that 1 mile will consume 0.06 gallons
therefore x miles will consume 0.06x gallons.
the consumption for any distance is given as
0.06x gallons.
Step two:
if x=240 miles
then the gallons consume will be
0.06(240)=14.4 gallons
Step three:
the remaining gallons of gas in the tank will be
24-14.4=9.6 gallons
The reamining gallons will be 9.6 gallons
What’s the factored form of f(x)=x^3-5x^2+4x