Answer:
The beam of the light is moving along the shoreline at the rate of [tex]\mathbf{ 160 \ \pi \ mi/min}[/tex]
Step-by-step explanation:
From the given information: Let say x is the distance between the lighthouse and the shoreline. Then, the tangent of trigonometry can be written as:
[tex]tan (\theta )=\dfrac{x}{4}[/tex]
In respect to time, the expression can be derived as:
[tex]sec^2 (\theta) \dfrac{d \theta}{dt} = \dfrac{1 }{4}\dfrac{dx}{dt}[/tex]
[tex]\dfrac{dx}{dt}=\dfrac{4}{cos ^2 (\theta) }\dfrac{d \theta}{dt}[/tex]
To estimate the value of [tex]\dfrac{dx}{dt}[/tex], we need to know cos²(θ) and D
where;
D = [tex]\sqrt{4^2+4^2}= \sqrt{32}\ mi[/tex]
[tex]cos (\theta) = \dfrac{4}{D}[/tex]
[tex]cos (\theta) = \dfrac{4}{\sqrt{32}}[/tex]
[tex]cos (\theta) = \dfrac{4}{\sqrt{16 \times 2}}[/tex]
[tex]cos (\theta) = \dfrac{4}{4 \sqrt{\ 2}}[/tex]
[tex]cos (\theta) = \dfrac{1}{ \sqrt{\ 2}}[/tex]
[tex]cos ^2 (\theta)= \dfrac{1}{2}[/tex]
Finally, we substitute the value of [tex]cos^2(\theta)[/tex] and [tex]\dfrac{d \theta}{dt}[/tex] in the expression derived earlier.
i.e.
[tex]\dfrac{dx}{dt} = \dfrac{4}{\dfrac{1}{2}}\times 10 \ rev/min[/tex]
where;
10 rev/min = (10 × 2π) rad/min = 20π rad/min
Then:
[tex]\dfrac{dx}{dt} = \dfrac{4}{\dfrac{1}{2}}\times 20 \ \pi[/tex]
[tex]\mathbf{\dfrac{dx}{dt} = 160 \ \pi \ mi/min}[/tex]
How to do this problem? Please explain this in steps if possible. Thanks!
Answer: 10
Step-by-step explanation:
If two triangles are congruent, then they will have the exact same sides and angle measures.
AB=3x+1
BC=6
DE=2x
Solve for X by making 2x=6 because DE and BC are corresponding sides, indicating they are equal.
x=3, plug that in
AB=10
Which points are solutions to the equation y=3x+5?
(2,11)
(7,16)
(−7,−16)
(−2,1)
(−3,−1)
PLSSS I GIVE 60 POINTSSS
Please put this in your own words Thank you and happy Halloween
Answer:
Please read explanation :)
Step-by-step explanation:
You can find the constant of proportionality of the ratio of the price to the number of bouquets from the table by dividing them. For example, it you divide 9 by 3 or 18 by 6, you get 3. Therefore, you know that every bouquet is 3 dollars. :) Hope this helps
(But please don't copy, that would be plagiarizing. Maybe you can put this in your own words? Thx <3)
what is the answer to this equation?? (-3)^2=( )( )=
Answer: 9
I did (-3)^2= cause I'm not sure if you meant to put ( ) ( ) in it. If you did well, sorry. I got (-3)^2=9.
You don’t have to explain just give me the answers for these few questions please asap
Answer:
lol do u r own work this is for help no the answers
Step-by-step explanation:
Answer:
same thing you did to me bud
Answer: wheidofnnndbxkdiwijsng Step-by-step explanation: Sorry I needed points
Quarter 1 Benchmark / 3 of 25
The diagram below is a scale drawing of a store, with the scale 1 in. = 16 feet.
4 inches
inches
3 inches
K2 inches -
What is the approximate area of the store in square feet?
O A 2.200
O B. 2,500
OC. 2,300
OD. 2,400
you’ve have by the end of today (12am)
Answer:
B. 2,500
Step-by-step explanation:
The diagram of the area of the store has been divided A and B as shown in the attachment below.
Dimensions of A:
(*Note: scale = 1 in to 16 ft)
Length = 4 inches
Actual length = 4*16 = 64 ft
Width = 1¾ inches
Actual width = 1¾*16 = 28 ft
Area of A = length * width = 64*28 = 1,792 ft²
Dimensions of B:
(*Note: scale = 1 in to 16 ft)
Length = 2¼ inches
Actual length = 2¼*16 = 36 ft
Width = 3 inches - 1¾ inches = 1¼ inches
Actual width = 1¼*16 = 20 ft
Area of A = length * width = 36*20 = 720 ft²
Area of the store = area of A and area of B = 1,792 + 720 = 2,512 ft²
Approximately, the are is 2,500 ft²
guys can you help me
What is the distance between the points (4,
(4, 7) and (4, – 5)
O O units
O 2 units
o 4 units
O 12 units
Plzzzzz nowwwwwww
Answer:
2 units I used the distance formula
What is the value of x?
Enter your answer in the box.
x = ____
Answer:
X=32
Step-by-step explanation:
since it is equilateral, all the angles are the same so they equal 60 , because those are the only possible angle measurements that an equilateral triangle can have.
we know that all the angles are equal to 60 so we set up an equation
2x-4=60
2x=64
x=64/2
x=32
The Pythagorean theorem is used to find the measurement of an angle.
True
False
Answer: False
You are welcome!
How many solutions exist for the given equation?
12(x - 5) = 16 (x - 5)
One
two
zero
Infinitely many
Justin’s mom just had a baby that weigh 8 pounds. Justin insisted that the baby weighed 128 ounces. Is Justin correct or incorrect? Justify your answer.
PPPPPLLLLLLLLLLLLLEEEEEEEEEEEEESSSSSSSSSEEEEEEEEEEEEEEEEE HELP ASAP PPPPLLLLLLEEEEEEEEEEEEEEEEEEEEEEEEEEEESSSSSWEEEEEEEEeeeeeeEEEE
Answer:
Yes, Justin is correct.
Step-by-step explanation:
1 pound equals 16 ounces, so if you multiply 16×8, it equals 128 ounces.
Answer:
read explanation
Step-by-step explanation:
convert pounds to ounces
using the measurement system, for every 16 ounces there is 1 pound
the baby weighs 8 pounds and justin says its equal to 128 ounces.
128 divided by 16 is indeed 8 so therefore justin is right, mom
geesh listen to your kids more
Write an equation of the line with the given slope, m, and y-intercept (0,b).
m= 3, b=7
Answer:
The equation would be y=3x+7. Please mark as helpful if it helps, thanks!
Is there a calculator for long-division that'll show you how the problem is done (ie breaking it down) instead of just answering?
Answer:
A website that sometimes shows breaking down long division is m a t h w a y
Step-by-step explanation:
Which describes the correlation shown in the scatterplot?
Answer:
There is no positive or negative correlation
Step-by-step explanation:
the x-values are increasing but the y-values are staying the same so if you drew a line through correlation... the slope would be around 0
PLEASE HELP ITS DUE SOON
How can you subtract mixed numbers when the fraction in the first mixed numbers is less than the fraction in the second mixed number?
When subtracting mixed numbers, if the fraction in the second mixed number is larger than the fraction in the first mixed number, rewrite the first mixed number by regrouping one whole as a fraction. Alternatively, rewrite all fractions as improper fractions and then subtract.
Elaine bought a total of 15 shirts and pairs of pants. She bought 7 more shirts than pants. How many of each did she buy? HELP
Answer:
7 shirts 8 pairs of pants
Step-by-step explanation:
:(
:)
Answer:
8 pants, and 7 shirts
Step-by-step explanation:
because there are only two factors in here, you can just subtract:
15-7=8
can i get brainliest please?
enter the measure of
Answer: I believe the answer is 45°
Step-by-step explanation: Hope it helps :)
Answer:
Step-by-step explanation:
sin M=8/22
[tex]\angle ~M=sin ^{-1}(\frac{8}{22}) \approx~21.32^\circ[/tex]
Please help! Find what the value of y is for each one. The value for x is given already. (Picture included)
Worth 30 points! :)
Ok. My answer I came up with is:
y=2-3x
Thanks
The distance Train A travels is represented by d = 69t, where d is the distance in kilometers and t is the time in hours. The distance Train B travels at various times is shown in the table. What is the unit rate of each train? Which train is going faster?
If d is distance measured in km and t is time measured in hours, then d = 69t tells you that train A is moving at a rate of 69 km/h.
Why? If t = 1, then d is the distance it moves in 1 hour, and that's precisely the unit rate. It's the rate at which the distance changes when 1 unit of time passes.
For train B, use the info in the given table. In 1 hour (between hours 4 and 5), the train covers a distance of 375 km - 300 km = 75 km. So it's moving at a rate of 75 km/h.
It should be clear which train is faster.
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
[tex]d(A) = 69t[/tex]
[tex]d(B) = 75t[/tex]
The unit rate is the coefficient of t which is the slope of the line because the trains distance traveled equation are linear.
Thus :
Train A's unit rate is 69 km per hour.
And
Train B's unit rate is 75 km per hour.
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Train B is going faster because its unit rate is greater than Train A's unit rate .
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Ariane borrows $200 on a 6−year loan. She is charged 5% simple interest per year. How much interest is she charged for 6 years? What is the total amount she has to pay back?
After 6 years, Ariane is charged $
in interest. She pays a total amount of $
.
Answer:
she is charged 80 in interest for 4 years, the total she has to pay back is 480
Step-by-step explanation:
what is an equation in point-slope form of the line that passes through the point (4,-1) and has a slope of 6
Answer:
y = 6x + (-1) or y = 6x - 1
Step-by-step explanation:
y = mx + b
M = Slope = 6
B = y-intercept = -1
Explain how to round to the hundredths 382.992
NEED HELP ON THIS QUESTION VERY EASY
Answer: B.
Step-by-step explanation: I UNDERSTAND HOW FRUSTRATING IT IS TO PUT AN ANSWER AND NO ONE ANSWERS IT, I DO, SO ALL I ASK IS FOR YOU TO GIVE ME BRAINLIEST. THANK YOU.
Answer:
b ive never had a brainliest ever in my life so can i have one
Step-by-step explanation:
pls GIVE ME BRAINLIEST not trynna demand
The amount of force needed to keep a 0.5 kg baseball moving at a constant speed of 4 m/s on frictionless ice is
Answer: 0 N
Step-by-step explanation:
6th grade math I mark as brainliest
Answer:
the answer is d :)
Step-by-step explanation:
write an integer for the situation.
Ascend 50 feet
Answer:
50 ft
Step-by-step explanation:
An integer is a whole number.
If you're Ascending that means to go up( or to increase in height. This means that the number would be positive. The 50 feet would give us our number, so our answer is (+) 50 ft.
Seven more than a number is less than or equal to -18
Answer:
7+x<=-18
subtract 7 from both sides
x<=-25
Step-by-step explanation:
The equation is 7+x<=-18 and the value of x = -25.
Given that,
Seven more than a number is less than or equal to -18Based on the above information, the calculation is as follows:
7+x<=-18
x = -25
Learn more: https://brainly.com/question/12522729?referrer=searchResults
Can you guys please help me out
Answer:
18
Step-by-step explanation:
xy = x times y
in our case, it is 6 times 3
so 18
