9514 1404 393
Explanation:
As written, the equation is not an identity. Perhaps you want to show ...
(csc(x) +cot(x))² = (cos(x) +1)/(1 -cos(x))
__
We will transform the left-side expression to the form of the right-side expression.
[tex](\csc(x)+\cot(x))^2=\left(\dfrac{1}{\sin(x)}+\dfrac{\cos(x)}{\sin(x)}\right)^2=\dfrac{(1+\cos(x))^2}{\sin(x)^2}\\\\=\dfrac{(1+\cos(x))^2}{1-\cos(x)^2}=\dfrac{1+\cos(x)}{1-\cos(x)}\cdot\dfrac{1+\cos(x)}{1+\cos(x)}=\boxed{\dfrac{\cos(x)+1}{1-\cos(x)}}[/tex]
A plane flying horizontally at an altitude of 3 miles and a speed of 500 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 4 miles away from the station. (Round your answer to the nearest whole number.)
Answer:
The rate at which the distance from the plane to the station is increasing is 331 miles per hour.
Step-by-step explanation:
We can find the rate at which the distance from the plane to the station is increasing by imaging the formation of a right triangle with the following dimensions:
a: is one side of the triangle = altitude of the plane = 3 miles
b: is the other side of the triangle = the distance traveled by the plane when it is 4 miles away from the station and an altitude of 3 miles
h: is the hypotenuse of the triangle = distance between the plane and the station = 4 miles
First, we need to find b:
[tex] a^{2} + b^{2} = h^{2} [/tex] (1)
[tex] b = \sqrt{h^{2} - a^{2}} = \sqrt{(4 mi)^{2} - (3 mi)^{2}} = \sqrt{7} miles [/tex]
Now, to find the rate we need to find the derivative of equation (1) with respect to time:
[tex]\frac{d}{dt}(a^{2}) + \frac{d}{dt}(b^{2}) = \frac{d}{dt}(h^{2})[/tex]
[tex] 2a\frac{da}{dt} + 2b\frac{db}{dt} = 2h\frac{dh}{dt} [/tex]
Since "da/dt" is constant (the altitude of the plane does not change with time), we have:
[tex] 0 + 2b\frac{db}{dt} = 2h\frac{dh}{dt} [/tex]
And knowing that the plane is moving at a speed of 500 mi/h (db/dt):
[tex]\sqrt{7} mi*500 mi/h = 4 mi*\frac{dh}{dt}[/tex]
[tex]\frac{dh}{dt} = \frac{\sqrt{7} mi*500 mi/h}{4 mi} = 331 mi/h[/tex]
Therefore, the rate at which the distance from the plane to the station is increasing is 331 miles per hour.
I hope it helps you!
Eva is a hairdresser. Before her lunch break, she gave 4 haircuts and colored the hair of 4 clients in 376 minutes. After lunch, she gave 2 haircuts and colored the hair of 4 clients in 336 minutes. How long does it take for Eva to perform each type of service, assuming the amount of time doesn't vary from client to client?
Step-by-step explanation:
ratio 6:8
376+336=712
6+8=14
712/14=50.86
haircut= 50.86*6=305.16
colour= 50.86*8=406.88
i hope this helps
Find the area of this triangle
Use Heron's formula.
A = sqrt{(s - a)*s - b)(s - c)}, where a, b, and c represent the sides of the triangle.
We need to find s first.
So, s = (a + b + c)/2.
s = (13 + 6 + 9)/2
s = 28/2
s = 14
We now plug everything into the Heron's area formula.
A = sqrt{(14 - 13)(14 - 9)(14 -6)}
A = sqrt{(1)(5)(8)}
A = sqrt{40}
A = 6.3245553203
Let us now round to one decimal place as instructed. We round to the tenths place, in other words.
A = 6.3 cm^2
Did you follow?
GIVING OUT BRAINLIEST ANSWER HELP PLSSSS
Answer:
x = 63.43...
Step-by-step explanation:
Ok, so the angle x is the same measure as the bottom right angle of the triangle because the bottom of the triangle and the dashed line are parallel. Knowing this we can simply solve for the bottom right angle and it will be the same as angle x.
To do this we can set up and equation with tangent because we are working with the opposite and adjacent sides of the triangle.
[tex]Tan(x) = \frac{opposite}{adjacent} = \frac{50}{25} = 2[/tex]
[tex]Tan(x)=2\\[/tex]
Now to isolate the variable, we can simply use the cotangent or inverse tangent.
[tex]Tan^{-1}(Tan(x)) = Tan^{-1}(2)\\x = Tan^{-1}(2)\\x = 63.43...[/tex]
A Business Has 384 cases of water. There Are 42 bottles of water does the business have
Answer:
Step-by-step explanation:
A new car is purchased for $26,000 and over time its value depreciates by one half
every 5 years. What is the value of the car 7 years after it was purchased, to the
nearest hundred dollars?
Answer: $203
Step-by-step explanation: We first start out with the exponential decay model which is y=a(1-r)^t, then plug in the numbers of your problem:
-y=26,000(1-0.50)^7
-y=26,000*0.50^7
-y=26,000*0.0078125
-y=203.125
Then, after rounding to the nearest hundred dollars you get your answer....
:) hope this helped a bit
The value of the car 7 years after it was purchased will be $203.
What is exponential decay?A quantity lowers gradually at first during exponential decay before rapidly declining after that. Half-life may be calculated using the exponential decay formula, which is also used to estimate population decrease.
It is given that, A brand-new car costs $26,000 to buy, and every five years, its value decreases by 50%.
We have to find the value of the car 7 years after it was purchased
The exponential decay model, y=a(1-r)t, is where we begin. The data from your problem are then entered.
y=-26,000(1-0.50)^7
y=-26,000*0.50^7
y=-26,000*0.0078125
y=-203.125 (-ve shows the value is declining)
Thus, the car will be worth $203 seven years after it was bought.
Learn more about the exponential decay here:
brainly.com/question/14355665
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there are 50 pupils in a class out of this 1/10 speak french only and 4/5 of the remainder speak both french and english. if the rest speak to english only, find the number of students who speaks both english and french?
English only?
Answer:
English and French:40 and English:10
Step-by-step explanation:
English and French:4÷5×50
=40
English:1÷10×50
=10
PLEASE HELP I NEED THIS TO PASS
Answer:
Step-by-step explanation:
total sum of Triangle's angles is 180 deg:
than: x = 180 -61-56 = 63
Answer:
63 degrees
Step-by-step explanation:
All three angles in a triangle is always 180, so 180-61-56=63 degrees
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Have a great weekend!
The total cost for one t the total cost for a dozen donuts includes the cost to make the donuts and the cost of the box. Create expression to model the cost for one dozen donuts where T represents the total surface area of the box
The expression that represents the total cost of the donuts is: c + d
How to determine the total expression?To determine the expression that represents the total cost, the following parameters are needed
The cost of the donut boxThe cost of the donut, itselfLet c represents the cost of the donut box, and d represents the cost of the donut, itself
Hence, the expression that represents the total cost is:
c + d
Read more about algebraic expressions at:
https://brainly.com/question/4344214
5. Find the surface area of the prism.
(1 point)
5 m
6 m
13 m
Not drawn to scale.
048 m2
O 346 m2
0780 m2
O 195 m2
Answer:
[tex]Area = 346m^2[/tex]
Step-by-step explanation:
Given
[tex]Length = 5m\\Width = 6m\\Height = 13m[/tex]
Required
Determine the surface area
This is calculated as:
[tex]Area = 2 * (Length * Width + Length * Height + Width * Height)[/tex]
So, we have:
[tex]Area = 2 * (5m * 6m + 5m * 13m + 6m * 13m)[/tex]
[tex]Area = 2 * (30m^2 + 65m^2 + 78m^2)[/tex]
[tex]Area = 2 * (173m^2)[/tex]
[tex]Area = 346m^2[/tex]
Find the area of the triangle 14 Ft 17 ft
Answer:
119
Step-by-step explanation:
14x17 = 238)/2
The hypotenuse of a right triangle is 8 meters longer than the shortest leg. The longest leg is 4 meters. Longer than the shortest leg find the length of the longest leg
Answer:
the leg is 6.9
Step-by-step explanation:
use the reverse Pythagorean therm
find the square root of 8(squared) - 4(squared) =6.9
Which of the following statements is true for the quadratic equation x2 – 16x + 64 = 0?
Answer:
Please provide the statements.
Step-by-step explanation:
Answer:
the equation has one anser
Step-by-step explanation:
According to a health statistics center, the mean weight of a 20-to-29-year-old female is 156.5 pounds, with a standard deviation of 51.2 pounds. The mean weight of a 20-to-29-year-old male is 183.4 pounds, with a standard deviation of 40.0 pounds. Who is relatively heavier: a 20-to-29-year-old female who weighs 160 pounds or a 20-to-29-year-old male who weighs 185 pounds
mind fact sub happy wala birthday quiz frist video
HELP! WILL GIVE BRAINLIEST!!!
Answer:
D
Step-by-step explanation:
As you can see from the image attached below, the equation that is being graphed is
F(x) = [tex]\frac{x}{(x+4)(x-1)}[/tex]
This equation splits off into various directions because the denominator is turns into a quadratic equation. Once solved it provides two values for which the quadratic equation would equal zero. Since this equation is the denominator 0 would give a null value and is why on the graph there is no y value for 1 or -4. Yet all other values are valid and have an different y output.
I need help with this qusetion
Answer:
Its A
Step-by-step explanation:
Answer:
D. Divide 151 by 479
Step-by-step explanation:
Given sin 0 = ā, find cos 0.
✓[?
cos e
=
ө
Step-by-step explanation:
when you look at the graphic and the right-angled triangle :
sine is the length of the vertical leg (opposite of the associated angle) divided by the length of the Hypotenuse (the baseline opposite of the 90° angle), because the sine function values are defined for the norm circle with radius 1. for any larger circle (or triangle inscribed in such a larger circle), we get the basic trigonometric function values by measuring the sides and norming to a radius of 1 (dividing them by the length of the actual radius).
cosine is the horizontal leg (at the "bottom").
the same principle applies. the cosine value is the length of that leg divided by the length of the Hypotenuse.
we know from the given ratio for sine, that the length of the Hypotenuse is 6.
so, we know 2 sides of the right-angled triangle :
the vertical leg is 5, the Hypotenuse is 6.
now, we use Pythagoras to get the horizontal leg :
6² = 5² + leg²
36 = 25 + leg²
11 = leg²
leg = sqrt(11)
and so cosine of the angle is
sqrt(11)/6
∠X=5x+30
∘
\angle \mathrm{Y}=3\mathrm{x}+60^{\circ}∠Y=3x+60
∘
Corresponding angles on parallel lines cut by a transversal are equal
5x + 30 = 3x + 60
Subtract 3x from both sides
2x + 30 = 60
Subtract 30 from both sides
2x = 30
Divide both sides by 2
X = 15
PLEASE HELP !! ILL GIVE BRAINLIEST !! 100 POINTS
Answer:
6t=9? let me know if that's correct x
Step-by-step explanation:
Two angles are complementary.
If one angle measures 45
degrees, then what is the
measure of the other angle? *
Answer:
45
Step-by-step explanation:
Size of each of mr sirac's classes
Answer:
You didn't add any images maybe it was a mistake?
Step-by-step explanation:
Please answer this for 15 points :) <333
Answer:
A.
Elena can run 3 miles per hour.
Step-by-step explanation:
Given that:
a circular running track = 1/5 mile
On this track, Elena runs completing each of the laps in 1/15 of an hour
We are to find Elena running speed.
It implies that the distance of Elena = [tex]\dfrac{1}{5}[/tex]
Time to run each lap = [tex]\dfrac{1}{15} \ of \ an \ hour[/tex]
Speed is the amount of distance covered in a specified period of time.
Recall that the formula for calculating speed is:
[tex]Speed = \dfrac{distance}{time}[/tex]
[tex]Speed = \dfrac{\dfrac{1}{5}}{\dfrac{1}{15}}[/tex]
[tex]Speed ={\dfrac{1}{5}\times \dfrac{15}{1}[/tex]
Speed = 3miles / hour
As such, Elena can run 3 miles each hour.
HELP WILL GIVE BRANLIEST!
Answer:
512
Step-by-step explanation:
To find the volume of a rectangular prism you multiply the length × width × height
= 8 × 8 ×8
= 512
Whats (1÷1/4) (3÷1/2) (1/4÷3)
Answer:
37
-----
56
Step-by-step explanation:
Please help me i dont understand
Answer:
It is linear. It is linear because it is a strait line which means that it is a function. A not linear line would look like a noodle.
One of Natalia's professors claims that 13% of the students at their college frequently wear hats. Natalia feels that the actual rate is much lower. She selects a random sample of 100 students at the college and finds that only 9 of them wear hats frequently. To determine if her data provide convincing evidence that the true proportion is less than 13%, she conducts 200 trials of a simulation. Natalia is testing the hypotheses. H o p = 13% and Ha p< 13%, where p = the true proportion of students at the college who frequently wear hats. Based on the results of the simulation, what is an estimate of the P-value of the test?
Answer:
0.005 or A
Step-by-step explanation:
EDGE2022
solve by completing the square! (will give brainliest for work!!!)
x ^ 2 - 2x = - 26
Answer:
Step-by-step explanation:
x²-2x=-26
add both sides (-2/2)² or 1
x²-2x+1=-26+1
x²-2x+1=-25
(x-1)²=25×-1
(x-1)²=5²×i²=(5i)²
x-1=±5i
x=1±5i
Find the area of the figure.
(20 pts)
Answer:
d. 122 units^2
Step-by-step explanation:
The sum of two consecutive numbers is 5. Find the equation representing
the same.
Answer:
Step-by-step explanation:
Let the smallest number = x
The next number will be x + 1
x + x + 1 = 5
2x + 1 = 5 This is likely the answer to the question although it could be the equation above.
if 4200 out of 5600 person's voted in an election the percentage which did not vote was
Answer:
25%
Step-by-step explanation:
If the total number of people is 5600, then to find the number of people that did not vote you subtract 4200 from 5600.
5600-4200=1400
Then you can set up the number of people who didnt vote as equal to a percentage over 100
1400/5600=x/100
140000/5600=x
25=x