Answer:
Step-by-step explanation:
(1-CotA)² + (tanA-1)² = 4csc2A(csc2A-1)
To prove this equation we will take the expression given in left hand side and will convert it into the expression given in right hand side of the equation.
L.H.S. = (1-CotA)² + (tanA-1)²
= 1 + Cot²A - 2CotA + 1 + tan²A - 2tanA
= cosec²A - 2CotA + Sec²A - 2tanA
[Since, (1 + Cot²A = cosec²A) and (1 + tan²A = Sec²A)]
= (cosec²A + Sec²A) - 2(CotA + tanA)
= [tex](\frac{1}{\text{SinA}})^{2}+(\frac{1}{CosA} )^{2}-2\text{(tanA}+\frac{1}{\text{tanA}})}[/tex]
= [tex]\frac{1}{(\text{SinA.CosA})^2}-2(\frac{tan^2A+1}{tanA} )[/tex]
= [tex]\frac{4}{\text{(Sin2A})^{2}}-4(\frac{1}{\text{Sin2A}} )[/tex]
[Since 2SinA.CosA = Sin2A and [tex]\frac{2(\text{tanA})}{1+\text{tan}^{2}A}=\text{Sin2A}[/tex]]
= 4Cosec²2A - 4Cosec2A
= 4Cosec2A(Cosec2A - 1)
= R.H.S. (Right hand side)
Hence the equation is proved.
Translate and solve: 54 greater than x is greater than 216
Answer:
x >162
Step-by-step explanation:
x+54 > 216
Subtract 54 from each side
x+54-54 > 216 - 54
x >162
Answer:
[tex]\huge \boxed{{x>162}}[/tex]
Step-by-step explanation:
[tex]x+54 > 216[/tex]
[tex]\sf Subtract \ 54 \ from \ both \ parts.[/tex]
[tex]x+54 -54> 216-54[/tex]
[tex]x>162[/tex]
(01.01 MC) Monica earned $60 from a bonus plus $8.50 per hour (h) she worked this week. Which of the following expressions best represents Monica's income for the week? 8.50h + 60 8.50 + 60 8.50 + 60h 8.50 + h + 60
Answer:
Option (1)
Step-by-step explanation:
Monica earned a bonus = $60
Per hour earning in addition to bonus = $8.50
Let she worked for 'h' hours this week.
Then total earning from the hourly rate = $8.50h
Total earning for the week = Earning of 'h' hours + Bonus earned
= $(8.50h + 60)
Therefore, Option (1) will represent Monica's earnings for the week.
Answer:
8.50h + 60
Step-by-step explanation:
somebody please help
You want to construct a pool that will hold 3496 ft. of water if the pool is to be 23 feet long and 19 wide how deep will it need to be
Answer:
8 feet deep
Step-by-step explanation:
volume = length x width x depth
3496 = 23 x 19 x d
3496 = 437 x d
divide both sides by 437
d = 8
Joseph is 33 years old. Five years ago, He was twice as old as Ann. How old will Ann be in 5 years time?
Answer:
19 years oldStep-by-step explanation:
[tex]Joseph = 33 \:years \:old\\ \\Let \: ann's \:age be x\\\\33-5 = 2x\\\\28 = 2x\\\\Divide \:both \:sides \:of \:the \:equation \: by \:2\\\\\frac{2x}{2} = \frac{28}{2} \\\\x = 14\\\\Ann's \:present \:age \:= 14\\\\In \:5 \:years \:time ; \\\\14+5 = 19\\[/tex]
What is a categorical variable
It's a variable that deals with various labels, rather than the usual type of numeric variable you may be used to.
One example of a categorical variable is color. You could have red, green, blue, yellow, and orange as the five choices for your categorical variable. Each color is a label or category.
This is an example of a qualitative variable. We don't have any numeric data attached to color. They're simply names or labels. In contrast, a quantitative variable is something like a person's height since a number is attached here (more specifically its a continuous quantitative variable).
Find the fourth roots of 16(cos 200° + i sin 200°).
Answer:
See below.
Step-by-step explanation:
To find roots of an equation, we use this formula:
[tex]z^{\frac{1}{n}}=r^{\frac{1}{n}}(cos(\frac{\theta}{n}+\frac{2k\pi}{n} )+\mathfrak{i}(sin(\frac{\theta}{n}+\frac{2k\pi}{n})),[/tex] where k = 0, 1, 2, 3... (n = root; equal to n - 1; dependent on the amount of roots needed - 0 is included).
In this case, n = 4.
Therefore, we adjust the polar equation we are given and modify it to be solved for the roots.
Part 2: Solving for root #1
To solve for root #1, make k = 0 and substitute all values into the equation. On the second step, convert the measure in degrees to the measure in radians by multiplying the degrees measurement by [tex]\frac{\pi}{180}[/tex] and simplify.
[tex]z^{\frac{1}{4}}=16^{\frac{1}{4}}(cos(\frac{200}{4}+\frac{2(0)\pi}{4}))+\mathfrak{i}(sin(\frac{200}{4}+\frac{2(0)\pi}{4}))[/tex]
[tex]z^{\frac{1}{4}}=2(cos(\frac{5\pi}{18}+\frac{\pi}{4}))+\mathfrak{i}(sin(\frac{5\pi}{18}+\frac{\pi}{4}))[/tex]
[tex]z^{\frac{1}{4}} = 2(sin(\frac{5\pi}{18}+\frac{\pi}{4}))+\mathfrak{i}(sin(\frac{5\pi}{18}+\frac{\pi}{4}))[/tex]
Root #1:
[tex]\large\boxed{z^\frac{1}{4}=2(cos(\frac{19\pi}{36}))+\mathfrack{i}(sin(\frac{19\pi}{38}))}[/tex]
Part 3: Solving for root #2
To solve for root #2, follow the same simplifying steps above but change k to k = 1.
[tex]z^{\frac{1}{4}}=16^{\frac{1}{4}}(cos(\frac{200}{4}+\frac{2(1)\pi}{4}))+\mathfrak{i}(sin(\frac{200}{4}+\frac{2(1)\pi}{4}))[/tex]
[tex]z^{\frac{1}{4}}=2(cos(\frac{5\pi}{18}+\frac{2\pi}{4}))+\mathfrak{i}(sin(\frac{5\pi}{18}+\frac{2\pi}{4}))\\[/tex]
[tex]z^{\frac{1}{4}}=2(cos(\frac{5\pi}{18}+\frac{\pi}{2}))+\mathfrak{i}(sin(\frac{5\pi}{18}+\frac{\pi}{2}))\\[/tex]
Root #2:
[tex]\large\boxed{z^{\frac{1}{4}}=2(cos(\frac{7\pi}{9}))+\mathfrak{i}(sin(\frac{7\pi}{9}))}[/tex]
Part 4: Solving for root #3
To solve for root #3, follow the same simplifying steps above but change k to k = 2.
[tex]z^{\frac{1}{4}}=16^{\frac{1}{4}}(cos(\frac{200}{4}+\frac{2(2)\pi}{4}))+\mathfrak{i}(sin(\frac{200}{4}+\frac{2(2)\pi}{4}))[/tex]
[tex]z^{\frac{1}{4}}=2(cos(\frac{5\pi}{18}+\frac{4\pi}{4}))+\mathfrak{i}(sin(\frac{5\pi}{18}+\frac{4\pi}{4}))\\[/tex]
[tex]z^{\frac{1}{4}}=2(cos(\frac{5\pi}{18}+\pi))+\mathfrak{i}(sin(\frac{5\pi}{18}+\pi))\\[/tex]
Root #3:
[tex]\large\boxed{z^{\frac{1}{4}}=2(cos(\frac{23\pi}{18}))+\mathfrak{i}(sin(\frac{23\pi}{18}))}[/tex]
Part 4: Solving for root #4
To solve for root #4, follow the same simplifying steps above but change k to k = 3.
[tex]z^{\frac{1}{4}}=16^{\frac{1}{4}}(cos(\frac{200}{4}+\frac{2(3)\pi}{4}))+\mathfrak{i}(sin(\frac{200}{4}+\frac{2(3)\pi}{4}))[/tex]
[tex]z^{\frac{1}{4}}=2(cos(\frac{5\pi}{18}+\frac{6\pi}{4}))+\mathfrak{i}(sin(\frac{5\pi}{18}+\frac{6\pi}{4}))\\[/tex]
[tex]z^{\frac{1}{4}}=2(cos(\frac{5\pi}{18}+\frac{3\pi}{2}))+\mathfrak{i}(sin(\frac{5\pi}{18}+\frac{3\pi}{2}))\\[/tex]
Root #4:
[tex]\large\boxed{z^{\frac{1}{4}}=2(cos(\frac{16\pi}{9}))+\mathfrak{i}(sin(\frac{16\pi}{19}))}[/tex]
The fourth roots of 16(cos 200° + i(sin 200°) are listed above.
An aluminum bar 4 feet long weighs 24 pounds. What is the weight of a similar bar that is 3 feet 3 inches long? WILL MARK BL
Answer:
19.5 pounds
Step-by-step explanation:
1 foot = 12 inches
3 inches = 3/12 = 0.25 feet
3 feet 3 inches = 3.25 feet
then:
24 pounds is 4 feet
A pounds is 3.25 feet
A = 24*3.25/4
A = 19.5 pounds
Answer:
19.50 pounds
Step-by-step explanation:
1 foot = 12 inches
3 inches = 3/12 = 0.25 feet
3 feet 3 inches = 3.25 feet
then:
24 pounds is 4 feet
A pounds is 3.25 feet
A = 24*3.25/4
A = 19.50 pounds
Word phrase for algebraic expression 15-1.5/d
Answer: 1.5 less than 15 is divided by a number d.
Step-by-step explanation:
Jesse bought 3 T-shirts for $6 each and 4 T-shirts for $5 each. What expression can you use to describe what Jesse bought?
You calculate the correlation between height and weight for a simple random sample of 50 students from your college. Another student does the same for a simple random sample of 200 students from the college. The other student should get:_________.
A. a correlation greater than 1.
B. a higher value for the correlation.
C. about the same value for the correlation.
D. a lower value for the correlation.
E. a correlation less than-1.
Answer:
B
Step-by-step explanation:
What is the correct standard form of the equation of the parabola? Enter your answer below. Be sure to show each step of your work.
Answer:
Step-by-step explanation:
eq. of directrix is y=4 or y-4=0
perpendicular distance of (x,y) from directrix =distance of (x,y) from focus (-3,2)
[tex]| \frac{y-4}{1}|=\sqrt{(x+3)^2+(y-2)^2} \\squaring~both~sides\\y^2-8y+16=(x+3)^2+(y-2)2\\(x+3)^2=y^2-8y+16-(y-2)^2\\(x+3)^2=y^2-8y+16-(y^2-4y+4)\\(x+3)^2=y^2-8y+16-y^2+4y-4\\(x+3)^2=-4y+12\\(x+3)^2=-4(y-3)[/tex]
g Which of the following is equivalent to P( A|B)? a. P(A and B) b. P(B|A) c. P(A)/P(B) d. None of these choices.
Answer:
The correct option is D.
But option B is correct if P(A) = P(B).
Step-by-step explanation:
P(A|B) is read as "The probability of A given B".
It is different from the options A, B, and C.
It is equal to option B only if the probability of A is equal to the probability of B. That is P(A|B) = P(B|A) if P(A) = P(B).
To paint his apartment, Alex but 6 gallons of paint to cover 1440 ft.². What is the ratio of square feet to gallons of paint?
Answer & Step-by-step explanation:
The ratio of square feet to gallons of paint:
[tex]1440:6[/tex]
This can also be written as:
[tex]\frac{1440}{6}[/tex]
This fraction can be simplified by dividing the numerator and denominator by 6:
[tex]\frac{1440}{6}=\frac{240}{1}[/tex]
So, the ratio of square feet to gallons of paint is:
1 gallon for every 240 ft².
:Done
What is the value of x to the nearest tenth?
Step-by-step explanation:
Hello!!!
Let's workout with this figure.
BC is a chord, O is the centre and OA is the perpendicular bisector.
AB = 1/2 of BC (according to circle's theorem)
so, A B = 1/2 × 25.6
Therefore, the measure of AB is 12.8.
now, let's have a small work with triangle AOB.
as it is a Right angled triangle, taking angle B as refrence angle we get,
p=x
b=12.8
h= OB = 16 (it is also a radius.)
now,
by Pythagoras relation we get,
[tex]p = \sqrt{ {h}^{2} - {b}^{2} } [/tex]
or, x = root 16^2- 12.8 ^2
by simplification, we get;
the measure of x is 9.6.
Therefore, the value of x is 9.6.
Hope it helps...
Can some body write a word problem using these numbers
Answer:
Mr Singh was travelling from England to Punjab, India. He arrived 5 hours after 0:00. When he was on the plane, there was a delay which caused the whole flight to be pushed 4 hours ahead. This would mean that he would arrive 9 hours after 0:00. Mr Singh was also with his son and he had some homework to do. He had to order the numbers [tex]-4,-2\frac{1}{3} ,0, \frac{3}{4} ,\sqrt{5},5[/tex] from lowest to highest.
PLEASE ANSWER ASAP!!
How many cubic centimeters (
[tex] {cm}^{3} [/tex]
) are there in a 5 gallon jug of water?
Must show your work!!!
any unrelated answer will be reported
Answer:
[tex]\boxed{\sf A}[/tex]
Step-by-step explanation:
[tex]\sf 1 \ gallon = 3785.41 \ cm^3[/tex]
[tex]\sf 5 \ gallon = \ ? \ cm^3[/tex]
[tex]\sf Multiply \ the \ gallon \ value \ by \ 3785.41.[/tex]
[tex]5 \times 3785.41 = 18927.1[/tex]
[tex]\sf Approximate \ the \ value.[/tex]
[tex]18927.1 \approx 19000[/tex]
how many hours are there from 10:30 on Monday to 11:30 on Tuesday
Answer:
25 hours.
Step-by-step explanation:
We are to find the number of hours from:
Monday at 10:30
to
Tuesday at 11:30
Since the question does not state whether the times are in A.M / P.M ,
There are 24 hours upto 10:30 on Tuesday.
Adding 1 hour gives 11:30
So the answer = 24 + 1 = 25 hrs
Answer:
25 hours
Step-by-step explanation:
1 day=24 hours
11.30-10.30=1 hour
----------------------------
add the total 25 hours
Please help with this
Answer:
B) x=80°
Step-by-step explanation:
This is a hexagon, so it has interior angles equaling 720°. (N-2)*180
So the equation would be
78+134+136+132+2x+x=720
480+3x=720
3x=720-480
3x=240
x=80°
Help me please thank y’all
x= 30 degrees
Step-by-step explanation:
there's 180 degrees in a triangle. You can see 60 degrees right there. Theres a 90 degree angle right next to it. 180-150=30
Can someone help I would really appreciate
Answer:
18/a
Step-by-step explanation:
quotient means divide
18/a
Which of the following units is incommensurable with kilograms
Answer:
All units of measurement that are not based on or do not measure mass or weight and volume are incommensurable with kilograms.
Step-by-step explanation:
A measure unit is said to be incommensurable with another if it does not have the same measurement basis with the other measure unit. For example, a measure in time cannot be measured in kilograms because time is measured in hours, minutes, seconds, days, etc. But, if a measurement base can be applied to two or more measurement units, then the measurement units are commensurable with the measurement base.
simplify radical -50
Answer:
[tex]5i\sqrt{2}[/tex]
Step-by-step explanation:
If we want to convert [tex]\sqrt{-50}[/tex] into a radical simplified, we need to find two numbers that multiply to be -50 and one of them can be squared.
[tex]\sqrt{-50} = \sqrt{-25 \cdot 2}[/tex]
The square root of -25 is 5i.
So:
[tex]5i\sqrt{2}[/tex]
Hope this helped!
Answer: [tex]=5i\sqrt{2}[/tex]
Step-by-step explanation:
[tex]\sqrt{-50}=\sqrt{-1}\sqrt{50}[/tex]
[tex]\sqrt{-1}\sqrt{50}[/tex]
[tex]\sqrt{5^2\cdot \:2}[/tex]
[tex]=\sqrt{2}\sqrt{5^2}[/tex]
[tex]\sqrt{5^2}=5[/tex]
[tex]=5\sqrt{2}[/tex]
Hi i need help on this im not that smart sorry, what is the x-intercept of the graph that is shown below
Answer:
(3, 0)
Step-by-step explanation:
x-intercept is where the line touches the x-axis
It is the point on the line where y=0
Answer:
3,0
Step-by-step explanation:
the point where the line cuts the x axis is the x-intecept
Please help!
Explain how changes in the dimensions of a cube dimensions affect the volume of a cube. Be specific, explaining how much the volume will change with each increase of 1 unit on the side lengths.
Answer:
when each side length of a cube increases by 1 unit, the volume increases by 3x² + 3x + 1 (units)³
Step-by-step explanation:
Let the initial length of the sides of the cube = x unit
when the length of the cube = x ; volume of the cube = length × breadth × height = x × x × x = x³ (unit)³
when the length increased by 1 unit,
new length = (x + 1) unit
New volume = (x + 1) × (x + 1) × (x + 1)
multiplying the first two brackets
New volume = (x² + 2x + 1 ) (x + 1)
espanding the brackets
New volume = x³ + 2x² + x + x² + 2x + 1
New volume = x³ + 3x² + 3x + 1 (unit)³
Change in volume:
(New volume) - (old volume)
(x³ + 3x² + 3x + 1) - (x³)
x³ + 3x² + 3x + 1 - x³
collecting like terms:
(x³ - x³) + 3x² + 3x + 1
0 + 3x² + 3x + 1
change in volume = 3x² + 3x + 1
Therefore, when each side length of a cube increases by 1 unit, the volume increases by 3x² + 3x + 1 (units)³
Jerry walked a dog from 6:40 a.m. to 7:30 a.m. one day. If he was paid at the rate of $6 per hour, how much did he cam that day?
HELP ME ILL GIV ROBUX Identify the property shown by the equation. 14 × 6 = 6 × 14 A. Commutative Property B. Associative Property C. Identity Property D. Distributive Property PLEASE HELP ME
Answer:
A. Commutative Property
Step-by-step explanation:
Hello!
This is the Commutative property which is when you can change the order of the numbers and the result does not change.
Hope this helps!
evaluate the expression for -c-12=
Answer:
-10
Step-by-step explanation:
We can substitute c into the equation as -2.
[tex]-(-2) - 12[/tex]
Two negatives make a positive:
[tex]2-12[/tex]
And [tex]2 - 12 = -10[/tex].
Hope this helped!
Was is a macroeconomics
Answer:
Macroeconomics is a study that deals with the whole economy and everything pertaining to it.
Step-by-step explanation:
when we talk about Macroeconomics, we mean the whole economy. It can be related to a country's import or export, governance, how resources are accurately allocated to people in the country and the like.
Find y using the Angle Sum Theorem
Step-by-step explanation:
Hey, there!!
Look this figure, simply we find that;
In triangle ABC,
angle CBD is an exterior angle of a triangle.
and its measure is 90°
Then,
angle CBD= y +48° {sum of interior opposite angle is equal to exterior angle or from theorem}.
or, 90°= y + 48°
Shifting, 48° in left side,
90°-48°= y
Therefore, the value of y is 42°.
Hope it helps...
