Answers
Answer: [tex]2tan(theta)[/tex]
Step-by-step explanation:
I know this is pre-calculus, but I want to let you know what this is actually used for in real calculus. This is a method of integration called "u-substitution" which tranforms the function of 'x' into a function of 'theta'. If we allow the value of 'x' to equal 2sec(theta), we can plug this into the function to get:
[tex]\sqrt{x^2-4} =\sqrt{(2sec(theta)^2-4} =\sqrt{4sec^2(theta)-4}[/tex]
Factor out a 4 to get:
[tex]\sqrt{4(sec^2(theta)-1)}[/tex]
Take the square root of 4 to get a 2 on the outside of the radical:
[tex]\sqrt{4(sec^2(theta)-1)}=2\sqrt{sec^2(theta)-1}[/tex]
Use the trig identity below to convert the secant to tangent:
[tex]tan^2(theta)+1=sec^2(theta)[/tex]
[tex]tan^2(theta)=sec^2(theta)-1[/tex]
Therefore our expression becomes:
[tex]2\sqrt{sec^2(theta)-1}=2\sqrt{tan^2(theta)}[/tex]
The square root of tangent is simply tangent:
[tex]2\sqrt{tan^2(theta)} =2tan(theta)[/tex]
Related Questions
What is the least common denominator for the fractions 1/3 and 1/6
Answers
Answer:
least common denominator=6
Step-by-step explanation:
For the fractions, 1/3 and 1/6th, 3*2=6. making the fraction 2/6 and leaving the other the same 1/6th.
100 Points!!!! Please help, Will Mark BRAINLIEST!!!!!!
Answers
Answer:
Part A: No. Based on the scatter plot, r = 0.01 is not an accurate value for this data, because 0.01 means pratically no corrlation, while the points on the graph are moderately correlatedPart B: you must describe a scenary where a variable is the cause of the number of strawberries picked. See below, the example of rainfall.
Explanation:
1. Part A:
Since the points in the scatter plot show a moderated upward trend, you must expect a correlation coefficient close to ± 0.5. A correlation coefficient of 0.01 is too close to 0, which would mean that the points are almost not correlated at all.
The correlation coefficients, r, measure the strength of the correlation of two variables and they can have values from - 1 to 1.
r = - 1 is a perfect negative correlation: the points will adjust perfectly to a line with negative slope.r = + 1 is a perfect positive correlation: the points will ajdust perfectrly to a line with positive slope.r = 0 means that the variables are not correlated at all.
Hence, the closer to zero, the worse the correlation is, and that is what r = 0.01 means, but the graph shows other thing.
Therefore, the calculated value of r = 0.01 is not accurate for t his scatter plot.
2. Part B.
A causal relationship means that the expllanatory variable (the independent variable) is the cause of the dependent variable.
Hence, you must find a reasonable variable that can be the cause of the number of strawberries picked.
I could imagine the amount of rainfall the week before of harvest.
Thus, the scenario could be:
Amout of rainfall in mm (x) Number of strawberries picked (y)
100 20
50 40
25 80
12.5 160
6.25 320
The amount of rainfall is the cause of the number of strawberries picked, and you could find a model (function) that relates both variables.
can i have help with this
Answers
Answer:
Option D
Step-by-step explanation:
Square:
Side = 25 ft
Area of square = side * side
= 25*25
= 625 square ft
Area of semicircle:
diameter = 25 ft
r = 25/2 = 12.5 ft
[tex]\boxed{\text{Area of semicircle =$ \dfrac{\pi r^{2}}{2} $}}[/tex]
[tex]=\dfrac{3.14 * 12.5*12.5}{2}\\\\\\= 245.3 \ square \ ft[/tex]
Area of the shaded region = area of square - area of semicircle
= 625 - 245.3
= 379.7 square ft
1. Two numbers have a product of 12 but their sum is -7 what are the numbers.
2. The sum of two numbers is 1 but their product is -30 what are the numbers.
Answers
Answer:
1. (-3) and (-4)
2. (-5) and 6; vise versa
Answer:
Step-by-step explanation:
hello :
1)Two numbers have a product of 12 but their sum is -7 :
means : xy=12 ....(*)
x+y = -7 ....(**)
solve this system : use (**) you have x = -y-7 put this value in (*)
so : (-y-7)y = 12
-y²-7y-12 = 0
y² +7y+12=0 a=1 b=7 and c= 12
the discriminant delta =b²-4ac delta = 7²-4(1)(12) = 1
y1 = (-7-1)/2 = -4 and y2 = (-7+1)/2 =-3
but x= -7-y
if :y = - 4 x= -7-(-4) =-3
if : y=-3 x = -7-(-3) =-4
2) same method : xy=-30
x+y=1
Pythagorean Theorem
(Rounding)
Find the length of the third side. If necessary, round to the nearest tenth.
SOMEONE PLEASE HELP ME ILL GIVE YOU BRAINLIST ANSWER AND POINTS!!!!
IMAGE DOWN BELOW!!
Answers
Pythag is a squared + b squared = c squared
We have c and b so we can sub those in to get a squared + 12 squared = 16 squared
Which equals a squared + 144 = 256
Then we - 144 from both sides to get a squared = 112
Then we square root 112 to get a = 10.6
Hope that helps
what is the sum of 1 To 101 only positive integers pease fast
Answers
Answer:
5050
Step-by-step explanation:
sum of first n natural num. = [n(n+1)]/2
sum of first 100 natural num. = (100x101)/2 = 5050
Answer : The sum of 1 to 101 positive integer is 5050
5052 will be sum of 1 to 101 only positive integer
Find the slope of the line that
passes through (4, 7) and (2, 10).
Simplify your answer and write it
as a proper fraction, improper
fraction, or integer.
Answers
-1.5 (integer)
-1 1/2 (proper fraction)
is the answer
Alexei wants to hang a mirror in his boat and put a frame around it. the mirror and frame must have an area of 19.25 square feet. the mirror is 3 feet wide and 5 feet long. which quadratic equation can be used to determine the thickness of the frame, x? 2x2 8x − 19.25 = 0 3x2 5x − 19.25 = 0 4x2 16x − 4.25 = 0 4x2 16x 15 = 0
Answers
The quadratic equation that can be used to determine the thickness of the frame will be B. 3x² + 5x - 19.25 = 0
What is a quadratic equation?It should be noted that a quadratic equation simply means an algebraic expression of the second degree in x.
In this case, the quadratic equation that can be used to determine the thickness of the frame will be 3x² + 5x - 19.25 = 0
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Answer:
The answer is C. 4x2 + 16x - 4.25 = 0.
Step-by-step explanation:
who can answer this help me bro/sis?
Answers
Answer: 144 degrees, 136 degrees
Question 1:
The first x should be 144 because a straight line should equal 180, so you just subtract the (left angle or 36 degrees) with 180 to get the opposite angle.
Question 2:
For the second x, add the 2 interior angles and subtract it by 180 or the total sum of the interior angles.
49 + 87 = 136
180 - 136 = 44
Then follow the same steps in the first question.
180 - 44 = 136
Jonathan is making his favorite pasta dish. His mom ate 2/7 of the pasta, and his brother ate 1/6 of the pasta. How much did they eat in all?
Answers
Answer:
23/42
Step-by-step explanation:
2/7 = 12/42
1/6 = 7/42
12/42 + 7/42 = 19/42
42/42 - 19/42 = 23/42
Put the same number in each box to make the
calculation correct.
140 + 10 - ___ = _____ - 30
Answers
Answer:
The number would be 90
Step-by-step explanation:
140 + 10 - 90 = 60
90 - 30 = 60
60 = 60
Answer: 90
Step-by-step explanation:
Let's use x as a placeholder to the number we are trying to find
[tex]140+10-x=x-30[/tex]
Now we need to isolate x
Step 1) Simplify both sides
[tex]140+10-x=x-30\\150-x=x-30[/tex]
Step 2) Add 30 to both sides
[tex]150-x+30=x-30+30\\180-x=x[/tex]
Step 3) Add x to both sides
[tex]180-x+x=x+x\\180=2x[/tex]
Step 4) Divide both sides by 2
[tex]\frac{180}{2}=\frac{2x}{2} \\90=x[/tex]
Step 5) Sub our value into the original equation and solve
[tex]140+10-x=x-30\\140+10-90=90-30\\150-90=60\\60=60[/tex]
First drop down : 1. Cylinder 2.sphere
Second drop down: 1.divide by 2
2. Divide by 4
3.multiply by w2
Third drop down: 85
100
70
Answers
Answer:
Below.
Step-by-step explanation:
To find the volume of the silo find the volum of the hemisphere with radius of 15 feet and add the volume of the cylinder with a radius of 15 feet and a height of (100 - 15) = 85 feet.
The total volume = 1/2 * 4/3 π (15)^3 + π (15)^2 * 85
= 67151.5 ft^3.
Step-by-step explanation:
find the volume of a sphere with a radius of 15 ft and divide by 2 (because there is only half a sphere on top of the silo).
then add the volume of a cylinder with a radius of 15 ft and a height of 85 ft (because we need to deduct the radius of the sphere from the total height to get the height of the cylinder itself).
Which of the scatter plots below shows the most accurate line of best fit?
A. Z
B. X
C. W
D. Y
Answers
Find the volume of a pyramid with a square base, where the perimeter of the base is 14 m and the height of the pyramid is 8.8 m. Round your answer to the nearest tenth of a cubic meter.
Answers
The volume of the pyramid with a square base, where the perimeter of the base is 14 m and the height of the pyramid is 8.8 m is 35.9 m³
How do i determine the volume of the pyramid?First, we shall determine the determine the area of the square base. This is shown below:
Perimeter of square (P) = 14 mArea of the square base (A) = ?P = 4L
14 = 4L
Divide both sides by 4
L = 14 / 4
L = 3.5 m
Now, the area is obtained as follow
A = L²
A = 3.5²
A = 12.25 m²
Finally, we shall determine the volume of the pyramid. Details below:
Area of the square base (A) = 12.25 m²Height of pyramid (h) = 8.8 mVolume of pyramid (V) = ?V = ⅓Ah
V = ⅓ × 12.25 × 8.8
V = 35.9 m³
Thus, we can conclude that the volume of the pyramid is 35.9 m³
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Clare asks Andre to play the following number puzzle:
Pick a number
Add 2
Multiply by 3
Subtract 7
Add your original number
Andre’s final result is 27.
Which number did he start with?
Answers
Answer:
The answer is 7.
Step-by-step explanation:
7 + 2 is 9.
9 x 3 =27
27 - 7 =20.
Since the original number is 7 then we add 7 to 20.
7 + 20 = 27.
So, the number he started with is 7.
.that bar of chocolate was divided into squares. i ate 1/12 of it, then headed downstairs. the next day i ate another 1/12 , then another 1/3. i couldn't help myself. what fraction was left?
Answers
Answer:
1/2 of the bar is left
Step-by-step explanation:
1/12 x2= 2/12
2/12+ 1/3=2/12+4/12
6/12=1/2
solve for z: -42z^2 = 14z
Answers
[tex]\\ \rm\Rrightarrow -42z^2=14z[/tex]
[tex]\\ \rm\Rrightarrow 42z^2=-14z[/tex]
[tex]\\ \rm\Rrightarrow 3z^2=-z[/tex]
[tex]\\ \rm\Rrightarrow 3z=-1[/tex]
[tex]\\ \rm\Rrightarrow z=-1/3[/tex]
Another root is 0Answer:
[tex] - \frac{844}{29} z[/tex]
Step-by-step explanation:
I hope to help
write 2.786 as a fraction in common form
Answers
First write down the decimal number divided by 1 like this:
2.786
1
As we have 3 digits after the decimal point in the numerator, we need to multiply both the numerator and denominator by 103 = 1000, so that there is no decimal point in the numerator
2.786 × 1000
1 × 1000
=
2786
1000
Since the greatest common factor of 2786 and 1000 is 2, we can simplify the fraction and show the same amount
2786 ÷ 2
1000 ÷ 2
=
1393
500
As the numerator is greater than the denominator, we have an improper fraction, so we can also express 2.786 as a mixed number, thus 1393/500 is equal:
2
393
500
Therefore, 2.786 as a fraction is 1393/500 and It is written as 2 393/500 in mixed number form.
What’s the domain and range?
Answers
Answer:
D [-1,3] and R [5,27]
Step-by-step explanation:
I explained the process of finding the domain and range in your previous questions therefore I will only give you the answer for this one.
D [-1,3] or [tex]-1\leq x\leq 3[/tex]
R [5,27] or [tex]5\leq y\leq 27[/tex]
For circle h, jn = 3, nk = x, ln = 2, and nm = 6. solve for x. circle h with chords jk and lm intersecting at n inside the circle 9 1 5 4
Answers
The circle is an illustration of intersecting chords.
The value of x is 4
How to determine the value of x?The given parameters are:
Chords: jk and lmPoint of intersection = njn = 3, nk = x, ln = 2, and nm = 6This means that:
jn * nk = ln * nm
So, we have:
3 * x = 2 * 6
Divide both sides by 3
x = 2 * 2
Evaluate the product
x = 4
Hence, the value of x is 4
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Kevin ours more than emily each time they work together. Using this information, complete the table
Sorry for bad quality
Answers
Answer:
i believe the last one would be 9 for the number of hours kevin works.
Step-by-step explanation:
Please i need help with this
Answers
The volumes of two similar cylinders have a ratio of 27:64. The area of the base of the smaller cylinder is 18in
What is the area of the base of the larger cylinder?
Enter your answer in the box.
Answers
Which inequality does this graph show? LOOK AR PIC PLS ANSWER FAST
Answers
Answer:
D.
Step-by-step explanation:
1) if the points (1;-1) and (4;0) belong to the line, then
2) the equation of this line is 3y-x=-4;
3) the inequality is 3y-x≤-4.
Are the given vectors normal? a = < 5 , − 2 > and b = < 6 , 15 > Equation editor does not include the grouping symbols " < " and " > " that are necessary for writing a vector in component form. For this question, use braces to write a vector in component form. For example, the vector < 2 , 3 > should be written as { 2 , 3 } .
Answers
Answer:
Yes.
Step-by-step explanation:
Yes. They are normal
Students in Mrs. Anderson’s health class are learning about how exercise affects your heart rate. Twelve students ran around the school track for different lengths of time. Then they measured their heart rates in beats per minute. Heart Rate Record Minutes Heart Rate (bpm) 7 121 8 136 7 122 4 96 3 90 6 120 7 118 4 98 2 84 5 110 7 118 8 128 Find the correlation coefficient of the data. Round to the nearest hundredth
Answers
Answer:
While resting, his heart rate is at 60 bpm. After sprinting, his heart rate is at 130bmp. The difference is 130 - 60 = 70
Step-by-step explanation:
i hope this helps
The correlation coefficient of the given data about time and heart rates is 0.98.
What is correlation coefficient?A correlation coefficient is a statistical measure of the degree to which changes to the value of one variable expect change to the value of another.
How to calculate correlation coefficient?We have been given time and heart rates of students in Mrs. Anderson's health class and we have to find the value of correlation coefficient.
The formula by Karl Pearson to calculate correlation coefficient is as under:
Correlation coefficient=
=∑(x-x bar)(y-y bar)/[tex]\sqrt{sum(x-x bar)^{2} } \sqrt{sum(y-y bar)^{2} }[/tex]
We have to calculate figures required to fill in the formula which are:
∑(x-x bar)(y-y bar)=350
∑[tex](x-x bar)^{2}[/tex]=44.67
∑[tex](y-y bar)^{2}[/tex]=2872.25
Correlation coefficient=350/[tex]\sqrt{44.67} \sqrt{2872.25}[/tex]
=350/6.68*53.59
=350/357.98
=0.977
After rounding off to nearest hundred it will be 0.98.
Hence the correlation coefficient of the data about time and heart rate is 0.98.
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Dylan has a loyalty card good for a 20% discount at his local pharmacy. What would his total in dollars and cents be, after the discount and before tax, if the total cost of all the items he wants to buy is $30.70? Round to the nearest cent.
Answers
Answer:
$6.14.
Step-by-step explanation:
$30.70×20%
there will be after the tax and discount.
What's the value f x?
[tex]5x-6=3x-8[/tex]
Answers
Answer:
-1Step-by-step explanation:
Given equation,
⇒ 5x - 6 = 3x - 8
Subtracting 3x from both sides :
⇒ 5x – 6 – 3x = 3x – 8 – 3x
⇒ 2x – 6 = – 8
Adding 6 to both sides we get :
⇒ 2x – 6 + 6 = – 8 + 6
⇒ 2x = – 2
Dividing both sides by 2 we get :
⇒ 2x/2 = – 2/2
⇒ x = – 1
Therefore,
The value of x is -1Answer:
[tex]\sf \boxed{\bold{x=-1}}[/tex]
Solving Stepwise:
[tex]\dashrightarrow \sf 5x-6=3x-8[/tex]
add 6 on both sides
[tex]\dashrightarrow \sf 5x-6+6=3x-8+6[/tex]
simplify
[tex]\dashrightarrow \sf 5x=3x-2[/tex]
subtract both sides by 3x
[tex]\dashrightarrow \sf 5x-3x=3x-2-3x[/tex]
simplify
[tex]\dashrightarrow \sf 2x=-2[/tex]
divide both sides by 2
[tex]\dashrightarrow \sf \dfrac{2x}{2} =\dfrac{-2}{2}[/tex]
simplify
[tex]\dashrightarrow \sf x =-1[/tex]
Check for the answer:
insert x = -1
[tex]\hookrightarrow \sf 5(-1)-6=3(-1)-8[/tex]
[tex]\hookrightarrow \sf -5-6=-3-8[/tex]
[tex]\hookrightarrow \sf -11=-11[/tex]
L.H.S = R.H.S. Hence the statement x = -1 is correct.A teacher is 15 y.o. older than her student. In 15 years, the ratio of their ages will be 3:2. Find their present ages
Answers
teacher:: 30 years
Answer:
teacher's age: 30
student's age: 15
Step-by-step explanation:
T = 15 + S
from above,
(T+15)/(s+15) = 3/2
by substitution,
(15+S +15)/(S+15) = 3/2
cross multiply,
2(S+30) = 3(S+15)
2S + 60 = 3S + 45
60 = S + 45
s = 15
T = 30
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