Answer:
Taking LHS
=1 by cos theta- cos theta
= (1- cos²0)/ cos0
= sin²0/ cos0 ( because 1-cos²0 is also equals to sin²0)
=RHS hence proved
Answer:
Step-by-step explanation:
Let theta be β.
So,
[tex]sec\beta - cos\beta = \frac{sin^2\beta }{cos\beta } \\=>\frac{1}{cos\beta } - cos\beta = \frac{1 - cos^2\beta }{cos\beta } \\=>\frac{1 - cos^2}{cos\beta } = \frac{1 - cos^2\beta }{cos\beta }[/tex]
Here , identity used = [tex]sin^2\beta + cos^2\beta = 1[/tex]
Give two points with integer coordinates that have a slope of 10/7 between them
Answer:
(0,0) and (7,10)
Step-by-step explanation:
recall that the slope - intercept form of a linear equation can be given as
y = mx + b
where m = slope and b = y intercept
in our case, we are given that slope, m = 10/7, hence our equation becomes
y = (10/7) x + b
since we are not given any information about the y-intercept, we can simply pick a value for b that is most convenient for us.
We pick b = 0, hence the equation simplifies to:
y = (10/7) x ----- eq 1
we can see immediately that if x = 0, y must also = 0
proof if x = 0:
y = (10/7)(0) =0
since 0 is an integer, then (0,0) must be the first point.
we can also observe that for y to be an integer, we must get rid of the denominator 7. We can do this by multiply the right side by 7. Hence we let x = 7:
y = (10/7) x 7
y = 10
hence (7,10) is the second point.
Use the given graph to determine the limit, if it exists. Find limit as x approaches three from the left of f of x. Please include an explanation in your answer, I don't really understand limits so I'll give brainliest to the best explanation.
Answer:
[tex]\displaystyle \lim_{x \to 3^-} f(x) = -1[/tex]
General Formulas and Concepts:
Calculus
Limits
Right-Side Limit: [tex]\displaystyle \lim_{x \to c^+} f(x)[/tex]Left-Side Limit: [tex]\displaystyle \lim_{x \to c^-} f(x)[/tex]Graphical Limits
Step-by-step explanation:
As we approach 3 from the left according to the graph (follow the left graphed line), we see that we approach -1.
∴ [tex]\displaystyle \lim_{x \to 3^-} f(x) = -1[/tex]
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits
Please someone answer this right
God bless you all :D
A blacksmith has been studying vector calculus and wants to calculate the total mass of a curved metal fitting. Given that the metal fitting has a helix shape parameterized by C:[0,π] → IR3 C(t) = (cos (t), sin(t), t) And the density of the metal material is given by the function:f(x,y,z) = 22 How can the black smith calculate the total mass of the fitting and what is this mass?
Answer:
4483.1
Step-by-step explanation:
Helix shape of the metal fitting parameterized :
C(t) = (cos(t), sin(t), t )
This shows that: x = cos(t), y = sin(t), z = t
density of the metal can be represented as
f (x(t), y(t), z(t) = 2z = 2t
To calculate the mass of the fitting an integral is generated below ( attached below is remaining part of the solution )
Sea level is defined as being at an elevation of O feet. The elevation of land is defined to be its height above or below sea level. The table shows the lowest elevations
in some states. Write the values in order from greatest to least.
Answer:
2,844 ft, 713 ft, 481 ft, 55ft.
Step-by-step explanation:
New Mexico has the highest of the lowest land elevations of the given states, at 2,844 feet. It is followed by Idaho, at 713 feet, which is followed by Nevada, at 481 feet. Arkansas has the lowest land elevation at 55 feet. The elevations in order from highest to lowest are thus 2,844 feet, 713 feet, 481 feet, and 55 feet.
There are 727272 boys and 909090 girls on the math team. For the next math competition, Mr. Johnson would like to arrange all of the students in equal rows with only girls or only boys in each row. What is the greatest number of students that can be in each row?
Answer:
You cant solve this question without knowing how many rows there are, and also without knowing how many seats there are per row.
Answer:
72 and 90 gcf
Step-by-step explanation:
Midpoint (10,4) Endpoint (9,-4), find the coordinates of the other endpoint.
Answer:
(11, 12)
Step-by-step explanation:
Mid point coordinates:
x = (x₁ + x₂)/2y = (y₁ + y₂)/2Since midpoint and one endpoint given (10, 4) and (9, -4), the other endpoint:
x₂ = 2x - x₁ = 2*10 - 9 = 11y₂ = 2y - y₁ = 2*4 - (-4) = 12So the other endpoint is: (11, 12)
Is the answer A B C D or E
Answer:
i think it might be D
An opinion poll surveyed 900 people and reported that 36% believe a certain governor broke campaign financing laws in his election campaign.a. Calculate a 95% confidence interval for the population proportion of people who believe the governor broke campaign financing laws. (Round your answers to three decimal places.)
Answer:
The confidence Interval = (0.329, 0.391)
Step-by-step explanation:
Formula for the Confidence Interval for proportion =
p ± z × √p(1 - p)/n
where
p = x/n
From the question
n = 900 people
x = 36% of 900 people
= 36/100 × 900
= 324
z = z score of 95% confidence Interval
z = 1.98
p = x/n
= 324/900
= 0.36
Confidence Interval = p ± z × √p(1 - p)/n
= 0.36 ± 1.96 × √0.36 (1 - 0.36)/900
= 0.36 ± 1.96 ×√0.36 (0.64)/900
= 0.36 ± 1.96 × √0.000256
= 0.36 ± 1.96 × 0.016
= 0.36 ± 0.03136
Confidence Interval = 0.36 ± 0.03136
= 0.36 - 0.03136
= 0.32864
Approximately to 3 decimal places = 0.329
= 0.36 + 0.03136
= 0.39136
Approximately to 3 decimal places = 0.391
Therefore, the 95% confidence interval for the population proportion of people who believe the governor broke campaign financing laws = (0.329, 0.391)
The square of X varies inversely as the square root of Y and directly as the variable M. When M = 27 and Y = 16, then X = 9. Find the exact value of Y when M = 7 and X = 2
Answer:
[tex]Y = 441[/tex]
Step-by-step explanation:
Given
M = 27 when Y = 16 and X = 9
Required
Find Y when M = 7 and X = 2
We start by getting the algebraic representation of the given statement
[tex]X^2 \alpha \frac{1}{\sqrt Y} \alpha M[/tex]
Convert the variation to an equation; we have
[tex]X^2 = \frac{KM}{\sqrt Y}[/tex]
Where K is the constant of variation;
When M = 27; Y = 16; X = 9, the expression becomes
[tex]9^2 = \frac{K * 27}{\sqrt{16}}[/tex]
This gives
[tex]81 = \frac{k * 27}{4}[/tex]
Make K the subject of formula
[tex]K = \frac{81* 4}{27}[/tex]
[tex]K = \frac{324}{27}[/tex]
[tex]K = 12[/tex]
Solving for Y when M = 7 and X = 2
Recall that [tex]X^2 = \frac{KM}{\sqrt Y}[/tex]
Substitute values for K, M and X
[tex]2^2 = \frac{12 * 7}{\sqrt{Y}}[/tex]
[tex]4 = \frac{84}{\sqrt{Y}}[/tex]
Take square of both sides
[tex]4^2 = (\frac{84}{\sqrt{Y}})^2[/tex]
[tex]16 = \frac{7056}{Y}[/tex]
Make Y the subject of formula
[tex]Y = \frac{7056}{16}[/tex]
[tex]Y = 441[/tex]
What is 57 divided by 20
Answer:
2.85
Step-by-step explanation:
Answer: 2.85
Step-by-step explanation:
57/20 = 2.85
Solve for x, where x is a real number.
√x+3=9
If there is more than one solution, separate them with commas.
If there is no solution, click on "No solution".
Answer:
x=36
only 1 solution
Find the inverse of f(x)=6x^5-11
Answer:
[tex]f^{-1}(x)=\sqrt[5]{\frac{x+11}{6}}[/tex]
Step-by-step explanation:
So we have the function:
[tex]f(x)=6x^5-11[/tex]
To find the inverse of a function, switch f(x) and x, change f(x) to f⁻¹(x), and solve for f⁻¹(x). So:
[tex]f(x)=6x^5-11\\x=6(f^{-1}(x))^5-11[/tex]
Add 11 to both sides:
[tex]x+11=6(f^{-1}(x))^5[/tex]
Divide both sides by 6:
[tex]\frac{x+11}{6}=f^{-1}(x)^5[/tex]
Take the fifth root of each side:
[tex]f^{-1}(x)=\sqrt[5]{\frac{x+11}{6}}[/tex]
And we're done :)
Answer:
[tex]f^-^1(x)=\sqrt[5]{\frac{x+11}{6} }[/tex]Step-by-step explanation:
[tex]f(x)=6x^5-11\\[/tex]
Let y equal the equation
[tex]y =6x^5-11\\y+11=6x^5\\\\Divide\:both\:sides\:of\:the\:equation\:by \: 6\\\frac{y+11}{6} = \frac{6x^5}{6} \\\\\frac{y+11}{6} = x^5\\ \\Quatric\:root\:both\:sides\\\sqrt[5]{\frac{y+11}{6} } = \sqrt[5]{x^5} \\\\\sqrt[5]{\frac{y+11}{6} } = x\\\\f^-^1(x) = \sqrt[5]{\frac{x+11}{6} }[/tex]
9/8m - 1/6m = -4 - 11/3
Answer:
m=-8
Step-by-step explanation:
im assuming the equation is: [tex]\frac{9}{8} m-\frac{1}{6} m=-4-\frac{11}{3}[/tex]
find common denominators i choose 24
9/8 = 27/24
1/6 = 4/24
11/3 = 88/24
4 = 96/24
now start solving:
(Note that because denominators are the same you can just ignore them and focus on the numerator)
simplify (27/24)m - (4/24)m to (23/24)m
simplify -(96/24) - (88/24) to -184/24
now you are left with 23/24 m = -184/24
get rid of denominators 23m=-184
Divide -184 by 23 to get m= -8
(x^2+4)^2−11(x^2+4)+24=0
find one solution for this equation
Answer:
Step-by-step explanation:
(x²+4)²-11(x²+4)+24=0
put x²+4=y
y²-11y+24=0
y²-3y-8y+24=0
y(y-3)-8(y-3)=0
(y-3)(y-8)=0
y=3,8
so x²+4=3
x²=-1=i²
x=±i
or x²+4=8
x²=4
x=±2
What is 7/8 + 5/6 equal to
Answer:
41/24
Step-by-step explanation:
Answer:
41/24
Step-by-step explanation:
transform the expression
21 + 20/24add the numbers
41/24alternate form
1 17/24, 1.70838 students out of a total of 20 attended my fifth period Class yesterday what percentage does that represent?
Answer:
40%
Step-by-step explanation:
[tex]\frac{8}{20} X 100%[/tex][tex]=40%[/tex]%
marissa has $4.40 in quarters and dimes. if she has 5 more quarters than dimes how many of each coin does she have?
Answer:
22
Step-by-step explanation:
Marissa has $4.40 quarter and dimes
she has 5 more quarters than dimes
that means she times
$4.40×5=22
Answer:
Dimes = 9 dimes.
Quarters = 14 quarters.
Step-by-step explanation:
Q = D + 5 (1)
25×Q + 10×D = 440. (2)
From eq(1) substitute the expression for Q into equation (2)
25×(D+5) + 10D = 440
25D + 125 + 10D = 440
35D = 440 - 125
35D = 315
D = 315/35
D = 9
so,
Dimes = 9 dimes.
and,
Quarters = 9+5
= 14 quarters.
Prove:25×Q + 10×D = 440
25×14 + 10×9 = 440
350 + 90 = 440
440 = 440
Proved.
You have a balance of $213 in a savings account you withdraw $68 one day and $128 the next day without making any deposit what is the new balance
Step-by-step explanation:
Here hope this helps........
5 to the 4th power times 5 to the 2 power
Answer:
1,250
Step-by-step explanation:
5 to the 4 power is 50,and 5 to the 2 power is 25 and then Multiply them and that should be your answer
how many numbers are between 0 and 4
Answer:
3 numbers
Step-by-step explanation:
Answer:
infinite rational numbers
Step-by-step explanation:
There are infinite rational numbers between 0 and 4. Now,single decimal value change like 2.34 and 2.35 can change the total value of a rational number. And there are infinite combinations of this decimal value between just two numbers.
What are the coordinates of point B on AC such that the ratio of AB to AC is 1:3
Answer:
B) (2/3, 3 2/3)
Step-by-step explanation:
I think whoever write this problem thought the distance from A to C was 10. It’s not. It’s 10.77. (See below). But following what they did, the answer must be B) (2/3, 3 2/3)
First, find the distance from A to C.
4²+10²=c²
16+100=c²
116=c²
c=√116
10=10.77
The coordinates of point B on AC such that the ratio of AB to AC is 1:3 is (2/3, 3 2/3) option (B) is correct.
What is a segment bisector?A segment bisector is a line, ray, line segment, or point that divides a line segment into two equal halves at its center.
It is given that:
The line segment shown in the picture is in the ratio of AB to AC is 1:3
AB : AC = 1 : 3
m : n = 1 : 3
The coordinate of point A is (2, 7)
The coordinate of point C is (-2, -3)
Let the coordinate of the point B is (x, y)
m = 1
n = 2
x1 = 2
x2 = -2
y1 = 7
y2 = -3
x = (-2+4)/3
x = 2/3
y = (-3+14)/3
y =11/3
y = 3 2/3
B = (x, y) = (2/3, 3 2/3)
Thus, the coordinates of point B on AC such that the ratio of AB to AC is 1:3 is (2/3, 3 2/3) option (B) is correct.
The options are:
A. (1/3, 2 5/6)
B. (2/3, 3 2/3)
C. (-2/3, 1 1/6)
D. (-2/3, 1/3)
Learn more about the segment bisector here:
brainly.com/question/4137998
#SPJ2
180 degree angle take away 134 degree angle equal
Answer:
46 degree
Step-by-step explanation:
180-134=46
=>46 degrees
2[x + 4y + z)]
Help please!!
Answer:
2x + 8y + 2z
Step-by-step explanation:
Answer:
Just use the 2 to multiply the numbers in the bracket.
which is
2x+8y+2z.
BRAINLIEST
Find an equation of the line that is perpendicular to 2x-3y=3 that passes through the point (1,2)
Answer:
The answer is
[tex]3x + 2y = 7[/tex]Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
To find the equation of the perpendicular line we must first find the slope of the original line
From the question the original line is
2x - 3y = 3
Write the equation in the general form above
That's
3y = 2x - 3
y = 2/3x - 1
Comparing with the general equation above
Slope = 2/3
Since the lines are perpendicular to each other the slope of the perpendicular line is the negative inverse of the original line
Slope of perpendicular line = - 3/2
So the Equation of the line using point
( 1 , 2) and slope - 3/2 is
[tex]y -2 = - \frac{3}{2} ( x - 1) \\ 2y - 4 = - 3(x - 1) \\ 2y - 4 = - 3x + 3 \\ 3x + 2y - 4 - 3 = 0[/tex]
We have the final answer as
[tex]3x + 2y = 7[/tex]
Hope this helps you
HELP PLEASE I WILL MARK YOU BRAINLIEST Jermias buys 6.5 pounds of ground beef at the grocery store. Ground beef costs $5.50 for one pound. How much does Jeremias spend?*
Answer: $35.75
Step-by-step explanation: 6.5x5.5=35.75
Answer:
the answer is drum rollll
Step-by-step explanation:
7.58
Help me on this please
Answer:
the measure of angle DCF is 75° + 54° = 129°
Help i dont understand pls help :(
Answer:
Answer is h(0)=1
Step-by-step explanation:
All you have to do is substitute x with 0 in the original equation.
Find the distance between the pair of points: (-6, 4) and (6,4)
Answer:
12.
Explanation:
Use the distance formula to determine the distance between two points.
Find the next number in the number sequence 3, 6, 10, 15.
Answer:
21
Step-by-step explanation:
3 + 3 = 6
6 + 4 = 10
10 + 5 = 15
so...
15 + 6 = 21