[tex]\text{L.H.S}\\\\=\dfrac{\sin A \tan A}{1- \cos A}\\\\\\=\dfrac{\sin A \cdot \tfrac{\sin A}{\cos A} }{ 1- \cos A}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~;\left[\tan A = \dfrac{\sin A }{\cos A}\right]\\\\\\=\dfrac{\tfrac{\sin^2 A}{ \cos A}}{1- \cos A}\\\\\\=\dfrac{\sin^2 A}{\cos A(1-\cos A)}\\\\\\=\dfrac{1-\cos^2 A}{\cos A( 1- \cos A)}~~~~~~~~~~~~~~~~~~~~~~~~;[\sin^2 A + \cos^2 A = 1]\\\\\\[/tex]
[tex]=\dfrac{(1+ \cos A)(1 - \cos A)}{\cos A(1 - \cos A)}\\\\\\=\dfrac{1+ \cos A}{ \cos A}\\\\\\=\dfrac{1}{\cos A} + \dfrac{\cos A}{ \cos A}\\\\\\=\sec A + 1 \\\\\\=1+ \sec A\\\\\\=\text{R.H.S}\\\\\text{Proved.}[/tex]
XY and BD are parallel lines
X is a point on AB and C is a point on BD.
XB = XC
a) Complete this sentence.
Angle XBC = 55° because = ?
b) Work out angle BXC.
Give a reason for each angle you work out.
Answer:
a) they are corresponding angles
b) B=55° (proven)
C=55 (Angles opposite equal sides)
B+C+X=180° ( sum of angles of a triangle)
55°+55°X=180
110°+X=180°
X=180°-110°
X=70°
Urgent! Brainliest to whoever solves it
Quadrilateral HGFJ is a rhombus
Answer:
16cm and 48 degrees
Step-by-step explanation:
Ryder used front-end estimation to estimate the product of (–24.98)(–1.29). What was his estimate?
–32
–20
20
32
Answer:
(d) 32
Step-by-step explanation:
An estimate is a value that is intended to approximate the result of a detailed calculation. Often, the target is an estimate that is within about 10% of the actual value. A "rough order of magnitude" (ROM) estimate is intended to be within about a factor of 3 of the actual value.
__
An estimate is generally made by using a reduced number of significant figures in the calculations. Often, the numbers used will be rounded to 1 or 2 significant figures. The math is often accomplished mentally, so methods of mental arithmetic are often used to simplify the calculations.
rounded valuesWe are asked for an estimate of the product (-24.98)(-1.29). We notice there are an even number of minus signs, so the result will be positive. The values are (25)(1.3) when rounded to 2 significant figures.
Along with the rounded values, it is often useful to make note of the direction and magnitude of the errors due to rounding. Here, we have rounded both numbers up. The number 25 is high by 0.02, and the number 1.3 is also high by 0.01. These can be used to estimate the error in the estimated value.
the productThe desired product can be computed several different ways. Either or both of the numbers 25 and 1.3 can be represented in a fashion that facilitates the (mental) arithmetic. Here are three (3) methods that could be used.
(25)(1.3) = 25(1 +0.3) = 25 +7.5 = 32.5 (a little high, so we can choose to round down to 32)(25)(1.3) = (100/4)(1.3) = 130/4 = 65/2 ≈ 64/2 = 32 (again, rounding down because we know 32.5 is too high)(25)(1.3) = 2.5(13) = 2(13) +13/2 = 26 +6.5 = 32.5 ≈ 32Ryder's estimate was 32.
_____
Additional comment
The actual product is ...
(25 -0.02)(1.3 -0.01) = (25)(1.3) -0.02(1.3) -0.01(25) +(0.02)(0.01).
As a first approximation of the error in the product 32.5, we can sum the middle two terms:
-0.02(1.3) and -0.01(25) = -0.026-0.25 = -0.276.
Then the first refinement of the estimate will give us ...
32.500 -0.276 = 32.224
The actual value is obtained by adding the final error term:
32.224 +0.0002 = 32.2242 . . . . the actual product with estimate errors resolved.
Answer:
yo
Step-by-step explanation:
its C, or 20
edge
ur welcome
find all solutions to the problem: 2/x+6 - 1/x+3 =2
Answer:
[tex]\displaystyle x=-\frac{9}{2},\:x=-4[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{2}{x+6}-\frac{1}{x+3}=2\\\\\frac{2(x+3)}{(x+6)(x+3)}-\frac{(x+6)}{(x+6)(x+3)}=2\\ \\\frac{(2x+6)-(x+6)}{(x+6)(x+3)}=2\\ \\\frac{x}{(x+6)(x+3)}=2\\ \\x=2(x+6)(x+3)\\\\x=2(x^2+9x+18)\\\\x=2x^2+18x+36\\\\0=2x^2+17x+36[/tex]
[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x=\frac{-17\pm\sqrt{(17)^2-4(2)(36)}}{2(2)}\\\\x=\frac{-17\pm\sqrt{289-288}}{4}\\\\x=\frac{-17\pm\sqrt{1}}{4}\\\\x=\frac{-17\pm1}{4}\\ \\x_1=\frac{-18}{4}=-\frac{9}{2},\: x_2=\frac{-16}{4}=-4[/tex]
What is the derivative of the function f(x)= 4cos2x + logx + x?
Answer:
[tex]f'(x)=-8\sin2x+\frac{1}{x} +1[/tex]
Step-by-step explanation:
I assume by [tex]\log(x)[/tex], the base is [tex]e[/tex], so let [tex]\log_e(x)=\ln(x)[/tex]:
[tex]\displaystyle f(x)=4\cos2x+\ln x+x\\\\f'(x)=\frac{d}{dx}(4\cos2x+\ln x + x)\\\\f'(x)=\frac{d}{dx}(4\cos2x)+\frac{d}{dx}(\ln x)+\frac{d}{dx}(x)\\\\f'(x)=-8\sin2x+\frac{1}{x}+1[/tex]
Remember that by the chain rule, to find the derivative of [tex]4\cos2x[/tex], you must find the derivative of the inside, which is [tex]\displaystyle \frac{d}{dx}(2x)=2[/tex], and multiply it by the outside derivative. Recall that [tex]\displaystyle \frac{d}{dx}\cos(x)=-\sin(x)[/tex], so replace [tex]-\sin(x)[/tex] with [tex]-4\sin(2x)[/tex], and multiply by 2 to get [tex]-8\sin(2x)[/tex] as your derivative.
Also remember that [tex]\displaystyle \frac{d}{dx}\ln(x)=\frac{1}{x}[/tex], one of the more basic derivatives.
The derivative of the function f(x)= 4cos2x + logx + x is f'(x)=-8sin2x+1/x+1.
What is Differential equation?A differential equation is an equation that contains one or more functions with its derivatives.
The given function is four times of cos2x plus logx plus x.
f(x)= 4cos2x + logx + x
We need to find the derivative of it f'(x)
d/dxf(x)=d/dx(4cos2x)+d/dx(logx)+d/dx(x)
f'(x)=4d/dx(cos2x)+d/dx(logx)+d/dx(x)
We know that
d/dx(cosx)=-sinx
d/dx(logx)=1/x
d/dx(x)=1
Apply in above equation
f'(x)=4d/dx(cos2x)+d/dx(logx)+d/dx(x)
f'(x)=4.2(-sin2x)+1/x+1
f'(x)=-8sin2x+1/x+1
Hence the derivative of function f(x)= 4cos2x + logx + x is f'(x)=-8sin2x+1/x+1.
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Matthew is grocery shopping for a taco Tuesday Bloc Party he is expecting 60 people including himself, and for each person to have 1 soft and 1 crispy taco. Soft tortillas coke in packs of 10. Crispy taco shells come in packs of 12. How many packages of each tortilla type does Mathew need to feed everyone?
The number of each tortilla type that Mathew would need to feed everyone is = 6 packages of Soft tortillas and 5 packages of Crispy taco shells.
Calculation of number of tortillaThe number of people Matthew is expecting including himself = 60
The Soft tortillas coke appear = 10/pack
The Crispy taco shells appear = 12/pack
Since each person is to get 1 soft and 1 crispy taco, the number of tortilla type that Mathew would need to feed everyone is
= 60/10 = 6 packages of Soft tortillas
= 60/12 = 5 packages of Crispy taco shells
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Pls Help I’m so confused how do you do this
Answer: A
Step-by-step explanation:
[tex]$$Given $m \angle A=9 x-7, \quad m \angle B=7 x-9, m \angle C=28-2 x$ \\For the triangle $m \angle A+m \angle B+m \angle c=180$$$\begin{aligned}&\Rightarrow(9 x-7)+(7 x-9)+(28-2 x)=180 \\&\Rightarrow 9 x+7 x-2 x-7-9+28=180 \\&\Rightarrow 14 x=180-28+16 \\&\Rightarrow 14 x=168 \\&\Rightarrow \quad x=12\end{aligned}[/tex]
[tex]$$Therefore,\\&m \angle A=9 x-7=9 \times 12-7=101^{\circ}\\&m \angle B=7 x-9=7 \times 12-9=75^{\circ} \\&m \angle C=28-2 x=28-2 \times 12=28-24=4^{\circ}\\[/tex]
[tex]$$Since $m \angle A=101^{\circ}$ so $B C$ is the longest side of a triangle $\triangle A B C$ \\\\Since $m \angle C=4^{\circ} S 0$ SB is the shortest side of a triangle $\triangle A B C$\\\\So listing the sides in $\triangle A B C$ from shortest to longest is: (a) $\overline{A B}, \overline{A C}, \overline{B C}$[/tex]
I donot understand what so ever but brainly has def been helping
Answer:
what happened to you brooooooooo
What is the answer to this
Find the slope and the y-intercept of the following linear equation. 5. 3x + 2y = 14
The slope and y-intercept of the equation are - 3 / 2 and 7 respectively.
How to find slope and y-intercept?The slope and y-intercept of an equation can be easily found using slope intercept equation.
y = mx + b
where
m = slopeb = y-interceptTherefore,
3x + 2y = 14
2y = -3x + 14
y = -3 / 2 x + 7
Therefore,
slope = - 3 / 2
y-intercept = 7
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Which graph represents exponential decay?
ty
80
60
40
20
80
60
40
20
2
1 2
3
80
60
40
20
ty
O
2 3
x
80
60
40
20
ty
1
2
3
Using exponential function concepts, it is found that the first graph to the similar problem represents an exponential decay.
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.As x goes to positive infinity, a exponential function approaches a constant, hence a graph similar to the first one of the similar problem linked below represents exponential decay.
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I am not divisible by 2,3,5 or 7. My two digits are not the same, but they are both squares. What two numbers could I be?
I NEED HELP FASTTT
Answer:
19 is suitable no in which 1 is square of itself and 9 is of 3
Somebody please help me with this question
Answer:
-2
-1
-2
-3
Step-by-step explanation:
For an odd function, f(-x) = -f(x).
f(2) = 2; f(-2) = -2
f(3) = 1; f(-3) = -1
f(4) = 2; f(-4) = -2
f(6) = 3; f(-6) = -3
6. Solve the equation: h/9 = 7.
A. h = -63
B. h=63
C. h=127
D. h = 7/g
Answer:
B) h=63
Step-by-step explanation:
Multiply both sides by 9.
h/*9=9*7
Simplify
h=63
[tex]\bf{\dfrac{h}{9}=7 \ \ \to \ \ \ Exercise \ to \ solve }[/tex]
Multiply both sides by 9.
h = 7 × 9Multiply 7 and 9 to get 63.
h = 63 ===> AnswerTherefore, the correct option is "B".
[tex]\red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]
Paul and Krystal spent 1 1/2 hours at the pool
Answer:
Paul and Krystal spent 13 hours at the pool
Step-by-step explanation:
I Thank
Find the volume of the prism.
9km 8km 6km
The correct answer is option B which is the volume of the prism is 216 km³.
What is the volume of the prism?A prism is a three-dimensional solid with a triangular base called a triangular prism. The volume of the triangular prism is equal to the product of the area of the base and the height of the prism.
The volume of the prism will be calculated by using the formula below:-
V = Area of the base x Height
Since the base is a right-angle triangle so we will calculate the area of the right-angle triangle.
V = Area of the triangle x Height
V = ( 1/2 ) x 8 x 6 x ( 9 )
V = 216 km²
Therefore the correct answer is option B which is the volume of the prism is 216 km³.
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Mollie wants to measure the capacity of the kitchen sink.
She has a 1 L container and a 10 mL container. Which should she use and why?
A.
10 mL container; the capacity of the sink is close to 10 mL.
B.
10 mL container; the capacity of the sink is less than 1 L so the 1 L container would not give an accurate measurement.
C.
1 L container; the capacity of the sink is at least 1 L.
D.
Either container; or the 10 mL container can measure the capacity as quickly as the 1 L container.
Answer:
1L container as the capacity of the sink is obviously at least 1L and most probably much more than 1L
Step-by-step explanation:
letter C
32 of the 49 8th Graders said that they
prefer dogs over cats.
22 of the 38 9th Graders said that they
prefer dogs.
Did a higher percentage of 8th Graders or
9th Graders prefer dogs?
8th Graders
9th Graders
Answer:
8th graders i think is the answer
Step-by-step explanation:
Answer:
The 9th grades had given a higher percentage because even without converting to a percent, you can tell just by seeing that there is a 1 number difference if you would try to add.
hello fellow indians Question: Lawrence poured 27.328 L of water into a right rectangular prism- shaped tank. The base of the tank is 40 cm by 28 cm. When he finished pouring the water, the tank was ⅔ full. ( 1L=1,000 cm 3).
Answer: andres is 5 years old pls banned him he called e a mean word like the N word
Step-by-step explanation:
The equation of line LM is y = 5x + 4. Write an equation of a line perpendicular to line LM in slope-intercept form that contains point (−3, 2).
Submitting a Bid
You want to bid on a project for the pool shown. The project involves ordering and installing the brown tile that borders the pool, and ordering a custom-made tarp to cover the surface of the pool. In the figure, each grid square represents 1 square foot.
You pay $5 per linear foot for the tile.
You pay $4 per square foot for the tarp
It takes about 15 min to install each foot of the tile
A) estimate the total cost for the tile and the tarp
Answer:
5,125
Step-by-step explanation:
Number 4, Use the net to complete the sentences. The square pyramids base that is_____ units on each side. The height of each triangular face is ______ units.
The distance to your brother's house is 481 miles, and the distance to the Grand Canyon is 814 miles. If it took 13 hours to drive to your brother's house, how long would you estimate the drive to the Grand Canyon to take?
The time taken to cover a distance of 814 miles for Caynon's home will be 22 hours.
What is speed?Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance.
Given that:-
The distance to your brother's house is 481 miles, and the distance to the Grand Canyon is 814 miles. If it took 13 hours to drive to your brother's house, how long would you estimate the drive to the Grand Canyon to take?The time will be calculated as:-
First, we will calculate the speed to cover the distance of Brother's house:-
Speed = Distance / Time
Speed = 481 / 13 = 37 miles per hour.
Now the time to cover a distance of 814 miles will be calculated as:-
Time = Distance / Speed
Time = 814 / 37
Time = 22 hours
Therefore the time taken to cover a distance of 814 miles for Caynon's home will be 22 hours.
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what is the solution to the trigonometric inequality 2sin(x)+3>sin ^2(x) over the interval
The intervals that satisfy the given trigonometric Inequality are; 0 ≤ x < 3π/2 and 3π/2 < x ≤ 2π
How to solve trigonometric inequality?We are given the trigonometric Inequality;
2 sin(x) + 3 > sin²(x)
Rearranging gives us;
sin²(x) - 2 sin(x) - 3 < 0
Factorizing this gives us;
(sin(x) - 3)(sin(x) + 1) < 0
Thus;
sin(x) - 3 = 0 or sin(x) + 1 = 0
sin(x) = 3 or sin(x) = -1
sin(x) = 3 is not possible because sin(x) ≤ 1.
Thus, we will work with;
sin(x) = -1 for the interval 0 ≤ x ≤ 2π radians.
Then, x = sin⁻¹(-1)
x = 3π/2.
Now, if we split up the solution domain into two intervals, we have;
from 0 ≤ x < 3π/2, at x = 0. Then;
sin²(0) - 2 sin(0) - 3
= 0² - 0 - 3
= -3 < 0
Thus, the interval 0 ≤ x < 3π/2 is true.
From 3π/2 < x ≤ 2π, take x = 2π. Then;
sin²(2π) - 2 sin(2π) - 3
= 0² - 0 - 3
= -3 < 0
Thus, the interval 3π/2 < x ≤ 2π is also true.
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which equation represents circle n? (17 points & will mark branliest)
Answer:
c. (x+7)^2+(y-6)^2=50
Step-by-step explanation:
The equation of a circle is; (x+7)²+(y-6)² = 50
What is circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
The points on the circle are L(-2, 11) and centre is N(-7, 6)
Find the radius,
D = √(-7+2)²+(6-11))²
D = √25+25
D = √50
We know that, the equation of a circle is given by,
( x − a )² + ( y − b )² = r² , where ( a , b ) represents the centre of the circle,
Here, centre is N(-7, 6)
Therefore, the equation of a circle is;
(x+7)²+(y-6)² = 50
Hence, the required equation is (x+7)²+(y-6)² = 50
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Describe how the product of 0.08 x 8 would look on a one hundred-square grid.
The product would have ____
squares shaded out of 100.
If 30% of a number is 78 and 65% of the same number is 169, find 95% of that
number.
Answer:
let say the number is x, then 30x÷100=78, x=260...from this we can calculate 95 percent of 260 which is equal to 247
The 95 percentage of the number is A = 247
What is Percentage?A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %
The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.
Percentage change is the difference between the measured value and the true value , as a percentage of the true value
Percentage change =( (| Measured Value - True Value |) / True Value ) x 100
Given data ,
Let the number be represented as n
Now , We can set up two equations based on the given information
30 percentage of the number is 78 ,
So , 0.3 ( n ) = 78
0.65 ( n ) = 169
Solving for n in the first equation, we get:
n = 260
Substituting n = 260 into the second equation, we can check that it is true:
0.65(260) = 169
Now, we can find 95% of the number by multiplying it by 0.95
0.95 x 260 = 247
Hence , 95% of the number is 247
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Which of the following rules is the composition of a dilation of scale factor 2, then a translation of three units to the right? a) (2x+3,y) b) (2x+6, 2y) c) (2x +3, 2y) d) (2x+6, y)
Answer:
The answer is C: (2x +3, 2y)
Step-by-step explanation:
When applying the dilation of a scale factor of 2, you have to apply it to both the x and y coordinate, which means you are multiplying the coordinates by 2.
Let's assume the coordinates you start with are (x, y). Apply the dilation of 2.
(x, y) -----> (2x, 2y)
Now you are moving the figure right. When moving right, this only effects the x coordinate since the x axis moves left and right. Moving right indicates you will add the number of units translated to the x coordinate.
Translation 2 units right:
(2x, 2y) -----> (2x +3, 2y)
PLEASE HELP ME WITH THIS!!!
Answer:
68 inches
Step-by-step explanation:
y = x + 2
x = 66
y = 66 + 2
y = 68
Use Order of Operations
to solve. PEMDAS
9 + 6(2²+4)
Answer:
57
Step-by-step explanation:
9+6(2^2+4)
Calculate 2 to the power of 2 and get 4.
9+6(4+4)
Add 4 and 4 to get 8.
9+6×8
Multiply 6 and 8 to get 48.
9+48
Add 9 and 48 to get 57.
57