Answer:
= 1/2[sin2Acos7A + cos2Asin7A + sin2Acos7A - cos2Asin7A]
we cut out
cos2Asin7A - cos2Asin7A
then we have
=1/2[sin2Acos7A + sin2Acos7A ]
= 1/2*2[ sin2Acos7A ]
cut out 2 we get
#sin2Acos7A
Howdy! Do you know if they make any plugins to protect against hackers? I'm kinda paranoid about losing everything I've worked hard on. Any recommendations? Ekdfeakeaged
Answer:use a VPN and also write down your passwords, never keep them saved on your computer in case of a leak/breach of privacy and information
Step-by-step explanation:
Other than that all you got a do is download a VPN and also write your passwords and then proceed to be careful by not sharing any private/key info to identify who you are
A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole with a speed of 4 ft/s along a straight path. How fast is the tip of his shadow moving when he is 45 ft from the pole?
Answer:
The tip of the man shadow moves at the rate of [tex]\frac{20}{3} ft.sec[/tex]
Step-by-step explanation:
Let's draw a figure that describes the given situation.
Let "x" be the distance between the man and the pole and "y" be distance between the pole and man's shadows tip point.
Here it forms two similar triangles.
Let's find the distance "y" using proportion.
From the figure, we can form a proportion.
[tex]\frac{y - x}{y} = \frac{6}{15}[/tex]
Cross multiplying, we get
15(y -x) = 6y
15y - 15x = 6y
15y - 6y = 15x
9y = 15x
y = [tex]\frac{15x}{9\\} y = \frac{5x}{3}[/tex]
We need to find rate of change of the shadow. So we need to differentiate y with respect to the time (t).
[tex]\frac{dy}{t} = \frac{5}{3} \frac{dx}{dt}[/tex] ----(1)
We are given [tex]\frac{dx}{dt} = 4 ft/sec[/tex]. Plug in the equation (1), we get
[tex]\frac{dy}{dt} = \frac{5}{3} *4 ft/sect\\= \frac{20}{3} ft/sec[/tex]
Here the distance between the man and the pole 45 ft does not need because we asked to find the how fast the shadow of the man moves.
To find the speed at which the tip of the man's shadow is moving, we need to solve a proportional relationship between the length of the shadow and the distance of the man from the pole. Using similar triangles and setting up a ratio, we can find the length of the shadow and then find its rate of change with respect to time. The tip of the shadow is not moving when the man is 45 ft from the pole.
Explanation:To solve this problem, we need to use similar triangles. Let's call the length of the shadow x. The height of the pole is 15 ft and the height of the man is 6 ft. So, we can set up the following ratio:
15 / x = 6 / (x + 45)
To find x, we can cross-multiply:
(15)(x + 45) = 6x
Now, we can simplify and solve for x:
15x + 675 = 6x
9x = 675
x = 75 ft
To find the rate of change of the shadow's tip, we can take the derivative of x with respect to time:
dx/dt = 0
So, the tip of the shadow is not moving when the man is 45 ft from the pole.
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u and v are position vectors with terminal points at (-1, 5) and (2, 7), respectively. Find the terminal point of -2u + v.
(0, -3)
(4, -3)
(4, 17)
(9, -8)
Answer:
(4, -3)
Step-by-step explanation:
-2u +v = -2(-1, 5) +(2, 7) = (-2(-1)+2, -2(5)+7)
= (4, -3)
The perimeter of the rectangle is 28 units.
what is the value of w?
Answer:
5
Step-by-step explanation:
Since this is a rectangle, opposite sides are congruent.
That is, the perimeter in terms of w is:
(2w-1)+(2w-1)+(w)+(w)
or
2(2w-1)+2(w)
We can simplify this.
Distribute:
4w-2+2w
Combine like terms:
6w-2
We are given that the perimeter, 6w-2, is 28.
So we can write an equation for this:
6w-2=28
Add 2 on both sides:
6w =30
Divide both sides by 6:
w =30/6
Simplify:
w =5
w is 5
Check if w=5, then 2w-1=2(5)-1=10-1=9.
Does 5+5+9+9 equal 28? Yep it does 10+18=28.
Answer:
w=5
Step-by-step explanation:
To find the perimeter of the rectangle
P = 2(l+w)
where w is the width and l is the length
Our dimensions are w and 2w-1 and the perimeter is 28
Substituting into the equation
28 = 2(2w-1 +w)
Combining like terms
28 = 2(3w-1)
Divide each side by 2
28/2 = 2(3w-1)/2
14 = 3w-1
Add 1 to each side
14+1 = 3w-1+1
15 = 3w
Divide each side by 3
15/3 =3w/3
5 =w
Is it proportional, inversely proportional or neither?? please explain
John and David are running around the same track at the same speed. When David started running, John had already run 3 laps. Consider the relationship between the number of laps that David run and the number of laps that John has run.
Answer:
neither
Step-by-step explanation:
The number of laps John has run is 3 + the number of laps David has run. That is, both numbers are not zero at the same time, so the relationship cannot be proportional.
The numbers have a constant difference, not a constant product, so they are not inversely proportional, either.
David's laps and John's laps are neither proportional nor inversely proportional.
The relationship between the number of laps David runs and the number of laps John has run is proportional because they increase at the same rate, with John always maintaining a 3-lap lead.
The question asks whether the relationship between the number of laps that David runs and the number of laps that John has run is proportional, inversely proportional, or neither. Since John and David are running at the same speed, but John started with a 3-lap lead, the relationship is linear. The more laps David runs, the more John runs as well, maintaining a constant gap of 3 laps. Thus, this scenario illustrates a proportional relationship where the number of laps run by each, ignoring the start difference, increases at the same rate. This relationship can be represented by a linear equation like y = x + 3, where x is the number of laps David runs, and y is the number of laps John runs.
From 1960 to 1970, the consumer price index (CPI) increased from 29.6 to 48.2. If a dozen donuts cost $0.89 in 1960 and the price of donuts increased at the same rate as the CPI from 1960 to 1970, approximately how much did a dozen donuts cost in 1970?
Answer:
$1.45
Step-by-step explanation:
The cost of a dozen doughnuts in 1970 is $1.44.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
To calculate the cost of a dozen doughnuts in 1970 we have to know the percentage increase in the price index from 1960 to 1970 and this will be:
Rate = [(48.2 – 29.6) / 29.6] × 100%
Rate = (18.6 / 29.6) × 100%
Rate = 62.83 %
Let's represent the price of a dozen doughnuts in 1970 by X and solve. This will be:
62.83 = (X - 0.89) × 100 / 0.89
(62.83 × 0.89 ) = 100X - 89
55.9 = 100X - 89
100X = 144.9
X = 144.9 / 100
X = $1.44
X = $1.44
Therefore, the cost of a dozen doughnuts in 1970 is $1.44.
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What is the area of a parallelogram with a base of 38 meters and a height of 12 meters?
For this case we have by definition that the area of a parallelogram is given by:
[tex]A = b * h[/tex]
Where:
b: It's the base
h: It's the height
According to the data we have:
[tex]b = 38\ m\\h = 12 \ m[/tex]
Substituting in the formula:
[tex]A = 38 * 12\\A = 456[/tex]
The area of the parallelogram is [tex]A = 456 \ m ^ 2[/tex]
Answer:
[tex]A = 456 \ m ^ 2[/tex]
Answer:
A=456m²
Step-by-step explanation:
(Will get brainliest) Simplify the expression: left square bracket left parenthesis 18 − 6 right parenthesis ⋅ 3 plus 1 right square bracket ⋅ 7
A.
43
B.
259
C.
7
D.
336
Answer:
B. 259
Step-by-step explanation:
This is an exercise in PEMDAS, the order of mathematical operations:
Parentheses, Exponents, Multiplication and Division, Addition and Subtraction
Parentheses: [(18 − 6)⋅3 + 1]⋅7
Subtraction: = [(12)·3 +1]·7
Multiplication: = [36 + 1]·7
Addition: = [37]·7
Parentheses: = 37·7
Multiplication: = 259
Answer:
259
Step-by-step explanation:
I need help . This problem is confusing me.
Answer:
The answer is 3093.
3093 (if that series you posted actually does stop at 1875; there were no dots after, right?)
Step-by-step explanation:
We have a finite series.
We know the first term is 48.
We know the last term is 1875.
What are the terms in between?
Since the terms of the series form a geometric sequence, all you have to do to get from one term to another is multiply by the common ratio.
The common ratio be found by choosing a term and dividing that term by it's previous term.
So 120/48=5/2 or 2.5.
The first term of the sequence is 48.
The second term of the sequence is 48(2.5)=120.
The third term of the sequence is 48(2.5)(2.5)=300.
The fourth term of the sequence is 48(2.5)(2.5)(2.5)=750.
The fifth term of the sequence is 48(2.5)(2.5)(2.5)(2.5)=1875.
So we are done because 1875 was the last term.
This just becomes a simple addition problem of:
48+120+300+750+1875
168 + 1050 +1875
1218 +1875
3093
A squirrel family collected 727272 nuts to store for the winter. They spread the nuts out evenly between their 666 favorite locations. Sadly, a crow stole half the nuts from one of the locations. How many nuts did the crow steal?
Answer:
546 nuts
Step-by-step explanation:
727272 / 666 = 1092 nuts in each location
crow stole half nuts in 1 location
1092 / 2 = 546 nuts stolen
Answer:
6 nuts.
Step-by-step explanation:
The number of nuts in each location is 72 / 6 = 12 nuts.
So the crow stole 1/2 * 12 = 6 nuts.
A formula for finding the area of a rectangle is A=l?w. If you know the area (A) and length (l) of a rectangle, which formula can you use to find the width (w)?
Answer:
[tex]w=\frac{A}{l}[/tex]
Step-by-step explanation:
The formula to find the area of a rectangle is: [tex]A=w \times l[/tex], where [tex]w[/tex] is width and [tex]l[/tex] is length.
So, if we knoe the area [tex]A[/tex] and the length [tex]l[/tex], we can find the width with the formula
[tex]w=\frac{A}{l}[/tex]
You can get this answer by using the defintion of area, which is the first equation, and isolating [tex]w[/tex].
Remember, when we want to move a factor to the other side of the equalty, we must pass it with the opposite operation. So, in this case, width was multiplying, and it passed to the other side dividing.
Therefore, the answer here is [tex]w=\frac{A}{l}[/tex]
What is the y-intercept of the line 10x - 5y = 407
Answer:
The y-intercept is (0,-407/5).
Step-by-step explanation:
The y-intercept can be found by setting x to 0 and solving for y.
10x-5y=407
10(0)-5y=407
0-5y=407
-5y=407
Divide both sides by -5:
y=(407/-5)
y=-407/5
The y-intercept is (0,-407/5).
Find the greatest common factor of 28 and 42.
2
4
7
14
The greatest common factor (or GCF) is, as the name says, the greatest factor a set of numbers have in common. We can find this by listing out all the possible factors (multiples) of each number:
For 28:
1, 2, 4, 7, 14, 28
For 42
1, 2, 3, 6, 7, 21, 42
(note you don't need to list out all the factors, I just did it for visual purposes)
As you can see, 28 and 42 have 3 factors in common, with 7 being the greatest.
Therefore, the answer would be C: the GCF is 7.
Hope this helps! :)
Answer:
it is 14... have a blessed and amazing day
Step-by-step explanation:
Use your TVM Solver to determine the future balance in a mutual fund account (a type of investment account) if you make weekly payments of $50 into an account that pays 2.0% interest compounded monthly. You open the account with $500 and pay into the account for 15 years.
Answer:
$46,141.71
Step-by-step explanation:
This looks about right, based on weekly deposits for the duration. However, I cannot vouch for it entirely, as the number of weekly deposits in 15 years will actually be 782.
_____
Computing this by hand doing the initial balance separately from the weekly deposits, I get a total of $46,252.10 using 782 weekly deposits. For that purpose, I tried to figure an equivalent weekly interest rate given monthly compounding and the fact there are 52 5/28 weeks in a year on average.
I suspect the only way to get this to the cent would be to build a spreadsheet with payment dates and interest computation/payment dates. Some months, there would be 5 deposits between interest computations; some years there would be 53 deposits.
Vector E is 0.111 m long in a 90.0 direction.Vector F is 0.234 m long in a 300 direction. What is the magnitude and direction of their vector sum?
Answer:
0.148623∠321.93°
Step-by-step explanation:
You can work these without too much brain work by converting the coordinates to rectangular coordinates, adding those, then converting back to a vector length and angle as may be required.
0.111∠90° + 0.234∠300° = 0.111(cos(90°), sin(90°)) +0.234(cos(300°), sin(300°))
= (0, 0.111) + (0.117, -0.2026499) = (0.117, -0.0916499)
The magnitude of this is found using the Pythagorean theorem:
|E+F| = √(0.117² +(-0.0916499)²) ≈ 0.148623
The angle can be found using the arctangent function, paying attention to the quadrant. This sum vector has a positive x-coordinate and a negative y-coordinate, so is in the 4th quadrant.
∠(E+F) = arctan(y/x) = arctan(-0.0916499/0.117) ≈ -38.07° = 321.93°
The vector sum is E+F = 0.148623∠321.93°.
__
You can also draw the triangle that has these vectors nose-to-tail and find the magnitude of the sum using the Law of Cosines. The two sides of the triangle are the lengths of the given vectors and the angle between those can be seen to be 30°. Then the length of the 3rd side of the triangle is ...
|E+F|² = |E|² +|F|² -2·|E|·|F|·cos(30°) = .012321 +.054756 -.044988 = 0.0220887
|E+F| = √0.0220887 ≈ 0.148623
The direction of the vector sum can be figured from the direction of vector E and the internal angle of the triangle between vector E and the sum vector. That angle can be found from the law of sines to be ...
(angle of interest) = arcsin(sin(30°)·|F|/|E+F|) = 128.07°
Then the angle of the vector sum is 450° -128.07° = 321.93°.
A diagram is very helpful for keeping all of the angles straight.
|E+F| = 0.148623∠321.93°
The polynomial below is a perfect square trinomial of the form A2 - 2AB + B2.
Answer: Option B.
Step-by-step explanation:
Given the polynomial:
[tex]16x^2-36x+9[/tex]
Observe that [tex]16x^2[/tex] and [tex]9[/tex] are perfect squares. Then, you can rewrite the polynomial in this form:
[tex](4x)^2-36x+(3)^2[/tex]
You can identify that:
[tex]A=4\\B=3[/tex]
Then, we can check if [tex]2AB=36[/tex]
[tex]2(4x)(3)=36x\\\\24x\neq 36x\\\\2AB\neq36x[/tex]
Since [tex]2AB\neq36x[/tex], the polynomial [tex]16x^2-36x+9[/tex] IS NOT a perfect square trinomial of the form [tex]A^2 - 2AB + B^2[/tex]
Answer: B
Step-by-step explanation:
Which is equivalent of 278.24 written in DMS form
Answer: [tex]278\°14'24''[/tex]
Step-by-step explanation:
You know that:
[tex]1\ hour=60\ minutes\\\\1\ minute=60\ seconds[/tex]
Then, in order to convert the given decimal degree to Degrees Minutes Seconds (DMS), you need to follow these steps:
1) The whole number 278 gives you the degrees.
2) Multiply 0.24 by 60:
[tex]0.24*60=14.4[/tex]
The whole number 14 gives you the minutes.
3) Multiply 0.4 by 60:
[tex]0.4*60=24[/tex]
This gives you the seconds.
Therefore, 278.24 written in DMS form is:
[tex]278\°14'24''[/tex]
Answer:
The answer is 278°14'24''
Step-by-step explanation:
Given : 278.24
To find : written in DMS form.
Solution : We have given that 278.24
Multiply 24 by 60 to convert it into minute
We can write it as 278 + .24(60).
278°14.4'
Rewrite 278°14+.4'
4' = 4 ( 60) to convert minute in to second.
278°14+.4(60)
278°14'24''
The answer is 278°14'24'' ....
Find all of the zeros of the function f(x) = x3 – 23x2 + 161x – 303.
Answer:
x = 3x = 10 ± iStep-by-step explanation:
A graph shows the only real zero to be at x = 3.
Factoring that out gives the quadratic whose vertex form is ...
y = (x -10)² +1
The roots of this quadratic are the complex numbers x = 10 ± i.
_____
For y = (x -10)² +1, the zeros are ...
(x -10)² +1 = 0
(x -10)² = -1 . . . . . . . . . . subtract 1
x -10 = ±√(-1) = ±i . . . . .take the square root
x = 10 ± i . . . . . . . . . . . . add 10
Answer:
3, 10±i
Step-by-step explanation:
Given is a function [tex]f(x) = x^3 - 23x^2 + 161x -303.[/tex]
By rational roots theorem, this can have zeroes as ±1, ±3,±101
By trial and error checking we find f(3) =0
Hence x-3 is a factor
f(x) = [tex](x-3)(x^2-20x+101)[/tex]
II being a quadratic equation we find zeroes using formula
[tex]x=\frac{20±\sqrt{400-404} }{2} =10+i, 10-i[/tex]
zeroes are 3, 10±i
A cubic inch of PVC material weight 0.063 pounds per cubic inch. What's the weight of a 36 inch piece of PVC pipe with an outside diameter of 0.82 inches and an inside diameter of 0.75 inches?
Answer:
0.196 lbs
Step-by-step explanation:
The area of the cross section is the difference of the areas of circles with the different diameters. The volume of the pipe material is the product of its cross section area and its length:
V = π(D² -d²)L/4 = π(0.82² -0.75²)36/4 ≈ 3.107 . . . in³
Then the weight of the material is this volume multiplied by the density.
W = V·δ = (3.107 in³)(0.063 lb/in³) ≈ 0.196 lb
Finding the weight of the PVC pipe involves calculating the volumes of the outer and inner cylinders then finding the difference, which is multiplied by the weight per cubic inch of PVC.
Explanation:The weight of a 36 inch piece of PVC pipe can be calculated using the formula for the volume of a cylinder and the given weight per cubic inch of PVC material. Firstly, calculate the volume of the outer cylinder, which we know the diameter and length (or height). The formula for the volume of a cylinder is πr²h, where r is the radius and h is the height. We need to halve the diameter to get the radius, which gives us 0.82/2 = 0.41 inches.
Secondly, we calculate the volume of the inner cylinder in the same way, except we use the inner diameter, which is 0.75 inches, halved gives us a radius of 0.375 inches. The volume of material used is then the volume of the outer cylinder minus the volume of the inner cylinder. Lastly, multiply the volume of material by the weight per cubic inch to get the total weight.
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How do you do this question?
Answer:
positive
Step-by-step explanation:
Find the sign of (2-2x+y) for any point (x,y) in quadrant 2.
In quadrant 2, the x's are negative and the y's are positive.
So choose a negative value for x and a positive value for y and evaluate:
2-2x+y
Let's try (-4,5):
2-2(-4)+5
2+8+5
15 (positive)
Let's try(-1/2 , 10):
2-2(-1/2)+10
2+1+10
3+10
13 (positive)
Let's try in general Let (x,y)=(-a,b) where a and b are positive:
2-2(-a)+b
2+2a+b
Since a and b are positive, then 2+2a+b is positive because you are adding three different positive numbers.
Which of the following is the function representing the graph below? graph begins in the third quadrant near the line y equals negative 3 and increases slowly while crossing the ordered pair 0, negative 2. When the graph enters the first quadrant, it begins to increase quickly throughout the graph.
f(x) = 4x
f(x) = 4x − 3
f(x) = 4x + 3
f(x) = 4(x + 3)
Answer:
f(x) = 4^x -3
Step-by-step explanation:
All of the listed functions are linear functions with a constant slope of 4. None of them goes through the point (0, -2).
__
So, we assume that there is a missing exponentiation operator, and that these are supposed to be exponential functions. If the horizontal asymptote is -3, then there is only one answer choice that makes any sense:
f(x) = 4^x -3
_____
The minimum value of 4^z for any z will be near zero. In order to make it be near -3, 3 must be subtracted from the exponential term.
Rectangle ABCD was dilated to create rectangle A'B'C'D.
What is AB?
6 units
7.6 units
9.5 units
12 units
Answer:
6
Step-by-step explanation:
Let's setup a proportion to find AB.
AB corresponds to A'B'.
BC corresponds to B'C'.
So setting up proportion this would look like:
[\tex]\frac{AB}{A'B'}=\frac{BC}{B'C'}[/tex]
[\tex]\frac{AB}{15}=\frac{3.8}{9.5}[/tex]
Cross multiply:
[tex]AB(9.5)=15(3.8)[/tex]
Divide both sides by 9.5:
[tex]AB=\frac{15(3.8)}{9.5)}[/tex]
Put into calculator:
[tex]AB=6[/tex]
Answer: AB=6 so A is correct, hope this help! Branliest would be awesome :)
Step-by-step explanation:
Since the larger rectangle and the smaller rectangle are essentially the same just bigger, they will be proportionate.
Therefore..
9.5/3.8=15/AB
You can cross multiply to find AB...
9.5AB=57
Divide 57 by 9.5 to separate AB, which you can think of like x...
AB=57/9.5
AB=6
In the figure below, if arc RS measures 100 degrees, what is the measure of angle Q?
Answer:
50 degrees
Step-by-step explanation:
The measure of an inscribed angle of a circle is half the degree measure of the intercepted arc.
m<Q = (1/2)m(arc)RS
m<Q = (1/2)(100 degrees)
m<Q = 50 degrees
Answer:
∠Q = 50°
Step-by-step explanation:
An inscribed angle whose vertex lies on a circle and whose sides are two chords of the circle is one half the measure of its intercepted arc.
arc RS is the intercepted arc, hence
∠Q = 0.5 × 100° = 50°
Probability of multiple Events
A.
B.
C.
D.
Given that [tex]P(Q)=\dfrac{3}{5},P(R)=\dfrac{1}{3}[/tex]
Also,
[tex]P(Q\wedge R)=P(Q)\cdot P(R)=\dfrac{3}{5}\cdot\dfrac{1}{3}=\dfrac{1}{5}[/tex]
We can conclude that,
[tex]P(Q\vee R)=P(Q)+P(R)=\dfrac{3}{5}+\dfrac{1}{3}=\boxed{\dfrac{14}{15}}[/tex]
The answer is B.
Hope this helps.
r3t40
A delivery truck is transporting boxes of two sizes: large and small. The combined weight of a large box and a small box is 70 pounds. The truck is transporting 70 large boxes and 55 small boxes. If the truck is carrying a total of 4450 pounds in boxes, how much does each type of box weigh?
Answer:
one large box is 40 pounds
one small box is 30 pounds
Step-by-step explanation:
let large be l and small be s ,
l + s = 70 ------- equation1
70l + 55s. = 4450 ------- equation 2
equation 1 multiply by 55,
55l + 55s = 3850 ------ equation 3
equation 3 - equation 2 ,
(70l + 55s) - (55l +55s) = 4450 - 3850
70l + 55s - 55l - 55s = 4450 - 3850
15l = 600
l = 40
sub l = 40 into equation 1
40 + s = 70
s = 70 - 40
s = 30
roblem: Report Error A partition of a positive integer $n$ is any way of writing $n$ as a sum of one or more positive integers, in which we don't care about the order of the numbers in the sum. For example, the number 4 can be written as a sum of one or more positive integers (where we don't care about the order of the numbers in the sum) in exactly five ways: \[4,\; 3 + 1,\; 2 + 2,\; 2 + 1 + 1,\; 1 + 1 + 1 + 1.\] So 4 has five partitions. What is the number of partitions of the number 7?
Answer:
There are 15 partitions of 7.
Step-by-step explanation:
We are given that a partition of a positive integer $n$ is any way of writing $n$ as a sum of one or more positive integers, in which we don't care about the numbers in the sum .
We have to find the partition of 7
We are given an example
Partition of 4
4=4
4=3+1
4=2+2
4=1+2+1
4=1+1+1+1
There are five partition of 4
In similar way we are finding partition of 7
7=7
7=6+1
7=5+2
7=5+1+1
7=3+3+1
7=3+4
7=4+2+1
7=3+2+2
7=4+1+1+1
7=3+1+1+1+1
7=2+2+2+1
7=3+2+1+1
7=2+2+1+1+1
7=2+1+1+1+1+1
7=1+1+1+1+1+1+1
Hence, there are 15 partitions of 7.
Bonnie is adding a ribbon border to the edge of her kite. Two sides of the kite measure 13.2 inches, while the other two sides measure 20.7 inches. How much ribbon does Bonnie need?
Answer:
Bonnie needs [tex]67.8\ in[/tex] of ribbon
Step-by-step explanation:
we know that
A Kite is a quadrilateral that has two pairs of equal sides
so
To find out how much ribbon Bonnie needs calculate the perimeter of the kite
[tex]P=2(L1+L2)[/tex]
where
L1 is the length of one side
L2 is the length of the other side
[tex]P=2(13.2+20.7)=67.8\ in[/tex]
Need some help with this problem please!!
Answer:
sin(2x) = 120/169
Step-by-step explanation:
A suitable calculator can figure this for you. (See below)
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You can make use of some trig identities:
sin(2x) = 2sin(x)cos(x)sec(x)² = tan(x)² +1cos(x) = 1/sec(x)tan(x) = sin(x)/cos(x)Then your function value can be written as ...
sin(2x) = 2sin(x)cos(x) = 2(sin(x)/cos(x))cos(x)² = 2tan(x)/sec(x)²
= 2tan(x)/(tan(x)² +1)
Filling in the given value for tan(x), this is ...
sin(2x) = 2(12/5)/((12/5)² +1) = (24/5)/(144/25 +1) = (120/25)/((144+25)/25)
sin(2x) = 120/169
The store has y shirts. It's almost alarm for $16 each, and the last dozen were sold on sale for $14 each. If it's all the shirts for $616, find the number of shirts sold.
The answer is 40 shirts.
Explanation
Equation: y= ((616-(14*12))/16)+12
First, multiply the 12*14 because we know that 12 shirts were $14. You'll get $168. Next, subtract that from 616, the total number of dollars, to get the 12 shirts out of the way. Your answer will be $448. Then, divide by 16 because that's the remaining money that was spent on the $16 shirts. You'll get 28 shirts. However, we can't forget about the dozen $14 shirts, so add 12 to your answer and you get 40 shirts.
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The value of is .
The value of the expression [tex]\rm { log _3 5}\times{log_{25} 9}[/tex] is 1
What is the Law of Base change in Logarithm ?According to the law of base change
[tex]\rm \log _b a = \dfrac{ log _d b}{log_d a}[/tex]
The given expression is
[tex]\rm { log _3 5}\times{log_{25} 9}[/tex]
This can be written as
[tex]\rm \rm { log _3 5}\times{log_{25} 9} = \dfrac{ log _{10} 5 *log _{10} 9 }{log_{10} 3*log _{10}25}[/tex]
[tex]\rm \rm { log _3 5}\times{log_{25} 9} = \dfrac{ log _{10} 5 *log _{10} 3^2 }{log_{10} 3*log _{10}5^2}[/tex]
[tex]\rm \rm { log _3 5}\times{log_{25} 9} = \dfrac{ log _{10} 5 *2log _{10} 3 }{log_{10} 3* 2 log _{10}5}[/tex]
On solving this the value of the expression [tex]\rm { log _3 5}\times{log_{25} 9}[/tex] is 1
To know more about Logarithm law
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Answer:
Step-by-step explanation: