In a unit circle a line reaching from origin to the circle's circumference specifies the trigonometric functions.
A point where the line which comes from origin to the circumference intersecting it has coordinates [tex](\cos\theta,\sin\theta)[/tex].
In our case [tex]\theta=45^\circ[/tex] which lifts the line up by 45 degrees and makes it intersect circumference at [tex](\cos45^\circ,\sin45^\circ)[/tex].
In the upper right quadrant the angle between x and y axis is 90 degrees so a line coming in at angle of 45 degrees would split the quadrant in half, that means sine and cosine 45 degrees will be equal.
As you may noticed a point has coordinates cos, sin which means the distance between 0 and y coordinate where the point on a circle is, is called [tex]\cos\theta=\cos45^\circ[/tex].
Because cosine 45 degrees is so simple in interpretation it has a known value of [tex]\cos45^\circ=\sin45^\circ=\frac{\sqrt{2}}{2}[/tex].
Hope this helps :)
The volume of a rectangular prism (shown below) is 48x^3+56x^2+16x Answer the following questions:
(1) What are the dimensions of the prism?
(2) If x = 2, use the polynomial 48x^3+56x^2+16x to find the volume of the prism.
(3) If x = 2, use the factors found in part a to calculate each dimension.
(4) Using the dimensions found in part c, calculate the volume. Show all work.
Answer:
(a)
[tex]Length = 8x\\Width = 3x + 2\\Height = 2x + 1[/tex]
(b)
[tex]P(2) = 640[/tex]
(c)
[tex]Length= 16[/tex]
[tex]Width = 8[/tex]
[tex]Height =5[/tex]
(d)
[tex]Volume = 640[/tex]
Step-by-step explanation:
Given
[tex]P(x) = 48x^3 + 56x^2 + 16x[/tex]
Solving (a): The prism dimension
We have:
[tex]P(x) = 48x^3 + 56x^2 + 16x[/tex]
Factor out 8x
[tex]P(x) = 8x(6x^2 + 7x + 2)[/tex]
Expand 7x
[tex]P(x) = 8x(6x^2 + 4x + 3x + 2)[/tex]
Factorize
[tex]P(x) = 8x(2x(3x + 2) +1( 3x + 2))[/tex]
Factor out 3x + 2
[tex]P(x) = 8x(3x + 2)(2x + 1)[/tex]
So, the dimensions are:
[tex]Length = 8x\\Width = 3x + 2\\Height = 2x + 1[/tex]
Solving (b): The volume when [tex]x = 2[/tex]
We have:
[tex]P(x) = 48x^3 + 56x^2 + 16x[/tex]
[tex]P(2) = 48 * 2^3 + 56 * 2^2 + 16 * 2[/tex]
[tex]P(2) = 640[/tex]
Solving (c): The dimensions when [tex]x = 2[/tex]
We have:
[tex]Length = 8x\\Width = 3x + 2\\Height = 2x + 1[/tex]
Substitute 2 for x
[tex]Length=8*2[/tex]
[tex]Length= 16[/tex]
[tex]Width = 3*2+2[/tex]
[tex]Width = 8[/tex]
[tex]Height = 2*2 + 1[/tex]
[tex]Height =5[/tex]
So, we have:
[tex]Length= 16[/tex]
[tex]Width = 8[/tex]
[tex]Height =5[/tex]
Solving (d), the volume in (c)
We have:
[tex]Volume = Length * Width * Height[/tex]
[tex]Volume = 16 * 8 * 5[/tex]
[tex]Volume = 640[/tex]
five brothers of 4, 9, 11, 13 and 16 years respectively, receive an inheritance of 1,500,000, the will stipulated that that amount must be shared by the heirs so that, placed the shares in a bank, they would result in equal capitalized amounts, when each one reached 21, could raise his share. Knowing that the bank charges an interest rate of 9% per year, what is the amount of each share?
9514 1404 393
Answer:
Youngest to oldest:
160,406.86246,805.83293,230.01348,386.58451,170.72Step-by-step explanation:
At 9% interest per year, the present value of 1 at age 20 is ...
p(a) = 1.09^(a-20)
Adding the present values for the different ages, we get a total of about 2.35528984846. Dividing the inheritance by that amount gives the multiplier for each of the present value numbers. The result is the list of shares shown above. At age 20, each brother will inherit about 636,864.29.
__
Additional comment
This is the sort of question that suggests the use of a graphing calculator or spreadsheet for doing the tedious number crunching.
(We assume the bank pays 9% per year, rather than charges 9% per year.)
The average of two numbers is 5x. If one of the numbers is 2x + 3, find the other number.
Answer:
8x-3
Step-by-step explanation:
Average of 2 numbers means add the two numbers and divide by 2
(y+z)/2 = 5x
Let z = 2x+3
(y+2x+3)/2 = 5x
Multiply each side by 2
y+2x+3 = 10x
Subtract 2x from each side
y+3 = 10x-2x
y+3 = 8x
Subtract 3
y = 8x-3
The other number is 8x-3
please solve the question
Answer:
[tex]g(-1) = -1[/tex]
[tex]g(0.75) = 0[/tex]
[tex]g(1)= 1[/tex]
Step-by-step explanation:
Given
See attachment
Solving (a): g(-1)
We make use of:
[tex]g(x) = -1[/tex]
Because: [tex]-1 \le x < 0[/tex] is true for x =-1
Hence:
[tex]g(-1) = -1[/tex]
Solving (b): g(0.75)
We make use of:
[tex]g(x) = 0[/tex]
Because: [tex]0 \le x < 1[/tex] is true for x =0.75
Hence:
[tex]g(0.75) = 0[/tex]
Solving (b): g(1)
We make use of:
[tex]g(x) = 1[/tex]
Because: [tex]1 \le x < 2[/tex] is true for x =1
Hence:
[tex]g(1)= 1[/tex]
In the picture below, which lines are lines of symmetry for the figure?
A. only 3
B. 1 and 3
C. 1, 2, and 3
D. none
Based on the lines drawn on the given picture, the number of lines of symmetry are D. none.
What are lines of symmetry?Lines of symmetry are those that divide a shape such that each side can be said to be a reflection of the other.
In the above image, there are no lines of symmetry because when any of the lines given divides the shape, either side would not be identical.
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PLEASE ANSWER
For a parabola where p > 0, the curve will open
Options
To the left
Up
Down
To the right
Answer:
‼️D) To the right‼️
Explanation
There is an easy way to tell whether the graph of a quadratic function opens upward or downward: if the leading coefficient is greater than zero, the parabola opens upward, and if the leading coefficient is less than zero, the parabola opens downward.
The Anthonys bought a home in January and borrowed $376000 to finance it. The mortgage interest and principal payment is $2011 per month. In the first year, they paid $22175 in interest, $7652 in principal, and $8312 in property taxes. They are in the 24% marginal tax bracket. Approximately, how much will they save in federal income taxes from home ownership the first year, if itemizing deductions?
Find the missing side of the right triangle.
Answer:
√65
Step-by-step explanation:
you have to use the pythagoras theorem to find x which is the hypotenuse
x²=7²+4²
x²=49+16
√x²=√65
x=√65
I hope this helps
10 times a certain number plus 5 times the same number equals 90 what is the number
Let the number be x
ATQ
[tex]\\ \sf\longmapsto 10x+5x=90[/tex]
[tex]\\ \sf\longmapsto (10+5)x=90[/tex]
[tex]\\ \sf\longmapsto 15x=90[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{90}{15}[/tex]
[tex]\\ \sf\longmapsto x=6[/tex]
Please help me will vote the person who does brainiest person or something
Answer:
quadratic
y=mx+c
Step-by-step explanation:
What is the measure of 7 shown in the diagram below?
110°
O A. 74.5°
B. 32°
X
O C. 71°
Z
D. 35.5°
Answer:
c
Step-by-step explanation:
Answer:
the correct choice is B
Step-by-step explanation:
The probability of a customer arrival at a grocery service counter in any one second is equal to 0.4. Assume that customers arrive in a random stream, so an arrival in any one second is independent of all others. (Round your answers to four decimal places.) (a) Find the probability that the first arrival will occur during the seventh one-second interval. 0.0187 Correct: Your answer is correct. (b) Find the probability that the first arrival will not occur until at least the seventh one-second interval.
Answer:
a. approximately 0.0187
b. 0.047
Step-by-step explanation:
q = 1-p
= 1-0.4
q = 0.6
a. the probability that the first arrival will occur during seventh one-second interval
probability(7) = 0.6⁷⁻¹ x 0.4
= 0.6⁶ x 0.4
= 0.046656 x 0.4
= 0.0186624
approximately 0.0187
b. probability that the first arrival will not occur until at least the seventh one second interval
p(y≥7) = 1-p(x<7)
= 1-[(0.4)(0.6)⁰ + (0.4)(0.6)¹ +(0.4)(0.6)²+(0.4)(0.6)³+(0.4)(0.6)⁴+(0.4)(0.6)⁵]
= 1-(0.4+0.24+0.144+0.0864+0.05184+0.031104
= 1-0.95334
= 0.04667
= 0.047
what is the constant proportionality in the equation y=2.5x
Answer:
Step-by-step explanation:
Use the Pythagorean theorem to find the missing lengths in the diagram below.
Answer:
anser b
Step-by-step explanation:
i had it
Answer:
x = √74
y = √17
Answered by GAUTHMATH
Please help me with this on the picture
Answer:
1. 748
2. 901
3. 27
4. 672
Step-by-step explanation:
1. 1011-263=748
2. 653+248=901
3. 1161÷43=27
4. 48×14=672
Given that the triangle ABC is at A= (2,4) B= (5,9) C =(1,7) and if the triangle is reflected across the line y=1, what is the new position of point B?
We need not consider a whole triangle but just point B.
Before reflection we know that [tex]B(5,9)[/tex].
Reflecting B over [tex]y=1[/tex] is relatively easy. First because its a reflection over the horizontal line the only coordinates that will change are y coordinates, while x coordinate will not change so half of the reflection is already done for us,
[tex]B(5,a)[/tex]
Now to what has changed, well currently the distance between 9 and 1 on the y axis is 8 up. But because we are reflecting the a must now be 8 down from 1 which means [tex]1 - 8 = -7[/tex] so our point is now [tex]\boxed{B(5,-7)}[/tex].
Hope this helps :)
9514 1404 393
Answer:
(5, -7)
Step-by-step explanation:
Reflection across the line y = c is accomplished by the transformation ...
(x, y) ⇒ (x, 2c -y)
For c=1 and point B, we have ...
B(5, 9) ⇒ B'(5, 2·1 -9) = B'(5, -7)
The image of point B is (5, -7).
Which of the following choices is equivalent to -6x > -42?
Answer:
Where is the rest?
Step-by-step explanation:
%7"7:7;9
Probability that a person is chosen at random
Answer:
152 / 370
Step-by-step explanation:
Total number of people
152+218 = 370
P( own a dog) = people said yes / total
= 152 / 370
Simplify the given equation.
6 - (3x+10) + 4(2 - x) = 15
O 4-7 x = 15
O4 - 4 x= 15
O 12 - 7 x= 15
Answer:
-7x-11
Step-by-step explanation:
expand brackets
6-3x-10+8-4x=15
4-7x=15
move 15 to left side
-7x-11
Answer:
4-7x=15
Step-by-step explanation:
[tex]6 - (3x + 10) + 4(2 - x) = 15 \\ 6- 3x - 10 + 8 - 4x = 15 \\ - 7x = 15 + 10 - 8 - 6\\ - 7x = 11 \\ the \: same \: one \: is \\ 4 - 7x = 15[/tex]
If 6.45% of the battery life of each mobile phone is used in a day by a typical user, for which mobile phone is 1.6125 hours of battery life used in a day?
The table shows the battery life of four different mobile phones. Mobile Phone Battery Life Phone Battery Life (hours) A 20 B 25 C 10 D 18 If 6.45% of the battery life of each mobile phone is used in a day by a typical user, for which mobile phone is 1.6125 hours of battery life used in a day?
B
Should be the answer
What is the shortest distance Jill can travel is she leaves her house, goes to City Hall, to the Post Office, and then returns home?
A. 9 miles
B. 16 miles
C. 38 miles
D. 48 miles
Answer:
the answer is B 16 miles
Step-by-step explanation:
so because every 3 cm is 1 mile if to make it to City Hall you would do 7 x 3 which would be 21 cm so you have 7 miles already so to make it to the post office from city hall it would be another 7 miles then 3 more cm and that would be 1 mile so 7 + 7 + 1 = 15 so then the closest number to 15 is 16 I know its right because I did the test and got it right.
Answer:
B
Step-by-step explanation:
g (x) = f ( x + 1).
graph
(2 marks) Q12 A sandwich shop owner makes 1 sandwich with brown bread for every 4 sandwiches he makes with white bread. Today he needs to make 600 sandwiches altogether. How many sandwiches should he make with brown bread today? sandwiches (1 mark) 30
The shop owner makes total 120 sandwiches with brown bread today.
What is linear equation in one variable?The linear equations in one variable is an equation which is expressed in the form of ax + b = 0, where a and b are two integers, and x is a variable and has only one solution.
According to the given question.
A sandwich shop owner makes 1 sandwich with brown bread for every 4 sandwiches he makes with white bread.
Let the total number of white bread sandwiches be 4x and white bread sandwiches be 1x.
Since, the shop owner have to make 600 sandwiches.
So, for the given scenario we have a linear equation in one variable.
[tex]\implies 600 = 4x+1x\\\implies 600 = 5x \\\implies x = \frac{600}{5} \\\implies x = 120[/tex]
Hence, the shop owner makes total 120 sandwiches with brown bread today.
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Solve the following system of equations by graphing.
y = -x-1
y = 14x - 4
A) (-4,3)
B) (-3,4)
C) (4,-3)
D) (3,4)
Answer:
(0.2, -1.2)
Step-by-step explanation:
When solving a system of equations by graphing, we first plot the two equations on a graph, then the point of intersection of the two graphs is the solution to the system of equations.
Therefore giving the equations y = - x - 1; and y = 14x - 4, we have to first plot the both linear equations using online geogebra graphing tool. The intersection of both linear graphs is the solution to the problem.
We can see that the point of intersection is A(0.2, -1.2)
The date is 3rd August. What was the date a week ago?
Answer:
27th July was a week ago
27th July
I could count backwards, but looking one line up in any calendar is way faster I guess. I see no gain in getting better in telling how many days each month has, but if you would like to it with counting, it's. 3red August -7, where the 31. July comes in the place of "the 0th August", si you could calculate it in two steps or just count backwards.
Find the length of the third side. If necessary, round to the nearest tenth.
6
8
PLS HELP
Answer:
a = 5.3
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean theorem
a^2 + b^2 = c^2
where a and b are the legs and c is the hypotenuse
a^2 + 6^2 = 8^2
a^2 +36 = 64
a^2 = 64-32
a^2 =28
Taking the square root of each side
sqrt(a^2) = sqrt(28)
a=5.29150
To the nearest tenth
a = 5.3
The length of the third side of the right triangle is; 5.3
What is the length of the third side of the triangle?The triangle given is a right triangle and hence, the length of the third side can be evaluated by using the Pythagoras theorem as follows;
a² = 8² -6²
a² = 64- 36
a² = 28
a = √28
a = 5.3
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Se practica un orificio circular de 2 cm de diámetro en la pared lateral de un gran depósito a una distancia de 10 m por debajo del nivel del agua. Calcule: a) la velocidad de salida, y b) el volumen que sale por unidad de tiempo. Sol. a) 14 m/s. b) 4.4 x 10-3 m3 /s
Answer:
I dont speak Spanish bro bro
The perimeter of Tamara's suitcase is 8x - 3 and the perimeter of Anna's suitcase is
3x + 2. Write an algebraic expression that represents
the difference between the perimeter of Tamara's suitcase
and the perimeter of Anna's suitcase?
Answer:
perimeter: 2
Step-by-step explanation:
8x-3 = 6x
8x – 6x = 3
2x = 3
x = 3/2
The required algebraic expression that represents the difference between the perimeter of Tamara's suitcase and the perimeter of Anna's suitcase is 5x - 5.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
The difference between the perimeter of Tamara's suitcase and Anna's suitcase can be found by subtracting the expression for the perimeter of Anna's suitcase from the expression for the perimeter of Tamara's suitcase:
(8x - 3) - (3x + 2)
Simplifying the expression by removing the parentheses and combining like terms, we get:
8x - 3 - 3x - 2
= 5x - 5
Therefore, the algebraic expression that represents the difference between the perimeter of Tamara's suitcase and the perimeter of Anna's suitcase is 5x - 5.
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amortization for house costs 35,000.00 at 6.5% interest for 10 years and payments of 400.00 were paid for 36 months what is the remaining balance
Answer:
$26,640.22
Step-by-step explanation:
a bridge costs 94,500 to repair. if the state pays twice as much as the city, how much did each pay?
