The amplitude of [tex]A\sin(\omega t+\phi)[/tex] is the absolute value of [tex]A[/tex]. So first you need to condense the given function into one sine expression.
Recall that
[tex]A\sin(\omega t+\phi)=A\sin(\omega t)\cos\phi+A\cos(\omega t)\sin\phi[/tex]
so you need to choose [tex]\phi[/tex] and [tex]\omega[/tex] accordingly.
If we line up the terms of the given function with the expanded one above, we should have
[tex]2\sin(4\pi t)+5\cos(4\pi t)\implies\begin{cases}A\cos\phi=2\\A\sin\phi=5\\\omega=4\pi\end{cases}[/tex]
Now, using the Pythagorean identity,
[tex](A\sin\phi)^2+(A\cos\phi)^2=2^2+5^2\implies A^2=29\implies A=\pm\sqrt{29}[/tex]
so the amplitude is √29.
Just for completeness, we also get
[tex]\tan\phi=\dfrac{\sin\phi}{\cos\phi}=\dfrac52\implies\phi=\tan^{-1}\left(\dfrac52\right)+n\pi[/tex]
where [tex]n[/tex] is any integer.
HELP ME PLEASE! So I’m working on this practice page before I start my quiz but I don’t understand these two problems, I was hoping someone would help me.
Answer: y = 1/2x - 6
Step-by-step explanation:
#4 We are going to use slope intercept form, (y = mx+b)
1. The line crossing the y-intercept at (0,-6)
2. The slope is 1/2 (increasing by 1 then over 2 --> RISE OVER RUN)
3. Make the equation: y= 1/2x - 6
Answer: 3 . y = -1/3 + 4/3 4. y= 1/2x -6
Step-by-step explanation:
3. In the first graph they have the coordinates, (-2,2) and (4,0). We have to solve for the slope and the y-intercept in other to write and equation.
To find the slope we have to find the change in the y values and divide it by the difference in the x values.
2-0 = 2
-2 -4 = -6
2/-6 = -1/3 Now we know that the slope is -1/3 so we need to find the y-intercept.
2= -1/3(-2) +b where be is the y intercept.
2= 2/3 + b
-2/3 -2/3
b= 4/3
Now we could write the equation as y= -1/3 + 4/3
4. The same with number 4.
We will find the slope and the y intercept by using some points on the number line.
(0,-6) This already have the y-intercept graphed so we will need to just find the slope.
(0,-6)
(4,-4)
-6 - (-4) = -2
0 - 4 = -4
-2/-4 = 1/2
Equation: y = 1/2x -6
Can someone please help me I’m stuck with this question I don’t know what’s the answer please help
Answer:
the SSS similarity theoremPlease see the attached picture...
Hope it helps...
Good luck on your assignment....
Jeremiah invested $x at a 6% simple annual interest rate account. Six times that amount was invested at an 9% simple annual interest rate account. How much was invested at the 6% account if the total annual return was $800.00?
Answer:
Step-by-step explanation:
We will make a table with the values for both a 6% account and a 9% account.
The formula for this problem is Prt = I, where P is the amount invested in each account, r is the interest rate each carries in decimal form, t is the time in years, and I is the interest earned from the multiplication of the 3 previous values. We don't know how much is invested in either account, but we do know that no matter how much is invested in the 6% account, there is 6 times that in the 9% account. We know that the 6% account has a decimal rate of .06 and that the 9% account has a decimal rate of .09. "Annual" means 1 year, so the time is 1 year. Filling in the table, then:
P * r * t = I
Acct 6% x .06 1
Acct 9% 6x .09 1
What we do with those number is multiply them straight across each row to get the amount of interest earned from each:
P * r * t = I
Acct 6% x * .06 * 1 = .06x
Acct 9% 6x * .09 * 1 = .54x
The amount of Interest for both ADDS UP to 800; therefore:
.06x + .54x = 800 and
.6x = 800 so
x = 1333.33
That's how much was invested in the account that earned 6% interest annually.
f(x) = 4x^2 – 4x
Find f(-7)
Answer:
f(-7)=224
Step-by-step explanation:
[tex]f(x) = 4x^2 -4x\\f(-7)= 4(-7)^2 - 4(-7)\\= 4(49) -+28\\=196+28\\f(-7) = 224[/tex]
find the sum and choose the correct answer. 2n^3+4n^2-7 and -n^3+8n-9.
A) -n^3-4^2-8n-16
B) n^3+4n^2+8n+16
C) n^3+4n^2+8n-16
D) 3 n^3+4n^4+8n-2
Answer:
C) [tex]n^3+4n^2+8n-16[/tex]
Step-by-step explanation:
[tex]2n^3+4n^2-7+(-n^3)+8n-9=\\n^3+4n^2-7+8n-9=\\n^3+4n^2+8n-9-7=\\n^3+4n^2+8n-16[/tex]
(Just combine like terms)
Only C) [tex]n^3+4n^2+8n-16[/tex] fits our answer.
Answer:
[tex] {n}^{3} + 4 {n}^{2} + 8n - 16[/tex]
Option C is the right option
Solution,
[tex]2 {n}^{3} + 4 {n}^{2} - 7 + ( - {n}^{3} + 8n - 9) \\ = 2 {n}^{3} + 4 {n}^{2} - 7 - {n}^{3} + 8n - 9 \\ [/tex]
combine like terms
[tex]2 {n}^{3} - {n}^{3} + 4 {n}^{2} + 8n - 7 - 9 \\simplify \\ = {n}^{3} + 4 {n}^{2} + 8n - 16[/tex]
hope this helps...
Good luck on your assignment..
9. If y = kx, where k is a constant, and y = -3
when x = 6, what is the value of x when y = 12?
Hey there! :)
Answer:
x = -24.
Step-by-step explanation:
Plug in the values to find the value of 'k':
-3 = k(6)
Divide both sides by 6 to solve for 'k':
-3/6 = k
k = -1/2
Plug this into the equation to solve for the value of x when y= 12:
12 = -1/2(x)
Divide both sides by -1/2:
-24 = x
x = -24.
Answer:
x would be -24
Step-by-step explanation:
since k is a constant, we have to find out what k is from the equation
. -3=6(k) divide both sides by 6 to get that k is -0.5/-1/2.
then, solve for what x is when y is 12 by setting up the equation 12=(-0.5)x. this would result in x being -24
Express 2x²+20x+7 in the form (x+p)²+q
Answer:
f(x) = (x + 5)² - 21.5
Step-by-step explanation:
Step 1: Subtract both sides by 7
2x² + 20x = -7
Step: GCF and divide
2(x² + 10x) = -7
x² + 10x = -7/2
Step 3: Complete the Square
x² + 10x + 25 = -7/2 + 25
(x +5)² = 43/2
Step 4: Subtract 43/2 to both sides
(x + 5)² - 43/2
And we have our equation!
Into how many equal parts can the same cake be cut if the cuts can only be made along the gridlines?
Answer:
I think its 20, hope this helps.
Which real-world transformations can be represented by dilations? Select two options. 1. turning a camera to take a photograph 2. cropping a photograph to a square by cutting only one side 3. reducing a photograph to half its dimensions 4. enlarging a photograph to double the dimensions 5. moving a photograph to a different page
Answer:
3 and 4
Step-by-step explanation:
A dilation is a transformation that produces an image that is the same shape as the original, but is a different size so here reducing a photograph to half its dimensions and enlarging a photograph to double the dimensions is dilation.
=> For dilation, we use a certain scale factor
=> In the 3rd option, scale factor is 1/2
=> In the 4th option, scale factor is 2.
Answer:
Step-by-step explanation:
Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?
Answer:
2nd option.
Step-by-step explanation:
3(8 - 4x) < 6(x - 5)
24 - 12x < 6x - 30
-12x - 6x < -30 - 24
-18x < -54
x > 3
Answer:
2nd graph
Step-by-step explanation:
3(8 – 4x) < 6(x – 5)
Distribute
24 -12x < 6x -30
Add 12x to each side
24-12x+12x < 6x-30+12x
24 < 18x-30
Add 30 to each side
24+30 < 18x-30+30
54 <18x
Divide by 18
54/18 < 18x/18
3<x
Open circle at 3 and line going to the right
Enter the solutions from least to greatest. (x +1)(3x +4)=0 urgent i need help
Answer:
x = - [tex]\frac{4}{3}[/tex], x = - 1
Step-by-step explanation:
Given
(x + 1)(3x + 4) = 0
Equate each factor to zero and solve for x
x + 1 = 0 ⇒ x = - 1
3x + 4 = 0 ⇒ 3x = - 4 ⇒ x = - [tex]\frac{4}{3}[/tex]
Solutions from least to greatest are
x = - [tex]\frac{4}{3}[/tex] , x = - 1
A car made a trip of 352 miles on 16.8 gallons of gasoline. Which is closest to the number of miles per gallon the car got on that trip?
Answer: divide both numbers
Step-by-step explanation:
20.95
There is a line that includes the point (10,3) and has a slope of 1/5 What is its equation in point-slope form?
Answer:
y -3 = 1/5(x-10)
Step-by-step explanation:
The point slope form of the equation of a line is
y-y1 = m(x-x1) where m is the slope and (x1,y1) is a point on the line
y -3 = 1/5(x-10)
Answer:
y - 3 = m(x - 10)
Step-by-step explanation:
The point-slope form is y - k = m(x - h). Here we are told that m = 1/5, h = 10 and k = 3, and therefore we have
y - 3 = m(x - 10)
In 1995, the USPS approximated that they handled
[tex]1.8 \times 10 ^{11} [/tex]
pieces of mail. In 2010, the USPS reported that they handled
[tex]1.7 \times 10 ^{11} [/tex]
pieces. How many more pieces of mail were handled in 1995 than in 2010?
Answer:
[tex]1 \times 10^{10}[/tex] more pieces of mail were handled in 1995 than in 2010.
Step-by-step explanation:
We are given that in 1995, the USPS approximated that they handled [tex]1.8 \times 10^{11}[/tex] pieces of mail and in 2010, the USPS reported that they handled [tex]1.7 \times 10^{11}[/tex] pieces.
To find how many more pieces of mail were handled in 1995 than in 2010, we do subtraction of the pieces of mail that were handled in both the years.
Pieces of mail handled in 1995 = [tex]1.8 \times 10^{11}[/tex]
Pieces of mail handled in 2010 = [tex]1.7 \times 10^{11}[/tex]
As it is clear that more pieces of mail were handled in 1995.
So, Pieces of mail handled in 1995 - Pieces of mail handled in 2010 = [tex](1.8 \times 10^{11}) -(1.7 \times 10^{11})[/tex]
= [tex]10^{11} \times (1.8 -1.7)[/tex]
= [tex]10^{11} \times 0.1[/tex] = [tex]1 \times 10^{10}[/tex]
Hence, [tex]1 \times 10^{10}[/tex] more pieces of mail were handled in 1995 than in 2010.
You invest $700 in an account that pays an interest rate of 6.5% compounded continuously calculate the balance of your account after 20 years round your answer to the nearest hundred
Answer:
$2466.55
Step-by-step explanation:
We use the formula for Compound Amount, the amount gotten after a particular time, to find the balance:
[tex]A = P(1 + r)^t[/tex]
where P = Principal = $700
r = rate = 6.5% = 0.065
t = time elapsed 20 years
Therefore:
[tex]A = 700(1 + 0.065)^{20}\\\\A = 700(1.065)^{20}\\[/tex]
A = $2466.55
The balance of the account will be $2466.55
Find the volume of this square
based pyramid.
10 in
12 in
[ ? ]
Answer:
480 in.^3
Step-by-step explanation:
volume of pyramid = (1/3) * (area of base) * height
Since this pyramid has a square for the base, the area of the base is
A = s^2, where s = length of the side of the square
volume = (1/3) * s^2 * h
volume = (1/3)(12 in.)^2 * (10 in.)
volume = (1/3)(144)(10) in.^3
volume = 480 in.^3
The volume of the square-based pyramid is 480 cubic inches as per the concept of the pyramid.
To find the volume of a square-based pyramid, we can use the formula:
Volume = (1/3) x base area x height.
In this case, the base of the pyramid is a square with a side length of 12 inches, and the height of the pyramid is 10 inches.
First, we calculate the base area of the pyramid, which is the area of the square base:
Base area = side length x side length
= 12 in x 12 in
= 144 square inches.
Now, we can substitute the values into the volume formula:
[tex]Volume = \frac{1}{3} \times 144 \times 10[/tex].
Multiplying these values, we get:
[tex]Volume = \frac{1}{3} \times1440 {in}^3[/tex]
Simplifying the expression, we have:
[tex]Volume = 480\ in^3[/tex].
To learn more about the pyramid;
https://brainly.com/question/17615619
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If x = 1 is a common root of ax² +ax + 2 = 0 and x² + x + b = 0 , then ab =
Answer:
ab = 2
Step-by-step explanation:
Given equations
ax² +ax + 2 = 0
x² + x + b = 0
root of both the equation
x= 1
then we can plug in x = 1 in both the equation
ax² +ax + 2 = 0 x² + x + b = 0
a*1² +a*1 + 2 = 0 1² + 1 + b = 0
a +a + 2 = 0 1 + 1 + b = 0
2a + 2 = 0 2 + b = 0
2a = - 2 b = -2
a = -2/2 = -1
Thus,
a = -1
b = -2
a*b = -1*-2 = 2
ab = 2
MY LAST 2 QUESTION WILL FOREVER BE GRATEFUL PLS HELP WILL GIVE BRANLIEST!! AT LEAST TAKE A LOOK!!!! PLS I AM BEGGING!!!
1. Which statement can be made based on the diagram below? IMAGE BELOW
A) m∠1 + m∠2 = 180
B) m∠2 + m∠3 = 180
C) ∠2= ∠3
D) ∠3=∠4
4. What is the difference between a formal and informal proof?
A) A formal proof provides the reasons for steps, whereas an informal proof does not.
B) A formal proof uses a table or a list of steps, whereas an informal proof uses paragraphs.
C) A formal proof is much shorter, whereas an informal proof is longer.
D) A formal proof uses equations, whereas an informal proof only uses text.
Which inequality is represented by this graph?
Answer:
C. y < -1/5x + 1
Step-by-step explanation:
We can eliminate A and B because the inequality sign is incorrect. If we were to graph those, the shaded area would be above the line, not below. We are left with C and D. Notice in our given graph that the line is dotted, so solution on the line are not included. So our answer would be C. because the inequality sign is y is less than and not y is less than or equal to.
How many unique triangles can be made where one angle measures 98° and another angle is an obtuse angle?
A.) 1
B.) 2
C.) More than 2
D.) None
None thats impossible. think about it
98+90= 180
its too high
no triangle
Answer:
None
Step-by-step explanation:
An obtuse angle means that the angle is larger than 90 degrees. Since the total interior angle measures in a triangle must add up to 180 degrees, you cannot have 2 angles more than 90 degrees. Hope this helps!
Circumference of circles
Answer:
Circumference = 6.28Step-by-step explanation:
[tex]C =2\pi*r\\r = 1\\\pi = 3.14\\C = 2 *3.14*1\\C = 6.28[/tex]
Owen’s grandmother put some money into his savings account on the day he was born. Today, Owen turns 18 years old, and he’s discovered that he has earned $225 in simple interest on his grandmother’s money. If the yearly interest rate was 5%, how much money did his grandmother deposit at the time of his birth?
Answer:
Step-by-step explanation:
The formula for simple interest is prt = I, where p is the initial investment (our unknown in this case), r is the interest rate in decimal form, t is the time in years, and I is the interest earned. That is NOT the same as the amount of money in the account t years later.
For us,
p = ??,
r = .05,
t = 18, and
I = 225.
Filling in:
p(.05)(18) = 225 and
.9p = 225 so
p = 250
Answer:
The answer is $250.
Step-by-step explanation:
First, the money that his grandmother deposited is called the principal, P. Substitute the given values into the formula, interest equals principal times rate times time, and solve for P. Here, I is 225 dollars and t is 18 years.
Next, the percent given represents the interest rate, r, but first it must be changed to a decimal. To change it, move the decimal point 2 places to the left.
Now, multiply point 0, 5, and 18 to simplify the right side of the equation. The product is point nine.
Finally, divide both sides of the equation by .9 . The result is P equals $225 The principal, or original deposit, is $250.
What is the multiplicative rate of change of the exponential function shown on the graph? Two-ninths 1 4 Nine-halves
Answer:
The answer is nine-halves, the last option.
Answer:
The answer will be nine-halves.
Step-by-step explanation:
pls anybody Answer me.
I will mark as BRAIN LIST. pls.
Answer:
(i) 12.25
(ii) 12.25.
Step-by-step explanation:
(1) cot^2 O = (7/2)^2 = 49/4
= 12.25.
(2) (1 - sin O) ( 1 + sin O) 1 - sin^2 O cos^2 O
---------------------------- = ------------- = --------------
(1 - cos O)(1 + cos O) 1 - cos^2 O 1 - cos^2 O
As cot O = 2/7, tan O = 1 /2/7 = 7/2.
Hypotenuse of the right triangle = √( 2^2 + 7^2)
= √53
So cos O = 7/√53
Therefore the original function = cos^2 O / (1 - cos^2 O)
= (7/√53)^2 / (1 - (7/√53)^2 )
= 49/53 / 4/53
= 49/4.
Please help I am in need
Answer:
Step-by-step explanation:
Locate the 1 on the x axis. This is one hour worked. Go up vertically along x = 1 and you "land" on the red line very quickly. If you go straight across to the left, you are at 14 on the y-axis. The y-axis indicates the amount of money Leo earns tutoring. If he works one hour and earns $14 and this is a straight line (linear function with a constant slope), that means that for every hour he works he will earn $14. Locate the 2 on the x-axis and go up x = 2 til you hit the red line. Read it to the left and you "land" on the y-axis at $28. $28 divided by 2 hours of work is $14 per hour of tutoring. The first choice is the one you want.
Which store offers the lowest unit rate for lettuce in dollars per pound?
I need help please. Ill mark u as whatever u want. Urgent
Answer:
70
Step-by-step explanation:
180-45-65
pls mark me brainliest i really need it
Can someone help me solve this 15 points
Answer:
see explanation
Step-by-step explanation:
∠ 1 and ∠ 2 are adjacent angles and supplementary, thus
∠ 2 = 180° - ∠ 1 = 180° - 110° = 70°
--------------------------------------------------
The chord- chord angle 3 is half the sum of the measures of the arcs intercepted by the angle and its vertical angle, thus
∠ 3 = [tex]\frac{1}{2}[/tex] (100 + 60)° = 0.5 × 160° = 80°
∠ 3 and ∠ 4 are adjacent angles and supplementary, thus
∠ 4 = 180° - 80° = 100°
Thus
Angle Value
1 110
2 70
3 80
4 100
What is 0.5 as a fraction in simplest form
Answer:
1/2
Step-by-step explanation:
Answer:
1/2
Step-by-step explanation:
0.5 is said as "five-tenths". This is because it is one place after the decimal. It would then become five-tenths, written as: 510. You would then simplify the fraction: 510=12
// have a great day //
250 + 200h = 300 + 180h 250 + 200h = 300 + 180h − 180h − 180h 250 + 20h = 300 h = credit hours
Answer:
h=5/2
Step-by-step explanation:
200h=180h+50
20h=50