Answers
ANSWER
[tex]h= 2 \cos(\pi(t + \frac{1}{2} )) + 5[/tex]
EXPLANATION
The given equation that models the height is
[tex]h(x) = - 2 \sin(\pi(t + \frac{1}{2} )) + 5[/tex]
This is sine a sine function that is reflected in the x-axis.
This function will coincide with the cosine function with the same amplitude, period, phase shift and vertical translation.
The function that can also model this height is
[tex]h= 2 \cos(\pi(t + \frac{1}{2} )) + 5[/tex]
The last choice is correct.
Related Questions
Question 4
Use the figure below to find the value of x and y
Answers
Answer:
[tex]x=4, y=8[/tex]
Step-by-step explanation:
step 1
Find the value of y
we know that
In the right triangle of the figure
[tex]cos(30\°)=\frac{4\sqrt{3}}{y}[/tex]
Remember that
[tex]cos(30\°)=\frac{\sqrt{3}}{2}[/tex]
so
[tex]\frac{\sqrt{3}}{2}=\frac{4\sqrt{3}}{y}[/tex]
Simplify
[tex]y=8\ units[/tex]
step 2
Find the value of x
In the right triangle of the figure
[tex]sin(30\°)=\frac{x}{8}[/tex]
Remember that
[tex]sin(30\°)=\frac{1}{2}[/tex]
so
[tex]\frac{1}{2}=\frac{x}{8}[/tex]
[tex]x=4\ units[/tex]
Lorena and Sebastian are both five years old. Every year they each get a cash present from their ncighbor.
Sebastian gets $1.50 for every year in his age, and Lorena gets $20. How old
will they be when Sebastian gets more money than Lorena
Answers
14, she will be 14 when she has more
Answer:
sebastian will be 14 when he gets more money than lorena
Whats is the equation of the following line?
Answers
D. Y= - 4/3 x Rise over run
The equation of the line is:
C. [tex]y=\dfrac{-3}{4}x[/tex]
Step-by-step explanation:The line passes through the point (0,0) and (4,-3).
By using the two point formula to find the equation of the line.
i.e. any line passing through two points (a,b) and (c,d) is calculated by using the formula:
[tex]y-b=\dfrac{d-b}{c-a}\times (x-a)[/tex]
Here (a,b)=(0,0) and (c,d)=(4,-3)
Hence, the equation of line is calculated as follows:
[tex]y-0=\dfrac{-3-0}{4-0}\times (x-0)\\\\i.e.\\\\y=\dfrac{-3}{4}\times x\\\\i.e.\\\\y=\dfrac{-3}{4}x[/tex]
Hence, the correct answer is: Option: C
Bert is planning to open a savings account that earns 1.6% simple interest yearly. He wants to earn exactly $192 in interest after 2 years. How much money should be deposit?
Answers:
A: $6,000
B: $600
C: $60
D: $3,072
Answers
B is correct. Hope I helped yah.
Which expression is equivalent to the algebraic expression below?
3(–2x – 1)
a x – 1
b –6x – 3
c x + 2
d –6x – 1
Answers
Answer:
b) -6x - 3
Step-by-step explanation:
3(-2x-1)=3*(-2x)+3*(-1)= -6x - 3
B. -6x - 3
Distribute the 3, or multiply it by everything in the parentheses.
You multiply 3 times -2x to get -6x, and you multiply 3 times -1 to get -3.
Put these together to get -6x-3.
Use the properties of logarithms to expand log(zy8).
(By 8, they mean the exponent of 8, or the eighth power.)
Each logarithm should involve only one variable and should not have any exponents. Assume that all variables are positive.
Answers
Answer:
log (y)+ 8 log (z)
Step-by-step explanation:
use the rules of logarithm
The expanded form of the given function is log (x)+ 8 log (y).
What is a logarithm?When you raise a number with an exponent, there comes a result.
Let's say you get
a^b = c
Then, you can write 'b' in terms of 'a' and 'c' using a logarithm as follows
[tex]b = \log_a(c)[/tex]
'a' is called base of this log function. We say that 'b' is the logarithm of 'c' to base 'a'
Given;
[tex]log(xy^8)[/tex]
use the rules of the logarithm;
log (x)+ 8 log (y)
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Louise completed the work shown below.
(5x3 + 3)2 = (5x3)2 + (3)2 = 25x6 + 9
Determine if Louise’s answer is correct. Explain.
Sample Response: Louise’s answer is not correct. She is missing the term 30x3. When squaring a binomial, it is best to write the product of the binomial times itself. Then you can use the distributive property to multiply each term in the first binomial by each term in the second binomial. Louise also could have used the formula for a perfect square trinomial, which is found by squaring a binomial.
Answers
Answer:
Louise is missing the term [tex]30x^3[/tex]
Step-by-step explanation:
Remember that the formula for squaring a binomial is:
[tex](a+b)^2=a^2+2ab+b^2[/tex]
Where
[tex]a[/tex] is the first term of the binomial
[tex]b[/tex] is the second term of the binomial
Our binomial is [tex](5x^3+3)^2[/tex], so [tex]a=5x^3[/tex] and [tex]b=3[/tex].
Replacing values
[tex](5x^3+3)^2=(5x^3)^2+2(5x^3)(3)+3^2[/tex]
[tex](5x^3+3)^2=5^2x^6+6(5x^3)+9[/tex]
[tex](5x^3+3)^2=25x^6+30x^3+9[/tex]
Since Louise’s answer is [tex](5x^3+3)^2=25x^6+9[/tex], we can conclude that she is missing the term [tex]30x^3[/tex]
Answer:
Louise’s answer is not correct. She is missing the term 30x3. When squaring a binomial, it is best to write the product of the binomial times itself. Then you can use the distributive property to multiply each term in the first binomial by each term in the second binomial. Louise also could have used the formula for a perfect square trinomial, which is found by squaring a binomial.
Step-by-step explanation:
In a bus there is, A pregnant lady 24 years old A security guard 37 years old A random woman 56 years old Driver 68 years old Who is the youngest?
Answers
Answer:
The baby
Step-by-step explanation:
If you count the baby inside the pregnant woman, then he is the youngest.
hahha funny the baby of course
I need help to solve this question.
Answers
Answer:
B
Step-by-step explanation:
2y-9x= 14 what’s y??
Answers
Answer:
the answer is y= 9/2 x+7
Did you mean the interception or solve for? Anyway I'll do both.
Solve for y:
[tex]
2y-9x=14\Longrightarrow 2y=14+9x \\
2y=14+9x\Longrightarrow y=\frac{14+9x}{2} \\ \boxed{y=7+\frac{9x}{2}, x\in\mathbb{R}}
[/tex]
Intercept: [tex]2y-9x=14\Longrightarrow2y=14\Longrightarrow y=7[/tex]
Solve for t.
-5 − 2t = 3t
Answers
First, we have to isolate the t, or keep it by itself, to solve. To do that, we need to move everything with t in it to on side.
-5 - 2t + 2t = 3t + 2t
The -2t and + 2t cross out, leaving us with t on one side, which is exactly what we want!
-5 = 5t
But t isn't alone yet. We need to get rid of its five. To do that, we need to use the same process: use the opposite symbol. In 5t, 5 is being multiplied by t. To get rid of, we need to divide 5. BUT the mega rule in algebra... what you do to one side you must do to the other, or else the equation would not be true anymore, so...
-5/5 = 5t/5
-1 = t
There's your answer! Hope this helps!
Derek's collection: 1950, 1952, 1908, 1902, 1955, 1954, 1901, 1910
Paul's collection: 1929, 1935, 1928, 1930, 1925, 1932, 1933, 1920
Find the indicated measures of center and the measures of variation for each data set. Round your answer to the nearest hundredth, if necessary.
Find the mean, median, range, IQR, MAD for Derek's collection and Paul's collection.
Answers
Answer:
Derek:
Mean:1929
Median: 1930
range: 54
IQR: 48
MAD: 23.75
Paul:
Mean: 1929
Median: 1929.5
range: 15
IQR: 6
MAD: 3.5
Step-by-step explanation:
For the Derek's collection:
1. Mean = 1930.375
2. Median = 1930
For the Paul's collection:
1. Mean = 1929.75
2. Median = 1931
For Derek's collection:
Mean:
Add up all the numbers and divide by the total number of numbers:
Mean = (1950 + 1952 + 1908 + 1902 + 1955 + 1954 + 1901 + 1910) / 8
= 1930.375
Median:
The median is the middle value of the set, so we first need to put the numbers in order:
1901, 1902, 1908, 1910, 1950, 1952, 1954, 1955
The median is the average of the middle two numbers, which are 1910 and 1950:
Median = (1910 + 1950) / 2
= 1930
For Paul's collection:
Mean:
Add up all the numbers and divide by the total number of numbers:
Mean = (1929 + 1935 + 1928 + 1930 + 1925 + 1932 + 1933 + 1920) / 8
= 1929.75
Median:
The median is the middle value of the set, so we first need to put the numbers in order:
1920, 1925, 1928, 1929, 1930, 1932, 1933, 1935
The median is the average of the middle two numbers, which are 1930 and 1932:
Median = (1930 + 1932) / 2
= 1931
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A gas at 89°C occupies a volume of 0.67 L. At what Celsius temperature will the volume increase to 1.12 L?
Answers
Answer:
V1 / T1 = V2 / T2
0.67 / (273 + 89) = 1.12 / (273 + t )
t = 332 °C
Given values:
Volume,
[tex]V_1 = 0.67 \ L[/tex][tex]V_2 = 1.12 \ L[/tex]Temperature,
[tex]T_1 = 89^{\circ} C \ or \ 362 \ K[/tex][tex]T_2 = \ ?[/tex]We know the relation,
→ [tex]\frac{V_1}{T_1} = \frac{V_2}{T_2}[/tex]
By substituting the values, we get
→ [tex]\frac{0.67}{362} = \frac{1.12}{T_2}[/tex]
→ [tex]T_2 = \frac{1.12\times 362}{0.67}[/tex]
[tex]= 332^{\circ} C[/tex]
Thus the answer above is right.
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how do i turn 1 and 1 fith in a decimal
Answers
Answer:
The answer is 1.2
Step-by-step explanation:
1/5 it basicly stands for 1 ÷ 5
1 ÷ 5 = 0.2
plus the one you already have
1 + 0.2 = 1.2
1.2
Hope this helped!
~Lunar Rose. Moon
Answer:
1.2
Step-by-step explanation:
Take 1/5, or make it larger into 2/10 and divide those.
2/10 is obviously .2, while 1/5 is also .2.
now take the .2+ the 1 we had and you get 1.2
A house worth $70,000 when purchased was worth $67,000 after the first year and $64,000 after the second year. If the economy does not improve and this trend continues, what will be the value of the house after 7 years? a) Write an explicit formula for the sequence. Explain where you found the numbers you are putting in the formula. b) Identify the value of n and explain where you found it. Use the explicit formula to solve the problem.
Answers
Answer:
a) The formula for the sequence is
[tex]a_n = 67,000 -3,000(n-1)[/tex]
b) [tex]a_7 = 49,000[/tex]
Step-by-step explanation:
Note that the difference between any two consecutive terms in the sequence is always equal to $3,000
[tex]67,000-70,000= -3,000\\\\64,000-67,000=-3,000[/tex]
Then we have an arithmetic sequence where each term increases by a magnitude of 3,000 with respect to the previous term.
The explicit formula for an arithmetic sequence is:
[tex]a_n = a_1 +d(n-1)[/tex]
Where d is the common difference between the consecutive terms of the sequence
[tex]d = -3,000[/tex]
[tex]a_1[/tex] is the first term, or the value of the house after year 1 [tex]a_1= 67,000[/tex]
n represents the number of years since the house was purchased
With
n={0, 1, 2, 3, 4, 5, 6, 7,.., n}
a) Then the formula for the sequence is
[tex]a_n = 67,000 -3,000(n-1)[/tex]
With
n={0, 1, 2, 3, 4, 5, 6, 7,.., n}
---------------------------------------------------------------------------------------------
b) Now we can use the formula to find the price of the house after 7 years
[tex]a_7 = 67,000 -3,000(7-1)[/tex]
[tex]a_7 = 67,000 -3,000(6)[/tex]
[tex]a_7 = 49,000[/tex]
Write the equation of the circle shown here.
Answers
Answer:
(x − 7)² + (y + 2)² = 52
Step-by-step explanation:
The equation of a circle is:
(x − h)² + (y − k)² = r²
where (h, k) is the center and r is the radius.
We know that (h, k) = (7, -2). But we need to find the radius. To do that, find the distance from the center to a point on the edge:
r² = (x₁ − x₂)² + (y₁ − y₂)²
r² = (7 − 1)² + (-2 − -6)²
r² = 6² + 4²
r² = 36 + 16
r² = 52
So the equation of the circle is:
(x − 7)² + (y + 2)² = 52
The equation of the circle is (x-2)^2 + (y-(-3))^2 = 5^2.
Explanation:To write the equation of a circle, we need to know the center and the radius of the circle. We can see from the diagram that the center of the circle is the point (2, -3), and the radius is 5 units.
The equation of a circle is given by the formula (x-h)^2 + (y-k)^2 = r^2,
where (h, k) is the center and r is the radius. Therefore, the equation of the circle is (x-2)^2 + (y-(-3))^2 = 5^2.
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In the diagram, rectangle ABCD is split in half by AC. What is the value of tan x?
A) 3/4
B) 4/5
C) 3/5
D) 5/4
E) 4/3
Random answers will be reported!
Answers
Answer:
Then tan(x) = 4/3
Step-by-step explanation:
Given that we have a rectangle ABCD, we can affirm the following:
AD = BC = 4
AB = DC = 3
Now, we now that tan = Opposite Side / Adjacent Side
Then the opposite side to the angle x is AB = 4, and the adjacent side to angle x is DC = 3.
Then tan(x) = Opposite Side / Adjacent Side = 4/3 = 1,3333.
Answer: E
Step-by-step explanation:
Solve for n. n + 1 = 4(n – 8) n = 1 n = 8 n = 11 n = 16
Answers
Answer:
The correct option is C) n= 11.
Step-by-step explanation:
Consider the provided equation.
[tex]n+1=4(n-8)[/tex]
Open the parentheses and apply the distributive property as shown:
Distributive property [tex]a(b+c)=ab+ac[/tex]
[tex]n+1=4n-32[/tex]
Now, isolate the variables by adding 32 and subtracting n on both the sides.
[tex]n+1-n+32=4n-32-n+32[/tex]
[tex]33=3n[/tex]
Now divide both the sides by 3.
[tex]\frac{33}{3}=\frac{3n}{3}[/tex]
[tex]11=n[/tex]
Hence the value of n is 11
Thus, the correct option is C) n= 11.
Answer: n=11 just took in on Engenuity
Step-by-step explanation:
50 POINTS! HELP! A restaurant manager is planning a new layout for the tables in his store. He will be placing tables of 2, tables of 4, and tables of 6 throughout the dining room. To help him decide how many of each he needs, he decides to keep track of all table requests by customers during a 2-week period. Which measure of central tendency would BEST indicate the typical table size needed?
A) mean
B) median
C) mode
D) range
Answers
Answer:
The best possible answer for this would be: D. Mode.
This is because mode measures how many times each number appears.
Answer:
mine said c is the correct answer
Step-by-step explanation:
A cake is shaped like a cylinder with a diameter of 9 in. The height of the cake is 6 in.
What is the exact volume of the cake?
Enter your answer in the box.
pi in^3
Answers
Answer: 121.5 pi in^3 or 381.7 in^3
Step-by-step explanation:
Volume of a cylinder = pi r^2(h)
Radius = 4.5 in, Height = 6 in
pi (4.5)^2(6)
pi(20.25)(6)
121.5 pi in^3 or 381.7 in^3
The exact volume of a cylindrical cake with a diameter of 9 inches and a height of 6 inches is 121.5π cubic inches.
The volume of a cylinder can be found using the formula V = πr^2h, where V stands for volume, r is the radius of the base of the cylinder, and h is the height of the cylinder. Given the diameter of the cake is 9 inches, the radius is half of that, which is 4.5 inches. Therefore, the exact volume of the cake is calculated as follows:
V = π × (4.5 )² ×2 × 6
Which simplifies to:
V = π × 20.25 ×2 × 6
So, the exact volume of the cake is:
V = 121.5π in^3
You rent a bicycle for $20 plus $2 per hour
Answers
Answer:
It all depends on how long you have the bike for if you have it for only 1 hour it will be $22 dollars. If you have it for 2 hours it will be $24 dollars.
What is the measure of each angel of a rectangle ?
Answers
Answer:
All 4 four angles of the rectangle are 90°
Answer:
Opposite sides of a rectangle are the same length (congruent). The angles of a rectangle are all congruent (the same size and measure.) Remember that a 90 degree angle is called a "right angle." So, a rectangle has four right angles.
four- 90 degrees
I need help please.
Answers
Answer:
No
Step-by-step explanation:
No it is not the correct answer.
The square of the sum of two consecutive positive even integers is 4048 more than the sum of the squares of these two numbers. Find the two numbers.
Answers
Answer:
The numbers are 44 and 46
Step-by-step explanation:
Let
x, x+2 ----> the two consecutive positive even integers
we know that
[tex](x+x+2)^{2} =4,048+x^{2} +(x+2)^{2} \\ \\(2x+2)^{2} =4,048+x^{2} +x^{2}+4x+4\\ \\4x^{2}+8x+4=2x^{2}+4x+4,052\\ \\2x^{2} +4x-4,048=0[/tex]
Solve the quadratic equation using a graphing calculator
The solution is x=44
see the attached figure
[tex]x+2=44+2=46[/tex]
therefore
The numbers are 44 and 46
factor completely x^3 + 1/8
Answers
Answer:
((2 x + 1) (4 x^2 - 2 x + 1))/8
Step-by-step explanation:
Factor the following:
x^3 + 1/8
Put each term in x^3 + 1/8 over the common denominator 8: x^3 + 1/8 = (8 x^3)/8 + 1/8:
(8 x^3)/8 + 1/8
(8 x^3)/8 + 1/8 = (8 x^3 + 1)/8:
(8 x^3 + 1)/8
8 x^3 + 1 = (2 x)^3 + 1^3:
((2 x)^3 + 1^3)/8
Factor the sum of two cubes. (2 x)^3 + 1^3 = (2 x + 1) ((2 x)^2 - 2 x + 1^2):
((2 x + 1) ((2 x)^2 - 2 x + 1^2))/8
1^2 = 1:
((2 x + 1) ((2 x)^2 - 2 x + 1))/8
Multiply each exponent in 2 x by 2:
((2 x + 1) (2^2 x^2 - 2 x + 1))/8
2^2 = 4:
Answer: ((2 x + 1) (4 x^2 - 2 x + 1))/8
[tex]x^3+\dfrac{1}{8}=\\ \\ =x^3+2^{-3} = \\ \\ =x^3+(2^{-1})^3 =\\ \\ = (x+2^{-1})(x^2-2^{-1}x+2^{-2}) = \\ \\ = \Big(x+\dfrac{1}{2}\Big)\Big(x^2-\dfrac{x}{2}+\dfrac{1}{4}\Big)\\ \\ \\ \boxed{a^3+b^3 = (a+b)(a^2-ab+b^2)}[/tex]
A rectangular safe can hold 5184 cubic inches. Gold bars that are 3 inches by 6 inches by 2 inches fit to completely fill the safe. What is the maximum number of girl bars that will fit in the safe? 36 288 144 72
Answers
Answer:
144 gold bars
Step-by-step explanation:
first you fine the area gold bars take up in cubic inches by multiplying the 3, 2, and 6 to get 36
once you have the space 1 gold bar takes up you divide the total space by that the total space is 5184 so you divide 5184 by 36 to get 144
Answer:
c. 144
Step-by-step explanation:
:)
4x+24=5x+1 what pus it really need answer
Answers
Subtract 4x from both sides
24 = 5x + 1 - 4x
Simplify 5x + 1 - 4x to x + 1
24 = x + 1
Subtract 1 from both sides
24 - 1 = x
Simplify 24 - 1 to 23
23 = x
Switch sides
x = 23
Answer:
Step-by-step explanation:
Subtract 4x from both sides
24 = 5x + 1 - 4x
Simplify 5x + 1 - 4x to x + 1
24 = x + 1
Subtract 1 from both sides
24 - 1 = x
Simplify 24 - 1 to 23
23 = x
Switch sides
x = 23
PLEASE ANSWERRRRRRR! THANKS!!!!!!!!!!!!!!!!!!!!!!
Solve for x.
57 = 3x + 12
Answers
57-12= 3x+12-12
45=3x
Divide by 3
x=15
Check answer
57= 3(15)+12
57=57
Answer is correct.
x= 15
a building casts a shadow that is 348 meters long at the same time a person who is 2 meters tall casts a shadow that is 6 meters long how tall is the building A.) 1044m B.) 116m C.) 64 m D) 100n
Answers
Answer:
Option B. [tex]116\ m[/tex]
Step-by-step explanation:
Let
x------> the height of the building
we know that
using proportion
[tex]\frac{2}{6}=\frac{x}{348} \\ \\x=348*2/6\\ \\x=116\ m[/tex]
Simplify 2x+x+x+2y x 3y x y
Answers
Answer:
3x+6y^3
Step-by-step explanation:
-First you add all the Xs
2x+x+x
-Then you multiply all the Ys
2y * 3y * y
* the Y has a 1 as an exponent by multiplying the Ys the exponents are added making the Y a Y^3
*the numbers are multiplied making it a 6
Together it forms 6y^3
-Ys and Xs cannot be added because they are different values so your answer would be 3x+ 6y^3
The simplification of the given algebraic expression 2x+x+x+(2y × 3y × y) is 4x + 6y³.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The simplification of 2x+x+x+(2y × 3y × y) can be done as,
2x + x + x + (2y × 3y × y)
= 4x + (2y × 3y × y)
= 4x + 6y³
Hence, the simplification of the given algebraic expression 2x+x+x+(2y × 3y × y) is 4x + 6y³.
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