Answer:
[tex]D.\ y = 3\sin(2(x + \frac{\pi}{4}))[/tex]
Step-by-step explanation:
Given
[tex]A = 3[/tex] --- Amplitude
[tex]C = \frac{\pi}{4}[/tex] --- Right phase shift
Required
Identify the function
A sinusoidal function is defined as:
[tex]y = A\sin(B(x + C)) + D[/tex]
Substitute values for A and C
[tex]y = 3\sin(B(x + \frac{\pi}{4})) + D[/tex]
By comparison, only option (D) has the above format where
[tex]y = 3\sin(2(x + \frac{\pi}{4}))[/tex]
Hence (D) is correct
The radius of a right circular cone is increasing at a rate of 1.1 in/s while its height is decreasing at a rate of 2.6 in/s. At what rate is the volume of the cone changing when the radius is 107 in. and the height is 151 in.
Answer:
The volume of the cone is increasing at a rate of 1926 cubic inches per second.
Step-by-step explanation:
Volume of a right circular cone:
The volume of a right circular cone, with radius r and height h, is given by the following formula:
[tex]V = \frac{1}{3} \pi r^2h[/tex]
Implicit derivation:
To solve this question, we have to apply implicit derivation, derivating the variables V, r and h with regard to t. So
[tex]\frac{dV}{dt} = \frac{1}{3}\left(2rh\frac{dr}{dt} + r^2\frac{dh}{dt}\right)[/tex]
Radius is 107 in. and the height is 151 in.
This means that [tex]r = 107, h = 151[/tex]
The radius of a right circular cone is increasing at a rate of 1.1 in/s while its height is decreasing at a rate of 2.6 in/s.
This means that [tex]\frac{dr}{dt} = 1.1, \frac{dh}{dt} = -2.6[/tex]
At what rate is the volume of the cone changing when the radius is 107 in. and the height is 151 in.
This is [tex]\frac{dV}{dt}[/tex]. So
[tex]\frac{dV}{dt} = \frac{1}{3}\left(2rh\frac{dr}{dt} + r^2\frac{dh}{dt}\right)[/tex]
[tex]\frac{dV}{dt} = \frac{1}{3}(2(107)(151)(1.1) + (107)^2(-2.6))[/tex]
[tex]\frac{dV}{dt} = \frac{2(107)(151)(1.1) - (107)^2(2.6)}{3}[/tex]
[tex]\frac{dV}{dt} = 1926[/tex]
Positive, so increasing.
The volume of the cone is increasing at a rate of 1926 cubic inches per second.
Help please I asp !!!
Answer:
Step-by-step explanation:
1
Plot 1 4/5 and 2 3/10
Answer:
You could change 1 4/5 to 1 8/10 to make it easier to plot.
Xavier shoots a basketball in which the height, in feet, is modeled by the equation,h(t) = -4t2 + 10 + 18, where t is time, in
seconds. What is the maximum height of the basketball?
Answer:
The maximum height of the basketball is of 24.25 feet.
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
[tex]f(x) = ax^{2} + bx + c[/tex]
It's vertex is the point [tex](x_{v}, y_{v})[/tex]
In which
[tex]x_{v} = -\frac{b}{2a}[/tex]
[tex]y_{v} = -\frac{\Delta}{4a}[/tex]
Where
[tex]\Delta = b^2-4ac[/tex]
If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].
Height of the basketball:
Given by the following function:
[tex]h(t) = -4t^2 + 10t + 18[/tex]
Which is a quadratic function with [tex]a = -4, b = 10, c = 18[/tex]
What is the maximum height of the basketball?
y(in this case h) of the vertex. So
[tex]\Delta = b^2-4ac = 10^2 - 4(-4)(18) = 388[/tex]
[tex]y_{v} = -\frac{388}{4(-4)} = 24.25[/tex]
The maximum height of the basketball is of 24.25 feet.
Help please!!! I don’t understand this question
Answer:
C
Step-by-step explanation:
Let us first write an equation. Using the SOHCAHTOA rule, we should know that the tangent of an angle equals it's [tex]\frac{opposite}{adjacent}[/tex]. The opposite of our given 20° angle is 9, and the adjacent side is x.
[tex]tan(20[/tex]°[tex])=\frac{9}{x}[/tex]
[tex]0.364=\frac{9}{x} \\x=\frac{9}{0.364}\\x=24.7[/tex]
C
I hope this helps! Let me know if you have any questions :)
Which expression is equivalent to 6/g^5 , if g >0
Answer:
The choose (D)
[tex] {g }^{ \frac{5}{6} } [/tex]
The expression equivalent to [tex]\sqrt[6]({g}^{5})[/tex] is [tex]g^{\frac{5}{6} }[/tex].
What is an exponent?The number of times a number has been multiplied by itself is referred to as an exponent. It could be an integer, a fraction, a negative integer, or a decimal. Powers or indices are other names for exponents. For instance, 6⁵ indicates that we are multiplying 6 by five. It is 6 × 6 × 6 × 6 × 6 in its expanded form.
How to solve this problem?The expression is [tex]\sqrt[6]({g}^{5})[/tex].
[tex]\sqrt[6]{g}[/tex] can be written as [tex]g^{\frac{1}{6} }[/tex].
Then the given expression can be written as [tex]g^{\frac{5}{6} }[/tex].
Therefore, the expression equivalent to [tex]\sqrt[6]({g}^{5})[/tex], g > 0 is [tex]g^{\frac{5}{6} }[/tex]. So, option D is correct.
Learn more about exponents here -
https://brainly.com/question/27850853
#SPJ2
Emile has calculated a one-tailed z-statistic of -1.97 and wants to see if it is significant at the 5% significance level.
What is the critical value for the 5% significance level? Answer choices are rounded to the hundredths place.
Answer:
Z = -1.65
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
What is the critical value for the 5% significance level?
One-tailed statistic, so Z with a p-value of 0.05.
Looking at the z-table, this is Z = -1.65, so this is the critical value for the 5% significance leve.
The table shows ordered pairs of the function y=8-2 x . What is the value of y when x=8 ?
The table shows ordered pairs of the function y=8-2 x . What is the value of y when x=8 ?
Solution:-The given value of x is 8.
we have to find the value of 'y' , so,
▶️ y = 8-2 x
▶️ y = 8-2 × 8
▶️ y = 8-16
▶️ y = -8
Answer:-The value of y is -8.
[tex] \\ \\ [/tex]
Please help! 15 points!
Suppose the sample space for a continuous random variable is 0 to 200. If the area under the density graph for the variable from 0 to 50 is 0.25, then the area under the density graph from 50 to 200 is also 0.25. O A. True B. False SUBMIT
Answer:
I guess it's False...Hope it helps you.
Answer:
true
Step-by-step explanation:
Bill makes $240 per hour for a standard 40 hour work week. He earns time- and - a - half for every overtime hour he works. Bill earned a total of$11,400 in one week,how many overtime hours did her work?
Answer:
5 overtime hours
Step-by-step explanation:
Given that :
Pay per hour = 240
Overtime pay = 1 1/2 * pay per hour = 1 1/2 * 240 = 360 per hour
Amount earned for the week = 11400
Let overtime hours = x
Total hours worked = 40 + x
Earning for the week based on hours worked :
240(40) + 360x = 11400
9600 + 360x = 11400
360x = 1800
x = 1800 / 360
x = 5 hours
Solve a,b,c,d and e.
Answer:
Step-by-step explanation:
a)
428721
Place of 2's 10s and 10,000s
Therefore its value is 20 and 20,000
Product of the place value = 20 x 20,000 = 4,00,000
b)
37,20,861
Place of 7 is 1,00,000
Therefore the place value is 7,00,000
c)
Greatest 7 digit number is 99,99,999
Adding 1 to it = 99,99,999 + 1 = 1,00,00,000
d)
85642 = 80000 + 5000 + 600 + 40 +2
e)
round off 85642 to nearest thousand = 86,000
Given that X = {April, August}, then ξ = {months that begin with the letter A}. True or False?
Answer:
False
Step-by-step explanation:
The cylinder has a radius of 5 feet and height of 20 feet. What is the volume of the cylinder in cubic feet?
Answer:
Well the volume is 1570.8 cubed. but i don't know what it would be in your range of answers.
Step-by-step explanation:
9.
slove this question
Answer:
[tex]\sqrt{x^2 + y^2}[/tex]
Step-by-step explanation:
to find diatance between AB
A(0 , 0) = (x1 , y1)
B(x , y) = (x2 , y2)
distance formula = [tex]\sqrt{(x2 - x1)^2 + (y2 - y1)^2}[/tex]
=[tex]\sqrt{(x - 0)^2 + (y - 0)^2}[/tex]
=[tex]\sqrt{x^2 + y^2}[/tex]
20.
168
Which equation matches the graph? Click on the picture
enlarge.
126
84
42
0
0
6 12
18
24
b) y = 42x
a) y = 7x
D c) y= 6x
d) y = 2x
cuantos terminos tiene -3xy
Answer:
El a+b tiene 1 terminó porque para separar un término el factor es el +Step-by-step explanation:
Please answer this question. I prey
Answer:
45°
Step-by-step explanation:
mLA : mLB : mLC = 1:2:1 => 1+2+1=4 (equivalent with 180°)
so, mL2 = mLC = 1/4 ×180° = 45°
slope of 3,-4 and 5,8
Answer:
Slope = 6
Step-by-step explanation:
Use the slope formula:
[tex]m=\frac{y_1-y_2}{x_1-x_2}\\m=\frac{-4-8}{3-5}\\m=\frac{-12}{-2}\\m=6[/tex]
Answer:
6
Step-by-step explanation:
(3,-4) and (5,8)
To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)
Plug in these values:
(8 - (-4)) / (5 - 3)
Simplify the parentheses.
= (8 + 4) / (5 - 3)
= (12) / (2)
Simplify the fraction.
12/2
= 6
This is your slope.
Hope this helps!
hi I need help on this
(a) A color printer prints 23 pages in 7 minutes. How many minutes does it take per page? minutes per page
7 min = 23 pages
To find out the amount of time the color printers to print one page we need to do 7/23 min.
Answer: 7/23
How can you find the y-coordinates of the midpoint of a vertical line segment with endpoints at (0,0) and (0,-12)? Check all that apply.
A. add the endpoints
B. divide 12 by 2
C. divide -12 by 2
D. multiply -12 by 2
a map shows that the top of a hill is 200m above sea level and the bottom of a lagoon is 15m below sea level. express these distancesat a distances from sea level and what is difference between the two heights
Answer:
200 m
-15 m
215 m
Step-by-step explanation:
Given :
Top of hill = 200 m above sea level ; height of hill top is positive 200m = 200 m
Bottom of lagoon = 15m *below sea level ; bottom of lagoon = - 15m
We have related the height of the two points with respect to sea level ; points above sea level are represented as positive ; points below are represented as negative.
Difference between the two heights :
Hill top - bottom of lagoon :
200 m - (-15) m
200 m + 15 m
215 m
Difference between the heights is 215 m
Please help I will give you Brainlyest
Answer:
below
Step-by-step explanation:
Clare's mistake was the writing of 4000 in standard form
he wrote 4 ×10²
instead of 4 ×10³
Answer:
Step 1
Step-by-step explanation:
I believe Claire's mistake is when she tries to simplify 4000
She says that 4000 = 4 × 10²
4000 is actually equal to 4 ×10³
Two cubical dice each have removable numbers 1 through 6. The twelve numbers on the two dice are removed, put into a bag, then drawn one at a time and randomly reattached to the faces of the cubes, one number to each face. The dice are then rolled and the numbers on the two top faces are added. What is the probability that the sum is 7?
a. 3/8 b. 2/11c. 2/3d. 1/3e. 2/9
Answer:
it might be 3 but I'm not sure
PLEASE HELP LAST THING I NEED ON MATH
WILL GIVE BRAINLIEST, THANKS AND 5* VOTE
TROLL = WILL GET ALL THEIR ANSWERS AND QUESTIONS REPORTED
Answers:
side a = 12.3 unitsangle B = 100 degreesside b = 15.8 units===========================================================
Explanation:
Let A = 50 degrees and C = 30 degrees. The side opposite angle uppercase C is lowercase c = 8. Convention usually has uppercase letters as the angles, while the lowercase letters are side lengths. A goes opposite 'a', B goes opposite b, and C goes opposite c.
Let's use the given angles to find the missing angle B
A+B+C = 180
50+B+30 = 180
B+80 = 180
B = 180-80
B = 100
Now we can apply the law of sines to find side b
b/sin(B) = c/sin(C)
b/sin(100) = 8/sin(30)
b = sin(100)*8/sin(30)
b = 15.7569240481953
b = 15.8
Make sure your calculator is in degree mode.
----------------------------
We'll do the same thing to find side 'a'
a/sin(A) = c/sin(C)
a/sin(50) = 8/sin(30)
a = sin(50)*8/sin(30)
a = 12.2567110899037
a = 12.3
Both values for 'a' and b are approximate (even before rounding).
-----------------------------
Extra info (optional)
As you can probably tell or guess, the phrasing "solve the triangle" means "find all sides and angles".Notice how if we erase the question marked sides and angles of the original drawing, we're left with something in the AAS case. Meaning that exactly one triangle is possible here. We don't have to worry about any ambiguous case.If you wanted, you could apply the law of cosines rule after you determine two sides and an included angle between them. This will yield the length of the side opposite the angle.Answer:
B=100
b=15.7
a=12.25
Step-by-step explanation:
first find the missing angle:
B=180-50-30
B=100
then use the law of sines:
[tex] \frac{a}{ \sin(a) } = \frac{b}{ \sin(b) ) } = \frac{c}{ \sin(c) } [/tex]
then
[tex] \frac{a}{ \sin(50) } = \frac{8}{ \sin(30) } \\ \\ a = 12.25[/tex]
use the same way to find the other side
[tex] \frac{b}{ \sin(100) } = \frac{8}{ \sin(30) } \\ b = 15.7[/tex]
PLSSSS HELP ASAP !!! PLSSS WILL MARK BRAINLIEST TO WHOEVER GETS IT RIGHT
Answer:
See below.
Step-by-step explanation:
Angle 7 and Angle 4Angle 1 and Angle 5Answer:4000000
Step-by-step explanation:783
The values for three sets of data are shown below.
Data
Data Set
Values
1
42, 48, 50, 88, 49
2
63, 29, 35, 28, 30
3
2, 5, 3, 8
Without calculating any statistics, Anna knows that data set 3 would have the least mean absolute deviation among the three sets. Which statement explains how she knows?
Sets 1 and 2 contain outliers.
Set 3 has the least mean.
Set 3 contains an outlier.
Sets 1 and 2 have an odd number of values.
Answer:
data set 3 would have the least mean absolute deviation among the three sets since there is less spread of the data and the data values in set-3 lie close to the mean.
Step-by-step explanation:
The mean absolute deviation is a measure of spread of the data.
If the data values in the given data set are widely spread then we obtain a higher mean absolute deviation.
if the data values of a given data set are close to each other i.e there is a less spread of the data and hence the mean absolute deviation will be low as the data values will lie close to the mean.
We are given three data set as:
set- 1 42, 48, 50, 88, 49
set- 2 63, 29, 35, 28, 30
set- 3 2, 5, 3, 8
Hence, we could observe that the data values in set 1 and set 2 are widely spread.
In set-1 the data value 88 is much higher value as compared to other data values.
Similarly in set-2 the data value 63 is again a much higher value as compared to other data values.
Whereas in set-3 the data values are all closely related and there is not much spread in the data.
Answer:
it seems like you already have this answered?
Answer:
data set 3 would have the least mean absolute deviation among the three sets since there is less spread of the data and the data values in set-3 lie close to the mean.
Step-by-step explanation:
The mean absolute deviation is a measure of spread of the data.
If the data values in the given data set are widely spread then we obtain a higher mean absolute deviation.
if the data values of a given data set are close to each other i.e there is a less spread of the data and hence the mean absolute deviation will be low as the data values will lie close to the mean.
We are given three data set as:
set- 1 42, 48, 50, 88, 49
set- 2 63, 29, 35, 28, 30
set- 3 2, 5, 3, 8
Hence, we could observe that the data values in set 1 and set 2 are widely spread.
In set-1 the data value 88 is much higher value as compared to other data values.
Similarly in set-2 the data value 63 is again a much higher value as compared to other data values.
Whereas in set-3 the data values are all closely related and there is not much spread in the data.
Solve the system of equations.
y = x + 4
y = x2 + 2
Answer:
(2,6) and (-1,3)
Step-by-step explanation:
Hi there!
We're given the system of equations:
y=x+4
y=x²+2
and we need to solve the system
You may first notice that both equations are equal to y, so we can set them to equal each other via a property known as transitivity (if a=b and b=c, then a=c)
x²+2=x+4
subtract x from both sides
x²-x+2=4
subtract 4 from both sides
x²-x-2=0
we can factor the polynomial
the numbers that add up to -1 and multiply to get -2 are -2 and 1
(x-2)(x+1)=0
solve
x=2, x=-1
both values of x work- so we'll have 2 solutions in this case
now we need to solve for y; we can do this by substituting the value of x into one of the equations to solve for y
let's use y=x+4
so if we'll use x=2,
y=2+4
y=6
one solution will be (2,6)
and if we use x=-1
y=-1+4
y=3
and the other will be (-1,3)
Hope this helps! :)
Determine the period of this Function.
Answer:
4p
Step-by-step explanation:
The period is basically the difference in x from one "peak" to the other "peak".
The peaks are the highest points of a sinosodial function, and the figure them out, use the formula:
[tex]|peak_1-peak_2|=period[/tex]
We know the first peak is at about x=0[tex]\pi[/tex]
We know the second peak is at about x=4[tex]\pi[/tex]
So plugging this in:
[tex]|0-4\pi |=4\pi[/tex]
So the period is [tex]4\pi[/tex]
I am assuming "p" stands for [tex]\pi[/tex], so the answer should be 4p.
There are other ways to find the period, for instance if you are given a sinusodial function in writing instead of a graph.
Here is an example:
5sin(5x+2)+3
If we want to find period, we need to find what we call "b"
b is the number in front of x, which we can identify as bx, which in this case is 5x above.
Now what do we do with this "b"?
This is the value we need to find our period.
If you know b, you can use this formula to find the period:
[tex]\frac{2\pi }{b}=p[/tex]
And when we plug in b:
[tex]\frac{2\pi }{5}[/tex]
=
1.257, which would be your period.
THis can also be reworked so that you can find b:
If the formula for period is [tex]\frac{2\pi }{b}=p[/tex], then the opposite formula would be [tex]\frac{2\pi }{ p}=b[/tex]
And when you plug the period you have in:
[tex]\frac{2\pi }{1.257}[/tex]
=
5
Anyway, your answer is 4p.
Hope this helps!
Classify the quadrilateral.
Answer:
Step-by-step explanation:
An answer should never depend on a diagram. The figure has 4 equal sides which means that it could be a square or a rhombus because both have 4 equal sides.
The question does depend on a diagram. Because the figure is leaning a little to the left, you should answer that it is likely a rhombus. You should object to the question.