Answer:
Step-by-step explanation:
This is a related rates problem from calculus using implicit differentiation. The main equation is going to be Pythagorean's Theorem and then the derivative of that. Pythagorean's Theorem is
[tex]x^2+y^2=c^2[/tex] where c is the hypotenuse and is a constant. Therefore, the derivative of this with respect to time, and using implicit differentiation is
[tex]2x\frac{dx}{dt}+2y\frac{dy}{dt}=0[/tex] and dividing everything by 2 to simplify a bit:
[tex]x\frac{dx}{dt}+y\frac{dy}{dt}=0[/tex]. Upon analyzing that equation, it looks like we need values for x, y, [tex]\frac{dx}{dt}[/tex], and [tex]\frac{dy}{dt}[/tex]. And here's what we were given:
[tex]\theta=45[/tex] and [tex]\frac{dx}{dt}=.5[/tex] In the greater realm of things, that's nothing at all.
BUT we can use the right triangle and the angle we were given to find both x and y. The problem we are looking to solve is to
Find [tex]\frac{dy}{dt}[/tex] at the instant that [tex]\frac{dx}{dt}[/tex] = .5.
Solving for x and y:
[tex]tan45=\frac{x}{6}[/tex] and
6tan45 = x ( and since this is a 45-45-90 triangle, y = x):
[tex]6(\frac{\sqrt{2} }{2})=x=y[/tex] so
[tex]x=y=3\sqrt{2}[/tex] and now we can fill in our derivative. Remember the derivative was found to be
[tex]x\frac{dx}{dt}+y\frac{dy}{dt}=0[/tex] so
[tex]3\sqrt{2}(\frac{1}{2})+3\sqrt{2}\frac{dy}{dt}=0[/tex] and
[tex]\frac{3\sqrt{2} }{2}+3\sqrt{2} \frac{dy}{dt}=0[/tex] and
[tex]3\sqrt{2}\frac{dy}{dt}=-\frac{3\sqrt{2} }{2}[/tex] and multiplying by the reciprocal of the left gives us:
[tex]\frac{dy}{dt}=-\frac{3\sqrt{2} }{2}(\frac{1}{3\sqrt{2} })[/tex] so
[tex]\frac{dy}{dt}=-\frac{1}{2}\frac{m}{s}[/tex]
Use a half-angle identity to find the exact value of cos 15
Answer:
It's too short. Write at least 20 characters to explain it well.
a cycle travel 1st km at therateof 10 km per hour the second km at the rate of 3 per hour and third at therate of 6 km.find the average speed of cyclea cycle travel 1st km at therateof 10 km per hour the second km at the rate of 3 per hour
Answer:
18 kilometers 120 kilometers
If anyone can help me I will really appreciate!!
Answer:
The decimal form of the equation is y = 2.5x + 10
The equivalent fraction form is y = (5/2)x + 10 because 5/2 = 2.5
===========================================================
Explanation:
We can pick any two columns from the table to form the two points needed.
I'll pick the first two columns
(1, 12.5)
(2, 15)
Then apply the slope formula to those points
m = (y2-y1)/(x2-x1)
m = (15-12.5)/(2-1)
m = (2.5)/(1)
m = 2.5
Now use that slope with either point mentioned to find the y intercept b.
y = mx+b
12.5 = 2.5*1 + b
12.5 = 2.5 + b
12.5 - 2.5 = b
10 = b
b = 10
Or
y = mx+b
15 = 2.5*2+b
15 = 5+b
15-5 = b
10 = b
b = 10
We end up with the same b value.
We found that m = 2.5 is the slope and b = 10 is the y intercept
Therefore we go from y = mx+b to y = 2.5x + 10
This is the same as saying y = (5/2)x + 10 since 2.5 = 5/2
The scatterplot shows the number of bedrooms in a house and the selling price for that house.
Calculate the residual for the house with 6 bedrooms, to the nearest thousand.
The residual for the house with 6 bedrooms is ___
-30k
-26k
26k
30k
Answer:
-26k, -26,000 ; (B)
ED2021
The residual for the house with 6 bedrooms is -26k.
What is Scatterplots?Scatterplots are the plotting of set of points on a vertical axis and an horizontal axis. The shows the correlation extent between the numbers of the observed quantities.
Given is a scatterplot showing the selling price of houses with the number of bedrooms.
Equation of the line of best fit is given as,
y = 6.3x + 4.8
Residual = Actual value - Predicted value
From the scatterplot,
Actual selling price of house with 6 bedrooms = 40 × 10,000 = 400,000
Predicted selling price for 6 bedrooms = (6.3 × 6) + 4.8
= 42.6 × 10,000
= 426,000
Residual = 400,000 - 426,000
= -26,000
Hence the residual is -26k.
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5 Cece draws these two figures to prove there is more
than one parallelogram with a 40° angle between a
2-cm side and a 6-cm side. Is Cece correct? Explain.
2 cm
40
4.
2 cm
Answer:
chash greatly ta 45uerywryrsyrsyrs
4. The rectangle shown below has been broken into four smaller rectangles. The area of three of the smaller
rectangles are shown in the diagram. Find the area of the fourth rectangle and justify your answer. [Think about
shared dimensions.]
Answer:
Step-by-step explanation:
Need the diagram for reference in order to answer...........
Due the end of the week pls help.
This problem seems like a lot when you read through it, but when you start to analyze the problem, the whole first line is extra information that we don't actually need. The part we really need to pay attention to is:
"p = qr - f, write the equation with q solved in terms of p, r, and f."
So, all we are doing here is some manipulating of the equation to get what we want. So, if p = qr - f, we can isolate the variable (q), to get p + f = qr. Now all we have to do is divide both sides by r to isolate the variable (q) even further, and we get [tex]$\frac{p+f}{r}=q$[/tex] or [tex]$r=\frac{p+f}{r}$[tex]
A chocolate chip cookie manufacturing company recorded the number of chocolate chips in a sample of 60 cookies. The mean is 22.36 and the standard deviation is2.97 . Construct a 80% confidence interval estimate of the standard deviation of the numbers of chocolate chips in all such cookies.
Answer:
2.665 < σ < 3.379
Step-by-step explanation:
Given :
s = 2.97
Sample size, n = 60
α = 80%
χ² Critical value (two - tailed), df = (60-1) = 59
χ² = 45.577 ; χ² = 73.279
The 80% confidence interval for the standard deviation :
s * √(n - 1) / χ² critical
2.97 * √(60 - 1) / 73.279 < σ < 2.97 * √(60 - 1) / 45.577
2.665 < σ < 3.379
8. Write (2x + 1)(x - 3)(x - 2) in standard form.
2x3 - 9x2 + 6
2x3 - 9x2 + 7x + 6
O
2x3 + 7x - 9x2 + 6
O
7x + 2x3 - 9x2 + 6
Answer:
2x^3 - 9x^2 + 7x + 6
Step-by-step explanation:
(2x + 1)(x - 3)(x - 2)=2x^3 - 9x^2 + 7x + 6
WILL GIVE BRAINLIEST ASAP
Answer:
Step-by-step explanation:
Answer the question given above
Answer:
See explanation
Step-by-step explanation:
This is how you are suppoussed to solve it:
Measure each and every side of the rectangle with a ruler and add it. This would be your perimeter
This cannot be solved unless the page is infront of us.
Emily, Yani and Joyce have a total of 3209 stickers. Yani has 2 times
as many stickers as Joyce. Emily has 279 more stickers than Yani. How
many more stickers does Emily have than Joyce?
Answer:
279+x
Step-by-step explanation:
Emily + Yani + Joyce=3209 stickers
if Yani has 2 times as many stickers as Joyce:this statement states that Joyce has x stickers and Yani has 2x stickers because x multiplied by 2"Emily has 279 more stickers than Yani":therefore the equation for Emily will be ;279+2xhow many stickers does Emily have than Joyce:
(279+2x)-(x)
279+2x-x
=279+x
Hi I need help with part c please and thank you so much if you can do so
For the hole in one pythagores theorem would work because a right angled triangle eill be formed and hole in one would be the hypotenuse which can be found using the theorem.
b²+p² = h²
Answered by Gauthmath must click thanks and mark brainliest
Point g is located at (3,6) on the coordinate plane. Point G is reflected over the x-axis to create point G'. Point G' is then reflected over the y-axis to create point G''. What ordered pair describes the location of G''.
-Answer:
(-3. -6)
Step-by-step explanation:
G (3,6)
x axis reflect
G' (3, -6)
y axis reflect
G'' (-3. -6)
Hoa mua 2 con gà . Lan mua 4 con gà. Hỏi cả 2 bạn mua bao nhiêu con gà
Answer: 6 con ga
Step-by-step explanation:
So ga ca 2 ban mua la:
2+4=6 (con ga)
Jill records the temperature outside every hour for 4 hours. She finds that the temperature dropped by the same amount each hour. After 4 hours, she finds that the temperature dropped a total of 20∘F. She writes this number sentence.
(−20)÷4=−5
What does the number sentence mean?
The total drop in temperature, −20∘F, divided by 4 hours equals −5∘F per hour. The temperature dropped 5∘F each hour.
The total number of drops, 20, divided by 4 hours equals 5 times per hour. The temperature dropped 5 times per hour.
The total number of hours, 20, divided by 4∘F equals 5 hours. The temperature dropped once every 5 hours.
The total drop in temperature, −20∘F, divided by 4∘F in the first hour, equals −5 drops. The temperature dropped 5 times.
Answer:
It is the first one, The total drop in temperature, −20∘F, divided by 4 hours equals −5∘F per hour. The temperature dropped 5∘F each hour.
Step-by-step explanation:
Help me please and thank you
Answer:
D. 3
Step-by-step explanation:
Answer:
3
step by step explanitation
look at the image to see the question
9514 1404 393
Answer:
1385.4 yd³
Step-by-step explanation:
The formula for the volume of a cylinder is ...
V = πr²h . . . . radius r and height h
For the given radius and height, the volume is ...
V = π(7 yd)²(9 yd) = 441π yd³ ≈ 1385.4 yd³
2/4= 4-2 true or false
Answer:
= Answer is falseStep-by-step explanation:
False is the ansHelp pleaseeeeeeeeeeeeeeeee
Answer:
D(- 1) = 2
Step-by-step explanation:
To evaluate D(- 1), substitute x = - 1 into D(x) , that is
D(- 1) = (- 1)² - 2(- 1) - 1 = 1 + 2 - 1 = 2
Find the equation of the line using the point-slope formula. Write the final equation using the slope-intercept form.
perpendicular to
7y = x − 4
and passes through the point
(−2, 1)
Answer:
[tex]y = -7x -13[/tex]
Step-by-step explanation:
Given
Perpendicular to
[tex]7y = x -4[/tex]
Passes through
[tex](-2,1)[/tex]
Required
The equation
First, we calculate the slope of:
[tex]7y = x -4[/tex]
Divide through by 7
[tex]y = \frac{1}{7}x - \frac{4}{7}[/tex]
A linear function is:
[tex]y=mx + c[/tex]
Where;
[tex]m \to slope[/tex]
So:
[tex]m = \frac{1}{7}[/tex]
For the perpendicular line; the slope is:
[tex]m_2 = -\frac{1}{m}[/tex]
So, we have:
[tex]m_2 = -\frac{1}{1/7}[/tex]
[tex]m_2 = -7[/tex]
The equation is:
[tex]y = m(x - x_1) + y_1[/tex]
So, we have:
[tex]y = -7(x - -2) + 1[/tex]
[tex]y = -7(x +2) + 1[/tex]
Open bracket
[tex]y = -7x -14 + 1[/tex]
[tex]y = -7x -13[/tex]
Which of the following numbers has the greatest value?
89 3/4
66 1/2
55 2/3
74 1/4
106 5/6
Answer:
106 5/6
Step-by-step explanation:
55 < 66 < 74 < 89 < 106
the fractions are irrelevant because the whole numbers are all different
The greatest of the numbers will be 106 5/6 since 106 is greater than the rest of the integers present in the mixed fractions.
Finding greatest value in a sequenceThe greatest value is the highest value in a given set of number.
Given the following numbers
89 3/4
66 1/2
55 2/3
74 1/4
106 5/6
The greatest of the numbers will be 106 5/6 since 106 is greater than the rest of the integers present in the mixed fractions.
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Which is a factor of: 2x^2 - 4x – 6?
I don’t understand how u get it in this form of an answer
Answer:
A
Step-by-step explanation:
2x^2-6x+2x-6=2x(x-3)+2(x-3)=(2x+2)(x-3).
Malek sets out for a hike at 8.00 am and returns at 17:15.
How long was Malek hiking for?
hours and
minutes
Answer:
9 hours and 15 mins
Step-by-step explanation:
17 - 8 (time calculation)
Identify the decimals labeled with the letters A B and a C
Answer:
A=3.1
B=4.2
C=2.7
Step-by-step explanation:
Please i need to find the era bounded by the following curves
Answer:
10 2/3 or 32/ 3
Step-by-step explanation:
5 - x^2 - (2 - 2x) =
= -x^2 + 2x + 3
Integral of (-x^2 + 2x + 3)dx from -1 to 3 =
= -x^3/3 + 2x^2/2 + 3x from -1 to 3
= -x^3/3 + x^2 + 3x from -1 to 3
= -27/3 + 9 + 9 - (1/3 + 1 - 3)
= -9 + 9 + 9 - 1/3 - 1 + 3
= 11 - 1/3
= 10 2/3 = 32/3
Answer:
32/3
Step-by-step explanation:
Check the pdf :)
A park is 5 miles east of Roxana's home. A library is 4 miles north of the park. How far is Roxana's home from the library?
Answer: 9 miles I think but I dont know where her house is exactly.
Find the volume of a pyramid with a square base, where the side length of the base is 17.6 m and the height of the pyramid is 13.4 m. Round your answer to the nearest tenth of a cubic meter.
Answer:
~1383.5 meters cubed
Step-by-step explanation:
(17.6 x 17.6 x 13.4) ÷ 3 = ~1383.5
Below is the graph of a polynomial function with real coefficients
(a) The function f is increasing over which intervals? Choose all that apply.
D(-0, -8)
O (-5,-2) O (-8, -2) O (-2,
2) (2,5)
O (5, 0 )
?
(b) The functionfhas local maxima at which x-values? If there is more than one value,
separate them with commas.
(c) What is the sign of the leading coefficient of f?
Select One
(d) Which of the following is a possibility for the degree of f? Choose all that apply.
4
5
6
Please help if you can thank you
9514 1404 393
Answer:
(a) (-∞, -8), (-5, -2), (2, 5)
(b) -8, -2, 5
(c) negative
(d) 6
Step-by-step explanation:
(a) The function is increasing on intervals where the graph slopes upward left-to-right. Those are (-∞, -8), (-5, -2), and (2, 5).
__
(b) The local maxima are at the right end of each interval on which the function is increasing: -8, -2, 5.
__
(c) The function opens downward (∩), so has a negative leading coefficient.
__
(d) There are three local maxima and two local minima (left end of an increasing interval), so a total o 5 turning points. The degree of the polynomial is at least one more than this: 6.
nearest number of 64653
Answer:
is it like this
64653=65000
Answer:
là 64652/64654
