Express the area of the following shaded region in terms of (a) one or more integrals with respect to x, and (b) one or more integrals with respect to y
Answers
To express the area of the shaded region, set up one or more definite integrals using the given functions as limits of integration, either with respect to x or y.
To express the area of the shaded region in terms of one or more integrals, first identify the functions that bound the region. Let f(x) and g(x) be the functions bounding the region in the x direction, and h(y) and k(y) be the functions bounding it in the y direction.
(a) With respect to x: Area = ∫[g(x) - f(x)] dx, evaluated from a to b, where a and b are the limits of integration in the x direction.
(b) With respect to y: Area = ∫[k(y) - h(y)] dy, evaluated from c to d, where c and d are the limits of integration in the y direction.
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Related Questions
A water ballon is launched straight up. The balloons flight is modeled by the function h(t)=16t^2+192t
Answers
Answer:Step by Step Solution
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Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
h*(t)-(16*t^2+192*t)=0
STEP
1
:
Equation at the end of step 1
ht - (24t2 + 192t) = 0
STEP
2
:
STEP
3
:
Pulling out like terms
3.1 Pull out like factors :
ht - 16t2 - 192t = t • (h - 16t - 192)
Equation at the end of step
3
:
t • (h - 16t - 192) = 0
STEP
4
:
Theory - Roots of a product
4.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation:
4.2 Solve : t = 0
Solution is t = 0
Equation of a Straight Line
4.3 Solve h-16t-192 = 0
Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).
"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.
In this formula :
y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis
The X and Y intercepts and the Slope are called the line properties. We shall now graph the line h-16t-192 = 0 and calculate its properties
Graph of a Straight Line :
Calculate the Y-Intercept :
Notice that when h = 0 the value of t is 12/-1 so this line "cuts" the t axis at t=-12.00000
t-intercept = 192/-16 = 12/-1 = -12.00000
Calculate the X-Intercept :
When t = 0 the value of h is 192/1 Our line therefore "cuts" the h axis at h=192.00000
h-intercept = 192/1 = 192.00000
Calculate the Slope :
Slope is defined as the change in t divided by the change in h. We note that for h=0, the value of t is -12.000 and for h=2.000, the value of t is -11.875. So, for a change of 2.000 in h (The change in h is sometimes referred to as "RUN") we get a change of -11.875 - (-12.000) = 0.125 in t. (The change in t is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = 0.125/2.000 = 0.062
Geometric figure: Straight Line
Slope = 0.125/2.000 = 0.062
h-intercept = 192/1 = 192.00000
t-intercept = 192/-16 = 12/-1 = -12.00000
t = 0
Step-by-step explanation:
How do you double integrate in polar coordinates?
Answers
Double integration in polar coordinates involves integrating a function over a two-dimensional region in the polar coordinate system. This is done by setting up a double integral in terms of r and θ, and integrating first with respect to r and then with respect to θ.
Double integration in polar coordinates involves integrating a function over a two-dimensional region in the polar coordinate system. The steps to double integrate a function in polar coordinates are as follows:
1. Determine the limits of integration for r and θ. These limits define the region over which the function will be integrated. Typically, the limits are determined by the boundaries of the region in the xy plane.
2. Write the function to be integrated in terms of r and θ. The function must be expressed in polar coordinates for integration in polar coordinates.
3. Set up the double integral by writing the function in polar coordinates, multiplying by the appropriate factors of r and integrating with respect to r first and then θ.
4. Integrate the function with respect to r, using the limits of integration for r determined in step 1.
5. Integrate the result from step 4 with respect to θ, using the limits of integration for θ determined in step 1.
The general form of a double integral in polar coordinates is:
∫∫f(r, θ)r dr dθ
where f(r, θ) is the function to be integrated, and r and θ are the polar coordinates.
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Circle T is shown where points Q and S are on the circle and ZQTS = 75°.
O
T
75°
S
The ratio of the central angle, ZQTS, to the whole circle is [DROP DOWN 1].
QS represents [DROP DOWN 2] of the circle's circumference.
Answers
which is approximately 3.864 times the length of QS.the circle is approximately 4 times the length of QS, or approximately 4 times 0.966 times the length of QS,
What is angle?An angle is a measure of the amount of turn between two lines or rays that meet at a common point, known as the vertex of the angle. The angle is typically measured in degrees or radians. In a Euclidean plane, an angle can range from 0 degrees (corresponding to two lines that are parallel to each other) to 180 degrees (corresponding to two lines that form a straight line). An angle greater than 180 degrees is called a reflex angle. Angles are used in many areas of mathematics and physics, such as geometry, trigonometry, and calculus, as well as in real-world applications such as navigation, architecture, and engineering.
by the question.
The ratio of the central angle ZQTS to the whole circle is 1/12, or 0.0833 (rounded to four decimal places). This is because there are 360 degrees in a circle, and 75 is 1/12 of 360.
QS represents 1/4 of the circle's circumference. This is because the central angle ZQTS is 75 degrees, which is 1/3 of a right angle (90 degrees). An inscribed angle that intercepts the same arc as a 1/3 angle will have twice the measure of the 1/3 angle, or 150 degrees. Thus, angle QTS is 150 degrees. Angle QOS is also 150 degrees, since it intercepts the same arc as QTS. Therefore, angle QOT is 60 degrees, since the angles in triangle QOT add up to 180 degrees. Since triangle QOT is an equilateral triangle, QT and QS are equal in length, and angle QTS is 75 degrees, we can use the sine function to find the length of QS. The sine of 75 degrees is approximately 0.966, so QS represents approximately 0.966 times the circumference of the circle. Since QS represents 1/4 of the circumference, the circumference of the circle is approximately 4 times the length of QS, or approximately 4 times 0.966 times the length of QS,
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construct a triangle ABC if AB = 4 cm, BC = 5 cm and Y = 30 °, then enter a circle
Answers
Answer:
Refer to the attachment \(\Huge {\nearrow}\)
Can't understand diagram? Don't worry See the Latex diagram coded below on webDiagram:-\(\Huge {\downarrow}\)\(\setlength{\unitlength}{1cm}\begin{picture}(20,15)\thicklines\qbezier (1,0)(1,0)(7,0)\qbezier(1,0)(1,0)(2,3)\qbezier (7,0)(7,0)(2,3)\put (0.5,-0.2){\sf X}\put(7.1,-0.2){\sf Y}\put(2,3.2){\sf Z}\end{picture}\)
what is ratio?
what is rote?
write each of ffg ratio in its simplest form . first make the units the same in each case
a)90 sec to 7min
b)48min to 3hours
c)2,5 days to 80hours
d)3 800mm to 3m
e)2,5 to 7am
f)5 300m to 2,5km
Answers
Answer:
a) 3 : 14
b) 4 : 15
c) 3: 4
d) 19 : 15
e) 53 : 25
Step-by-step explanation:
a)90 sec to 7min
We convert 7 mins to seconds
1 minute = 60 seconds
7 minutes = x seconds
Cross Multiply
x = 7 × 60 seconds = 420 seconds
Hence,
Our ratio is
90 seconds : 420 seconds
Divide both sit by 30
= 3 : 14
b)48min to 3hours
We convert 3 hours to minutes
1 hour = 60 minutes
3 hours = x minutes
Cross Multiply
x = 3 × 60 minutes = 180 minutes
Hence,
Our ratio is
48 minutes : 180 minutes
Divide both sides by 12
4 : 15
c)2.5 days to 80hours.
We are converting 2.5 days to hours
1 day = 24 hours
2.5 days = x
Cross Multiply
x = 2.5 × 24 hours = 60 hours
Hence,our ratio
60 hours : 80 hours
Divide both sides by 20
3: 4
d)3 800mm to 3m
We convert 3 m to mm
1 m = 1000 mm
3 m = x mm
Cross Multiply
x mm = 3 × 1000 mm
x mm = 3000mm
Hence, ratio is
3800 mm : 3000mm
Divide both sides by 200
19 : 15
e)5300m to 2.5km
We convert km to m
1 km = 1000 m
2.5 km = x m
Cross Multiply
x m = 2.5 × 1000m
x = 2500m
Hence, our ratio
5300m : 2500m
Divide both sides by 100
53 : 25
Use the definition of Taylor series to find the Taylor series (centered at c ) for the function. f(x)=e 4x
,c=0 f(x)=∑ n=0
[infinity]
Answers
The answer is , the Taylor series (centered at c=0) for the function f(x) = e^(4x) is given by:
\($$\large f(x) = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n$$\)
The Taylor series expansion is a way to represent a function as an infinite sum of terms that depend on the function's derivatives.
The Taylor series of a function f(x) centered at c is given by the formula:
\(\large f(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(c)}{n!}(x-c)^n\)
Using the definition of Taylor series to find the Taylor series (centered at c=0) for the function f(x) = e^(4x), we have:
\(\large e^{4x} = \sum_{n=0}^{\infty} \frac{e^{4(0)}}{n!}(x-0)^n\)
\(\large e^{4x} = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n\)
Therefore, the Taylor series (centered at c=0) for the function f(x) = e^(4x) is given by:
\($$\large f(x) = \sum_{n=0}^{\infty} \frac{4^n}{n!}x^n$$\)
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The Taylor series for f(x) = e^(4x) centered at c = 0 is:
f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...
To find the Taylor series for the function f(x) = e^(4x) centered at c = 0, we can use the definition of the Taylor series. The general formula for the Taylor series expansion of a function f(x) centered at c is given by:
f(x) = f(c) + f'(c)(x - c) + f''(c)(x - c)^2/2! + f'''(c)(x - c)^3/3! + ...
First, let's find the derivatives of f(x) = e^(4x):
f'(x) = d/dx(e^(4x)) = 4e^(4x)
f''(x) = d^2/dx^2(e^(4x)) = 16e^(4x)
f'''(x) = d^3/dx^3(e^(4x)) = 64e^(4x)
Now, let's evaluate these derivatives at x = c = 0:
f(0) = e^(4*0) = e^0 = 1
f'(0) = 4e^(4*0) = 4e^0 = 4
f''(0) = 16e^(4*0) = 16e^0 = 16
f'''(0) = 64e^(4*0) = 64e^0 = 64
Now we can write the Taylor series expansion:
f(x) = f(0) + f'(0)(x - 0) + f''(0)(x - 0)^2/2! + f'''(0)(x - 0)^3/3! + ...
Substituting the values we found:
f(x) = 1 + 4x + 16x^2/2! + 64x^3/3! + ...
Simplifying the terms:
f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...
Therefore, the Taylor series for f(x) = e^(4x) centered at c = 0 is:
f(x) = 1 + 4x + 8x^2 + 32x^3/3 + ...
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San Francisco is known for its fine chocolates. If a deluxe box of fancy chocolates weighs 1 pound 8 ounces and contains 32 chocolate pieces, about how much does each piece weigh? What equation solves this problem? A) 32/24 = n B) 28/32 = n C) 24/32 = n D) 18/32 = n
Answers
Answer:
24/32 which is C
Step-by-step explanation:
1 pound = 16 oz
1/2 pound = 16/2 = 8 oz
The box of chocolates weighs 1 1/2 pounds which is 16 + 8 =24 oz
So 32 chocolates weighs 24 oz
1 chocolate = x
32/1 = 24/x Equation. Cross multiply
32x = 24 Divide by 32
x = 24/32
Find m(-10) if m(t) = -(t + 6).
Find a(-6)if a (n)=7+n
Any help is greatly appreciated.
Answers
So, for m(-10) if m(t) = -(t + 6):
m(-10) = -((-10)+6)
Remember, flip the equation since it's a negative outside the parentheses.
m(-10) = (10 – 6); m(-10) = 4
Same for the second equation.
a(-6) if a(n) = 7 + n
a(-6) = 7 + (-6)
a(-6) = 7 – 6
a(-6) = 1
So these are your answers:
m(-10) = 4
a(-6) = 1
What is the Q1 and Q3?
4,6,8,9,13,21,31
Answers
The data is already sorted for us. If it wasn't, then you would have to write the values from smallest to largest.
The median is the middle most value 9 (in slot 4)
The median separates the data into two halves, which I'll call the lower and upper half
lower half = {4,6,8}
upper half = {13,21,31}
The median of the lower half is 6, and this is the value of Q1.
The median of the upper half is 21. This is the value of Q3
4a-{3b+2c} BIG POINT IF ANSWERED FAST AND RIGHT
Answers
Answer:
=4a−3b+2c
Step-by-step explanation:
There's not enough information to solve. Comment and I'll reply with an answer
Evaluate X ds, where C is the straight line segment x=t;y= from (0,0) to (20,4) the parabolic curve x =t, y =12, from (0,0) to (2,4) For the straight line segment, x ds
Answers
Xds for the given straight line segment and parabolic curve are Xds = (2/9) (1+(1.5x)²)\(^(3/2)\)+ C.
What is the formula for Xds?The parabolic curve x =t, y =12, from (0,0) to (2,4), for the straight line segment, x ds, use the formula:
Xds = ∫√(1+dy/dx²)dx.
For the given straight line segment, x=t;y= from (0,0) to (20,4), the equation is y = 4x/20, or y = 0.2x.
Therefore, dy/dx = 0.2.
Xds = ∫√(1+(0.2)²)dx= ∫√(1+0.04)dx= ∫√(1.04)dx
Evaluating this integral using the substitution method, let u = 1.04x,
we have:
Xds = 1/√1.04 ∫√u du
= 1/√1.04ˣ(2/3) u\(^(3/2)\) + C
= 1/√1.04 ˣ (2/3) (1.04x)\(^(3/2)\) + C
= 0.9626(1.04x)\(^(3/2)\) + C.
For the given parabolic curve x =t, y =12, from (0,0) to (2,4), the equation is y = 12x²/16 = 0.75x².
Therefore, dy/dx = 1.5x. Substituting this value in the formula above, we have:
Xds = ∫√(1+(1.5x)²)dx
Again, using the substitution method, let
u = 1+(1.5x)²,
we have:
Xds = (2/3)∫√u du= (2/3) ˣ (1/3) u\(^(3/2)\) + C= (2/9) (1+(1.5x)²)\(^(3/2)\) + C.
Therefore, Xds for the given straight line segment and parabolic curve are:
For straight line segment:
Xds = 0.9626(1.04x)\(^(3/2)\) + C.For parabolic curve:
Xds = (2/9) (1+(1.5x)²)\(^(3/2)\)+ C.
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in a meeting of county officials, 6 people exchange greetings. how many greetings are exchanged, if everyone greets each other once? (hint: each greeting involves two people).
Answers
There are 15 greetings exchanged among the 6 county officials in the meeting.
There are a total of 15 greetings exchanged in the meeting of county officials if everyone greets each other once. To arrive at this answer, that calculates the number of possible handshakes or greetings in a group. This formula is n(n-1)/2, where n represents the number of people in the group. In this case, there are 6 people in the meeting, so we can substitute n=6 into the formula:
6(6-1)/2 = 15
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What is sextillion divided by nonmillion times 10,000 minus 200 million plus 5000.
Answers
The answer to this arithmetic expression is approximately 9.9998 x 10¹⁸
Define the term expression?A combination of numbers, variables, and operators that represents a quantity or mathematical relationship is called an expression.
First, divide sextillion (10²¹) by nonmillion (10⁶) to get 10¹⁵.
Next, multiply 10¹⁵ by 10,000 to get 10¹⁹.
Subtract 200 million (2 x 10⁸) from 10¹⁹ to get 9.9998 x 10¹⁸.
Finally, add 5,000 to get the result of approximately 9.9998 x 10¹⁸ + 5,000 = 9.9998 x 10¹⁸ + 0.0005 x 10¹⁸ = 9.9998 x 10¹⁸.
Therefore, the answer to this arithmetic expression is approximately 9.9998 x 10¹⁸
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use the given conditions to write an equation for the line. passing through (−9,2) and parallel to the line whose equation is
Answers
The given conditions to write an equation for the line passing through (−9,2) and parallel to the line whose equation is y = −3x+ 2.
What is an equation?There are many different methods to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically include one or more variables.
More than one variable may be present in a linear equation. An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.
\($$We have the equation of a parallel line and a point which it passes through. To write the equation of the line in point-slope form, we will use the following formula:y−y1=m(x−x1)We know that the slope of parallel lines are same and we are given the equation for parallel line, y=−3x+2$$\)
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Before beginning voice lessons, Troy already knew how to sing 1 piece, and he expects to
learn 1 new piece during each week of lessons. After 47 weeks of voice lessons, how many
pieces will Troy be able to sing, in total?
Answers
After 47 weeks of voice lessons there are 48 pieces will Troy be able to sing.
What is voice lessons?
Singing classes are profitable due to the fact they come up with the possibility to enhance your voice via education and practice. Vocal instructors are capin a position to reveal you attempted and examined strategies to get you making a song louder and on-key.
Given:
Before beginning voice lessons, Troy already knew how to sing 1 piece.
He expects to learn 1 new piece during each week of lessons.
Let w be the number of weeks.
So,
1 + w = Number of lessons sing
1 + 47 = 48
Hence, after 47 weeks of voice lessons there are 48 pieces will Troy be able to sing.
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do you see a pattern or possible shortcut to simplify more quickly?
Answers
The length of a rectangle is 4 cm longer than its width.
If the perimeter of the rectangle is 52 cm, find its length and width.
Answers
Step by step
2(w+4)+2w=52
2w +8 +2w=52
4w +8=52
4w=52-8
4w=44
W=11
L=11+4=15
A batch consists of 12 defective coils and 88 good ones. Find the probability of getting two good coils when two coils are randomly selected if the first selection is replaced before the second is made.
Answers
Answer:
0.7744 = 77.44% probability of getting two good coils when two coils are randomly selected
Step-by-step explanation:
For each coil, there are only two possible outcomes. Either it is good, or it is not. Since the coil taken is replaced, the probability of choosing a good coil on a trial is independent of any other trial, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
And p is the probability of X happening.
88 out of 100 are good:
This means that \(\pi = \frac{88}{100} = 0.88\)
Find the probability of getting two good coils when two coils are randomly selected.
This is P(X = 2) when n = 2. So
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
\(P(X = 2) = C_{2,2}.(0.88)^{2}.(0.12)^{0} = 0.7744\)
0.7744 = 77.44% probability of getting two good coils when two coils are randomly selected
2.
Triangles ABC and PQR are similar.
(a) Work out angle Q.
(b)Work out the length PQ.
Answers
Answer:
2. a)
As per the Angle sum property
∠P + ∠Q + ∠R = 180°
22° + ∠Q + 54° = 180°
∠Q = 180° - 76°
∠Q = 104°
b)
Now as per the question,
ΔABC ≅ ΔPQR
Which implies that
AB = PQ
So,
PQ = 8 cm
Step-by-step explanation:
3/5x = -15 one or two step equations
Answers
Answer:
x=1/25
Step-by-step explanation:
Answer: -25
Step-by-step explanation:
You would have to divide both sides by 3/5 which is the same as multiplying by 5/3.
x = -15*5/3
x = -75/3 = -25
Part A The X and Y coordinates (in feet) of station Shore are 654,127 26 and 394,087.52, respectively, and those for station Rock are 652,531.72 and 392,133.86, respectively. Suppose a point P is located near the straight line connecting stations Shore and Rock. What is the perpendicular distance from P to the line if the X and Y coordinates of point P are 653,594.81 and 393,436.47, respectively?
Answers
The perpendicular distance from point P to the line connecting stations Shore and Rock is approximately 668,389.33 feet.
To find the perpendicular distance from point P to the line connecting stations Shore and Rock, we can use the formula for the distance between a point and a line.
The equation of the line connecting stations Shore and Rock can be determined using the slope-intercept form of a straight line: y = mx + b, where m is the slope and b is the y-intercept.
First, let's calculate the slope of the line:
slope = (Y2 - Y1) / (X2 - X1)
= (392,133.86 - 394,087.52) / (652,531.72 - 654,127.26)
= -1,953.66 / -1,595.54
≈ 1.224
Next, we can find the y-intercept (b) by substituting the coordinates of either station (e.g., Rock) into the slope-intercept form and solving for b:
392,133.86 = 1.224 * 652,531.72 + b
b ≈ 392,133.86 - 799,247.25
b ≈ -407,113.39
So, the equation of the line connecting Shore and Rock is:
y ≈ 1.224x - 407,113.39
Now, let's calculate the perpendicular distance from point P to the line using the formula:
distance = |Ax + By + C| / sqrt(\(A^2\) + \(B^2\))
where A, B, and C are the coefficients of the line equation in the form Ax + By + C = 0. In this case, the equation of the line can be rewritten as:
-1.224x + y + 407,113.39 = 0
Therefore, A = -1.224, B = 1, and C = 407,113.39. Plugging in the coordinates of point P (653,594.81, 393,436.47) into the formula, we get:
distance = |-1.224 * 653,594.81 + 1 * 393,436.47 + 407,113.39| / sqrt((-1.224)^2 + 1^2)
= |-799,103.63 + 393,436.47 + 407,113.39| / sqrt(1.497)
= |1,001,446.23| / 1.225
≈ 818,003.79 / 1.225
≈ 668,389.33
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2x - 8 algebraic expression
Answers
Answer:
Because. I need to keep this balanced. I just bring down 2x I didn't do anything with him 8 minus 8 is 0 bring down my equal sign and 20 minus 8 is 12.
Step-by-step explanation:
can you me as brainliest if its right? i need 10000 points and 35 brainliest's to rank up to genius
The sum of squares of two
numbers is 80 and the square of
difference between the two numbers
is 36. Find the product of two
numbers .
Answers
Answer:
the product of the 2 numbers is 22
Step-by-step explanation:
x² + y² = 80
(x - y)² = 36
=>
x - y = 6
or y - x = 6
let's start with the first one x-y=6
x = 6 + y
=>
(6+y)² + y² = 80
y² + 6y +6y + 36 + y² = 80
2y² + 12y + 36 = 80
2y² + 12y - 44 = 0
y² + 6y - 22 = 0
the solution of a quadratic equation
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case here we have an squadron in y.
a=1
b=6
c=-22
(-6 ± sqrt(36 + 4×22))/2 = (-6 ± sqrt(36+88))/2 =
= (-6 ± sqrt(124))/2 = (-6 ± sqrt(4×31))/2 =
= (-6 ± 2×sqrt(31))/2 = -3 ± sqrt(31)
y1 = -3 + sqrt(31)
y2 = -3 - sqrt(31)
=>
x1 = 6 + -3 + sqrt(31) = 3 + sqrt(31)
x2 = 3 - sqrt(31)
control :
(-3 + sqrt(31))² + (3 + sqrt(31))² = 80
9 - 3 sqrt(31) - 3 sqrt(31) + 31 + 9 +3 sqrt(31) + 3 sqrt(31) + 31 = 80
9 + 31 + 9 +31 = 80
18 + 62 = 80
80 = 80 correct
solving now for y-x=6
delivers exactly the same calculations, just with x and y trading places.
so, the resulting 2 number pairs are the same.
the product of the 2 numbers :
(3 + sqrt(31))(-3 + sqrt(31)) = -9 - 3 sqrt(31) + 3 sqrt(31) + 31 =
= -9 + 31 = 22
(3 - sqrt(31))(-3 - sqrt(31)) = -9 + 3 sqrt(31) - 3 sqrt(31) + 31 =
= 22
so, the product is the same in both cases.
ackrabbits are capable of reaching speeds up to 40 miles per hour. How fast is this in feet per second? (Round to the earest whole number.)
5,280 feet = 1 mile
Answers
Answer:
Therefore, ackrabbits can reach speeds of approximately 59 feet per second.
Step-by-step explanation:
First, we need to convert miles to feet:
40 miles/hour * 5,280 feet/mile = 211,200 feet/hour
Then, we need to convert hours to seconds:
1 hour = 60 minutes/hour * 60 seconds/minute = 3,600 seconds/hour
211,200 feet/hour / 3,600 seconds/hour = 58.67 feet/second
Rounding to the nearest whole number, we get:
59 feet/second
Therefore, ackrabbits can reach speeds of approximately 59 feet per second.
Sandra wants to fill her lunch box with pasta. The lunch box is the shape of a rectangular prism. It has a length of 22 centimeters, a width of 11 centimeters, and a height of 9 centimeters.What is the volume of the lunch box?
A. 2,277 cubic centimeters
B. 2,178 cubic centimeters
C. 2,376 cubic centimeters
D. 2,420 cubic centimeters
Answers
find all points having an x-coordinate of calculator
Answers
To find all points with a specific x-coordinate, you need to have the equation of the curve or the data points representing the graph. If you have an equation, you can substitute the desired x-coordinate into the equation and solve for the corresponding y-coordinate.
If you have data points, you can look for the points that have the specified x-coordinate.
For example, let's say you have the equation of a line: y = 2x + 3. If you want to find all points with an x-coordinate of 5, you can substitute x = 5 into the equation to find y. In this case, y = 2(5) + 3 = 13. So the point (5, 13) has an x-coordinate of 5.
to find points with a specific x-coordinate, you need the equation of the curve or the data points. You can substitute the desired x-coordinate into the equation or look for the points that have the specified x-coordinate in the given data.
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For the function k(x)=-1/16x-8 what is the inverse function of k^-1(x)?
Answers
Answer:
k^-1(x) = -1/128+16x
Domain = ]-infinity,-8[ U ]-8,infinity[
Range = ]-infinity,0[ U ]0,infinity[
Step-by-step explanation:
k(x) = -1/16x = -8
y = -1/16x = -8
x = -1/16y = -8
y = -1/128+16x
k^-1(x) = -1/128+16x
Answer:
D
Step-by-step explanation:
e2021 on god
if a bakery offers, tuna, and vegetable sandwiches on a plain or onion bagel how many possible sandwiches are there?
Answers
Answer:6
6
66
66
6
6
66
6
6
6
6
6
Step-by-step explanation:
6 sandies sir/ma'am have fun
John wrote the equation tim.0 to represent there in decrees er a substance had been tested for minutes Describes be temperature of the substance and the been heated A The temperature initially de trees Cels B. The temperature increased by dores every 0. Based on John's equation, how many minutes does the substances to be heated to reach a temperature of 100 decrees Celtus?
Answers
Answer:
ur english is so bad i can barely discern what ur trying to say and the correct answer is 5
Step-by-step explanation:
The following three points are the locations of important facilities in a transportation network: (26,16), (51,59), and (36,41). The coordinates are in miles. a. Calculate the Euclidean distances (in miles) between each of the three pairs of facilties. (Enter your responses rounded to wo decimal places.) dAB= miles; dBC= miles; dAC= miles. b. Calculate these distances using rectlinear distances. (Enter your responses as integers.) dAB= miles; dBC= miles, dAC= miles.
Answers
a. To calculate the Euclidean distances between the three pairs of facilities, we use the formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) and (x2, y2) are the coordinates of the two points. Calculating the Euclidean distances:
dAB = sqrt((51 - 26)^2 + (59 - 16)^2) ≈ 47.39 miles
dBC = sqrt((36 - 51)^2 + (41 - 59)^2) ≈ 23.53 miles
dAC = sqrt((36 - 26)^2 + (41 - 16)^2) ≈ 25.00 miles
b. To calculate the rectilinear distances, we use the formula:
d = |x2 - x1| + |y2 - y1|
Calculating the rectilinear distances:
dAB = |51 - 26| + |59 - 16| = 25 + 43 = 68 miles
dBC = |36 - 51| + |41 - 59| = 15 + 18 = 33 miles
dAC = |36 - 26| + |41 - 16| = 10 + 25 = 35 miles
Therefore, the Euclidean distances are approximately dAB = 47.39 miles, dBC = 23.53 miles, and dAC = 25.00 miles. The rectilinear distances are dAB = 68 miles, dBC = 33 miles, and dAC = 35 miles.
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