Write the equation of the circle centered at ( 7 , 3 ) that passes through ( − 15 , 15 ) .
Answers
So a equation of a circle is:
(x-h)^2 + (y-k)^2 = r^2; (h,k) is center
(x-(7))^2 + (y-(3))^2 = r^2; place in (x,y)
((-15)-(7))^2 + ((15)-(3))^2 = r^2; subtract
(-22)^2 + (12)^2 = r^2; square
484 + 144 = r^2
628 = r^2; square root both sides
r = square root 628; simplify
r (radius) = 2 square root 157
Rewrite the equation with radius:
(x - 7)^2 + (y - 3)^2 = 2 square root 157^2;
Related Questions
Recall that the cigarette industry requires that models in cigarette ads must appear to be at least 25 years old. Also recall that a sample of 50 people is randomly selected at a shopping mall. Each person in the sample is shown a "typical cigarette ad" and is asked to estimate the age of the model in the ad. The p -value for testing H0 versus Ha can be calculated to be 0.0038.
Determine whether H0 would be rejected at each of ? = .10, ? = .05, ? = .01, and ? = .001. (Round your answer to 4 decimal places.)
p-value Reject H0 at ? =
Answers
The p-value for testing H0 (null hypothesis) versus Ha (alternative hypothesis) is 0.0038. We need to determine whether H0 would be rejected at different significance levels: α = 0.10, α = 0.05, α = 0.01, and α = 0.001.
To make the decision, we compare the p-value with the chosen significance level. If the p-value is less than or equal to the significance level, we reject H0. Otherwise, we fail to reject H0.
At α = 0.10: Since the p-value (0.0038) is less than 0.10, we reject H0.
At α = 0.05: Since the p-value (0.0038) is less than 0.05, we reject H0.
At α = 0.01: Since the p-value (0.0038) is greater than 0.01, we fail to reject H0.
At α = 0.001: Since the p-value (0.0038) is greater than 0.001, we fail to reject H0.
In summary:
H0 would be rejected at α = 0.10 and α = 0.05.
H0 would not be rejected at α = 0.01 and α = 0.001.
Please note that the decision to reject or fail to reject the null hypothesis depends on the chosen significance level, and different levels of significance can lead to different conclusions.
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The following equation describes the motion of a certain mass connected to a spring, with viscous friction on the surface 3ÿ + 18y + 102y = f(t) where f(t) is an applied force. Suppose that f(t) = 0 for t <0 and f(t) = 10 for t≥ 0. a. Plot y(t) for y(0) = y(0) = 0. b. Plot y(t) for y(0) = 0 and y(0) =
Answers
The plot of y(t) will show how the mass oscillates with time, starting from the equilibrium position and gradually coming to rest due to the damping effect of the friction.
The given equation represents the motion of a mass connected to a spring with viscous friction. To plot the displacement, y(t), we need to solve the differential equation. With initial conditions y(0) = 0, we can find the solution using the Laplace transform. After solving the equation, we can plot y(t) for t < 0 and t ≥ 0 separately. For t < 0, the applied force, f(t), is zero, so the mass will not experience any external force and will remain at rest. For t ≥ 0, the applied force is 10, and the mass will respond to this force and undergo oscillatory motion around the equilibrium position.
To solve the given differential equation, we can start by finding the characteristic equation by setting the coefficients of y, its derivative, and its second derivative to zero:
s^2 + 18s + 102 = 0.
Solving this quadratic equation gives us the roots s1 = -3 + 3i and s2 = -3 - 3i. These complex roots indicate that the mass will undergo damped oscillations.
Using the Laplace transform, we can solve the differential equation and obtain the expression for Y(s), the Laplace transform of y(t):
(s^2 + 18s + 102)Y(s) = F(s),
where F(s) is the Laplace transform of f(t). Since f(t) = 10 for t ≥ 0, its Laplace transform is F(s) = 10/s.
Solving for Y(s) gives us:
Y(s) = 10 / [(s^2 + 18s + 102)].
To find y(t), we need to inverse Laplace transform Y(s). Using partial fraction decomposition, we can express Y(s) as:
Y(s) = A / (s - s1) + B / (s - s2),
where A and B are constants to be determined. After finding A and B, we can inverse Laplace transform Y(s) to obtain y(t).
With the given initial condition y(0) = 0, we can solve for A and B by setting up equations using the initial value theorem:
A / (s1 - s1) + B / (s1 - s2) = 0,
A / (s2 - s1) + B / (s2 - s2) = 0.
Solving these equations will give us the values of A and B. Finally, we can substitute these values back into the inverse Laplace transform of Y(s) to obtain y(t).
For t < 0, since the applied force f(t) is zero, the mass will not experience any external force. Therefore, y(t) will remain at its initial position, y(0) = 0.
For t ≥ 0, the applied force f(t) is 10, and the mass will respond to this force and undergo oscillatory motion around the equilibrium position. The displacement, y(t), will depend on the properties of the mass, the spring, and the viscous friction. The plot of y(t) will show how the mass oscillates with time, starting from the equilibrium position and gradually coming to rest due to the damping effect of the friction.
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75 people to 25 people
Answers
Answer: GCD 25, As A Reduced Fraction 3/1
Step-by-step explanation: 75 People To 25 People, Is The Same As 75 To 25. So, The Answer 25. The Fraction Is 3/1 Because 75/25 Is Simplified To That Fraction.
please help me in this question.(law of indices)
Answers
Answer:
X^5
Step-by-step explanation:
Note: 1/X^-3 = 1÷X^-3=1÷ (1÷ X^3)= 1×X^3=X^3
Two lines intersecting at a right angle
A. Form a line
B.are parallel
C. are perpendicular
D. Form a ray
Answers
Answer:
420 69
Step-by-step explanation:
620 +90 = 42069
Answer: C. are perpendicular
Step-by-step explanation:
I took the test and got it right
Solve for the value of t.
Answer: t =
(6t)
60
Answers
Answer:
10 is the answer
Step-by-step explanation:
6 times what equals 60?
10
The difference of a number and six is the same as five times the sum of a number and two what is the number
Answers
the difference of x and 6 is x - 6 and
5 times the sum of x and 2 is 5(x + 2)
Equate both expressions
5(x + 2) = x - 6 ← distribute left side
5x + 10 = x - 6 ( subtract x from both sides )
4x + 10 = - 6 ( subtract 10 from both sides )
4x = - 16 ( divide both sides by 4 )
x = - 4 → A
Kirk and martin, two experimental physicists, want to change the diameter of a laser beam while keeping its rays propagating parallel
Answers
Kirk and martin, two experimental physicists, want to change the diameter of a laser beam while keeping its rays propagating parallel so the value of distance l is l = fs - fa.
In a partly ionized plasma with several species, we investigate the propagation of electromagnetic waves (or incompressible waves with little thermal pressure) through the magnetic field. Due of variances in mass and density, each species responds to and hence influences electromagnetic field disturbances differently.
For the first lens , ray of light from distant object are parallel , so image will formed at the focal length of first lens.
For second lens,
object distance (u) = fa + l
image distance (v) = ∞
By lens formula,
1/v - 1/u = -1/fs
u = fs
fa + l = fs
l = fs - fa
Collisions between all of the species complicate the process even further. Based on a multi-fluid treatment and Faraday's and Ampere's laws, including the displacement current, a linear analysis is used to derive the dispersion relation of parallel propagation covering a wide range of frequencies, from magnetohydrodynamics (MHD) waves to light waves, with an arbitrary combination of multiple positively charged species, negatively charged species, and neutral species.
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Complete question:
Kirk and martin, two experimental physicists, want to change the diameter of a laser beam while keeping its rays propagating parallel.
For this set up to work, what must be the distance l ?
Solve for x
a. 25
b. 180
c. 120
d. 20
Answers
Answer:
25
Step-by-step explanation:
2x+10 + 4x+20= 180(linear pair)
6x+30 = 180
6x= 150
x= 25
Describe the sampling distribution of p. Assume the size of the population is 25,000 n=500, p=0.763 Describe the shape of the sampling distribution of P. Choose the correct answer below. B O A. The shape of the sampling distribution of p is approximately normal because ns0.05N and np(1-P) < 10. The shape of the sampling distribution of Dis approximately normal because ns0.05N and np(1-P) 2 10. OC. The shape of the sampling distribution of p is not normal because ns0.05N and np(1 - p) < 10. OD The shape of the sampling distribution of is not normal because ns0.05N and np(1 - p)2 10. Determine the mean of the sampling distribution of P. HA = 0.763 (Round to three decimal places as needed.)
Answers
The shape of the sampling distribution of p is approximately normal because n/N ≤ 0.05 and np(1 - p) < 10.
The mean of the sampling distribution of p is 0.763.
The shape of the sampling distribution of p is approximately normal if the sample size (n) is large enough compared to the population size (N) and if np(1 - p) is greater than or equal to 10.
We have n = 500 and N = 25,000, so we can check if np(1 - p) is greater than or equal to 10.
np(1 - p) = 500×0.763 × (1 - 0.763)
= 500 × 0.763 × 0.237
= 90.305.
Since np(1 - p) is greater than 10.
The shape of the sampling distribution of p is approximately normal because n/N ≤ 0.05 and np(1 - p) < 10.
2. The mean of the sampling distribution of p is equal to the population proportion, which is denoted by p.
The population proportion is given as p = 0.763.
Therefore, the mean of the sampling distribution of p is also 0.763.
On average, the sample proportions calculated from different samples of the same size will be centered around the population proportion.
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5. Sherman bought 17
items at the dollar store,
and used a coupon for a
discount. If his total after
the coupon was $16.15,
what percent discount did
he get?
Answers
Answer:
Step-by-step explanation: if you subtract 17 from 16.15 you will get your answer of 0.85 so if you turn that to a percentage you will get .00085
Which statement is true about the function?
Answers
In Exercises 1-16 a set of objects is given, together with operations of addition and scalar multiplication. Determine which sets are vector spaces under the given operations. For those that are not vector spaces, list all axioms that fail to hold. The set of all triples of real numbers (x, y, z) with the operations 1. (x, y, 2) + (x', y', z') = (x + x', y +y', z+2) k(x, y, z) = (kx, y, z)
Answers
The given set of objects is a vector space under the given operations.
Given set of objects is all triples of real numbers (x, y, z) with the operations
1. (x, y, 2) + (x', y', z') = (x + x', y +y', z+2) k(x, y, z) = (kx, y, z)
To determine which sets are vector spaces under the given operations, we need to check if it satisfies the axioms of vector space.
A vector space is a set of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars in this context.
1. Closure under addition The first condition states that for any u and v in V, the sum u + v is also in V.
If we let V be the set of all triples of real numbers (x, y, z), then we need to show that (x, y, 2) + (x', y', z') = (x + x', y +y', z+2) satisfies this condition.(x, y, 2) + (x', y', z') = (x + x', y +y', z+2) is closed under addition since the sum of two triples of real numbers (x, y, z) is also a triple of real numbers (x + x', y +y', z+2) and is in the set V.
Thus, the first condition holds.
2. Associativity of addition The second condition states that for any u, v, and w in V, the sum (u + v) + w is equal to u + (v + w). Associativity of addition can be checked as follows:
(x, y, 2) + [(x', y', z') + (x", y", z")] = (x, y, 2) + (x' + x", y' + y", z' + z") [(x, y, 2) + (x', y', z')] + (x", y", z") = (x + x', y + y', z + 2) + (x", y", z") We can see that the left and right-hand sides are equal.
Thus, the second condition holds.
3. Commutativity of addition The third condition states that for any u and v in V, the sum u + v is equal to v + u.
Commutativity of addition can be checked as follows:
(x, y, 2) + (x', y', z') = (x + x', y +y', z+2) (x', y', z') + (x, y, 2) = (x' + x, y' + y, z' + 2) We can see that the left and right-hand sides are equal.
Thus, the third condition holds.
4. Additive identity The fourth condition states that there exists a vector 0 in V such that u + 0 = u for any u in V.
In this case, we have (x, y, 2) + (0, 0, -2) = (x, y, 0).
Thus, the fourth condition holds.
5. Additive inverse The fifth condition states that for any u in V, there exists a vector -u in V such that u + (-u) = 0. Let u = (x, y, 2), then -u = (-x, -y, -2) and u + (-u) = (x - x, y - y, 2 - 2) = (0, 0, 0).
Thus, the fifth condition holds.
6. Closure under scalar multiplication The sixth condition states that for any u in V and any scalar k, the product k.u is also in V.
If we let V be the set of all triples of real numbers (x, y, z), then we need to show that k(x, y, z) = (kx, y, z) satisfies this condition.
k(x, y, z) = (kx, y, z) is closed under scalar multiplication since the product of a scalar k and a triple of real numbers (x, y, z) is also a triple of real numbers (kx, y, z) and is in the set V.
Thus, the sixth condition holds.
7. Distributivity of scalar multiplication over vector addition The seventh condition states that for any u and v in V and any scalar k, k.(u + v) = k.u + k.v.
Distributivity of scalar multiplication over vector addition can be checked as follows:
k [(x, y, 2) + (x', y', z')] = k (x + x', y + y', z + 2 + z') k(x, y, 2) + k(x', y', z') = (kx, y, z) + (kx', y', z')
We can see that the left and right-hand sides are equal.
Thus, the seventh condition holds.
8. Distributivity of scalar multiplication over scalar addition The eighth condition states that for any u in V and any scalars k and l, (k + l).u = k.u + l.u. Distributivity of scalar multiplication over scalar addition can be checked as follows:
(k + l)(x, y, 2) = (kx + lx, y, 2) k(x, y, 2) + l(x, y, 2) = (kx, y, 2) + (lx, y, 2)
We can see that the left and right-hand sides are equal.
Thus, the eighth condition holds.
9. Multiplicative identity The ninth condition states that for any u in V, 1.
u = u. 1(x, y, 2) = (x, y, 2)
We can see that the left and right-hand sides are equal.
Thus, the ninth condition holds.
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Write an equation for a line given a slope of 2/3 through the pt (-6,10).
Answers
Equation for a line given a slope of 2/3 through the pt (-6,10) is y = \(\frac{2}{3}\) x + 16.
How do I find the slope and intercept?A line's steepness may be determined by looking at its slope. Slope is computed mathematically as "rise over run" (change in y divided by change in x).Y = mx + b, where m denotes the slope and b the y-intercept, is how the equation of the line is expressed in the slope-intercept form. We can see that the slope of the line in our equation, y = 3 x + 5, is 3.The values of the slope and y-intercept provide details on the relationship between the two variables, x and y. The slope shows how quickly y changes for every unit change in x. When the x-value is 0, the y-intercept shows the y-value.Given data :
The equation of a line in point slope form is
y - y1 = m ( x - x1 )
where m represents the slope and ( x1, y1 ) a point on the line here
m = 2 / 3 and ( x1, y1 ) = ( -6, 10)
y - 10 = \(\frac{2}{3}\) ( x - - 6 )
y - 10 = \(\frac{2}{3}\) ( x + 6 )
y = \(\frac{2}{3}\) ( x + 6 ) + 10
y = \(\frac{2}{3}\) x + 16
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Mary’s cat lost two pounds in five weeks. Which rational number does not show the average change in the cat’s weight?
A. −(2/5)
B. −2/5
C. −2/−5
D. 2/-5
Answers
Answer:B
Step-by-step explanation:
Answer:
The answer is C. -2/-5
Step-by-step explanation:
I tried B, but it was incorrect, so then I tried C, turns out C was correct my dudes.
ROOFTOP Lucia is 5.5 feet tall. She is standing on the roof of a building that is 80 feet tall. She spots a fountain at ground level that she knows to be 122 feet away from the base of the building. What is the measure of the angle of depression formed by Lucia’s horizontal line of sight and her line of sight to the fountain? Round your answer to the nearest degree.
Answers
Answer:
Step-by-step explanation:
rtet
The function f is defined by the following rule
f(x)=2x-1
Complete the function table
Answers
The table can be filled as,
-7
-5
-1
1
9
The volume of this cone is 643,072 cubic inches. What is the radius of this cone?
Use ≈ 3.14 and round your answer to the nearest hundredth.
Answers
The radius of the cone is 783.84/√h
What is volume of a cone?A cone is the surface traced by a moving straight line (the generatrix) that always passes through a fixed point (the vertex).
Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.
The volume of a cone is expressed as;
V = 1/3πr²h
643072 × 3 = 3.14 × r²h
r²h = 614400
r² = 614400/h
r = 783.84/√h
therefore the radius of the cone is 783.84/√h
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Consider the function f(x) = x2 - 4x + 8 on the interval 0, 4. Verify that this function satisfies the three hypotheses of Rolle's Theorem on the inverval f(x) is f(x) is and f(0) on [0, 4] on (0, 4) f(4) Then by Rolle's theorem, there exists at least one value c such that f'(c) = 0. Find all such values c and enter them as a comma-separated list. Values of c =: (1 point) Consider the function graphed below. P n ? Does this function satisfy the hypotheses of the Mean Value Theorem on the interval a, b ? Does it satisfy the conclusion?? f(b) f(a)2 At what point c is f'(c) b - a
Answers
Verifying that this function satisfies the three hypotheses of Rolle's Theorem on the inverval f(x) is f(x) is and f(0) on [0, 4] on (0, 4) f(4) Then by Rolle's theorem, there exists at least one value c = 2 such that f'(c) = 0.
Given:
Consider the function f(x) = x2 - 4x + 8 on the interval 0, 4. Verify that this function satisfies the three hypotheses of Rolle's Theorem on the inverval f(x) is f(x) is and f(0) on [0, 4] on (0, 4) f(4) Then by Rolle's theorem, there exists at least one value c such that f'(c) = 0.
f(x)=x^2−4x+8, [0,4]
when, x = 0
f(x) = x^2 -4x +8
f(0) = y = 0 - 0 + 8 = 8
when, x=4
f(5) = y = 16 - 16+8 =
thus, we have 2 points (0, 8) ; (4, 8)
slope,m = {8-(8)} / {4-0} = 0
hence, we have to calculate all the points,x where 0<x<8 and slope=0
f '(x) = 2x - 4 = 0
or, f '(c) = 2c - 4 = 0
c = 4/2 =2 ( 0<x<4)
hence, the there is only one solution c=2 which satisfies Rolle's theorem.
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Over the past 4 years, a customer's fixed income portfolio value has dropped by 5%. During the same period, the Consumer Price Index has dropped by 2%. Based on these facts, which statement is TRUE?
Answers
The statement that is TRUE based on the given facts is that the customer's fixed income portfolio has experienced a greater decline in value than the decrease in the Consumer Price Index (CPI).
To elaborate, the customer's fixed income portfolio has dropped by 5% over the past 4 years. This means that the value of their portfolio has decreased by 5% compared to its initial value. On the other hand, the Consumer Price Index (CPI) has dropped by 2% during the same period. The CPI is a measure of inflation and represents the average change in prices of goods and services.
Since the customer's portfolio has experienced a decline of 5%, which is larger than the 2% drop in the CPI, it indicates that the value of their portfolio has decreased at a higher rate than the general decrease in prices. In other words, the purchasing power of their portfolio has been eroded to a greater extent than the overall decrease in the cost of goods and services measured by the CPI.
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Santa lost 7 cents on Monday and 12 cents on Tuesday. What was the effect on Santa's piggy bank?
Answers
Answer:
I believe it's that Santa loses 19 cents total.
Santa lost 7 cents on Monday and 12 cents on Tuesday. 7 + 12 = 19.
An Amtrak official obtains data on a particular day concerning the length of time (in minutes) that the metroliners leaving New York take to reach Philadelphia, with the following results:
93 89 91 87 91 89
Find the sample variance.
a. 3.6
b. 5.6
c. 6.8
d. 7.6
e. 4.4
Answers
The sample variance for the given data is 4.4 minutes. This corresponds to option e. in the list of choices provided.
The sample variance is a measure of how much the individual data points in a sample vary from the mean.
It is calculated by finding the average of the squared differences between each data point and the mean.
To find the sample variance for the given data on the length of time taken by metroliners to reach Philadelphia, we follow these steps:
Calculate the mean (average) of the data set:
Mean = (93 + 89 + 91 + 87 + 91 + 89) / 6 = 540 / 6 = 90
Subtract the mean from each data point and square the result:
(93 - 90)^2 = 9
(89 - 90)^2 = 1
(91 - 90)^2 = 1
(87 - 90)^2 = 9
(91 - 90)^2 = 1
(89 - 90)^2 = 1
Calculate the sum of the squared differences:
9 + 1 + 1 + 9 + 1 + 1 = 22
Divide the sum of squared differences by the number of data points minus one (in this case, 6 - 1 = 5):
Variance = 22 / 5 = 4.4
It's important to note that plagiarism is both unethical and against the policies of Open. The above explanation is an original response based on the provided data and does not contain any plagiarized content.
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#1 )) . which inequality best represents the range of the graphed exponential function ?
a . y<0
b . y<-1
c . x<0
d . x<-1
#2 )) . which function is best represented by this graph ?
a . f(x)= ^2-1
b . f(x)= ^2+1
c . f(x)= -x^2+x-1
d . f(x)= -x^2+1
(( PLEASE HELP , I HAVE MORE QUESTIONS TO POST FEEL FREE TO HELP )) .
Answers
The range of the graphed exponential function is b . y < -1.
The function which is best represented by the graph is f(x) = -x² + 1.
1) Given an exponential function.
We have to find the range of the function.
The range of the function is the set of all the y values for the x values where the function is defined.
From the graph, it is clear that for any x values, the y values are all either -1 or numbers less than -1.
So the range is y < -1.
2) Given a graph of a parabola opens downwards.
So the function will be quadratic. That is, the highest degree of the variable will be 2.
For a function of the form, (parent function), y = -x², the parabola passes through the point (0, 0), which will be the vertex and the parabola is opened downwards.
Here vertex is (0, 1).
That is the parabola is shifted up to 1 unit.
A function f(x) after the translation to k units up becomes f(x) + d.
So here since the original function is shifted up 1 units, it becomes,
f(x) = -x² + 1
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plsss help if you actually truly know this
Answers
Answer: x=25
Step-by-step explanation: x/5 - 3=2
Multiply each side by 5x - 15=10Then add 15X=25Answer:
x = 25
Step-by-step explanation:
Now we have to,
→ Find the required value of x.
The equation is,
→ (x/5) - 3 = 2
Then the value of x will be,
→ (x/5) - 3 = 2
→ x/5 = 2 + 3
→ x/5 = 5
→ x = 5 × 5
→ [ x = 25 ]
Hence, the value of x is 25.
Consider the following three points: A = (-3, 10, 19) B = (19, 0, 6) C=(5, 5, -21) Which point is closest to the yz-plane? What is the distance from the yz-plane to this point? Which point is the fart
Answers
i.)
We say that Point A (-3, 10, 19) is closest to the yz-plane,
ii.) the distance from the yz-plane to this point is 3 units.
iii.) The farthest Point will be point B (19, 0, 6) because it has the largest absolute value.
How do we calculate?for Point A = (-3, 10, 19):Distance from yz-plane = |x-coordinate of A| = |-3| = 3.
for Point B = (19, 0, 6):This point is not the closest point to the yz-plane because the x-coordinate of point B is non-zero and is also not on the yz-plane.
for Point C = (5, 5, -21):Distance from yz-plane = |x-coordinate of C| = |5| = 5.
In conclusion Point A (-3, 10, 19) is closest to the yz-plane as it has distance of 3 units.
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what is 32 divided by 0.06?
Answers
Answer:
800
Step-by-step explanation:
hopefully i’m right
If you buy a radio that cost $860 and sales tax is 6%. Find the total price you would pay.
Answers
Answer: $911.60
Step-by-step explanation: 860 time 6% is 911.60
Maria decorated her notebook with 44 rectangular stickers. Each sticker was \frac{1}{2}
2
1
inch wide and \frac{11}{16}
16
11
inch long.
Answers
Answer:
\(A=\dfrac{121}{8}\ in^2\)
Step-by-step explanation:
There are 44 rectangular stickers
Length of each sticker= (1/2) inch
The width of each sticker = (11/16) inch
We need to find the area of the all stickers. The area of a rectangle is given by :
\(A=l\times b\\\\A=44\times \dfrac{1}{2}\times \dfrac{11}{16}\\A=\dfrac{121}{8}\ in^2\)
So, the area of all stickers is equal to \(\dfrac{121}{8}\ in^2\).
(20 %) ū and ū are both nonzero n dimensional vectors. If u and ü have the same length, is it true that the projection of į onto ū and the projection of v onto ū always have the same length? If ū and 7 do not have the same length, is it possible that the projection of u onto ū and the projection of ū onto ü have the same length? You should explain your answers to get full credit.
Answers
If ū and ū have the same length, then the projection of u onto ū and the projection of ū onto ū will always have the same length. This is because the projection of a vector onto another vector is simply the vector that is parallel to the first vector and has the same length as the first vector.
If the two vectors have the same length, then the projection of one vector onto the other will also have the same length. If ū and ū do not have the same length, then it is possible for the projection of u onto ū and the projection of ū onto ū to have the same length.
This is because the projection of a vector onto another vector is not necessarily the same length as the first vector. If the two vectors are not parallel, then the projection of one vector onto the other will be shorter than the first vector. However, if the two vectors are perpendicular, then the projection of one vector onto the other will be the same length as the first vector.
The projection of a vector onto another vector is a vector that is parallel to the first vector and has the same length as the first vector. The projection of u onto ū can be calculated using the following formula:
proj_ū(u) = (u ⋅ ū) / ||ū||^2 * ū
where u ⋅ ū is the dot product of u and ū, and ||ū|| is the magnitude of ū. The projection of ū onto u can be calculated using the following formula:
proj_u(ū) = (ū ⋅ u) / ||u||^2 * u
where ū ⋅ u is the dot product of ū and u, and ||u|| is the magnitude of u. If ū and ū have the same length, then ||ū|| = ||u||. This means that the two formulas for the projection are the same, and the projection of u onto ū will have the same length as the projection of ū onto u.
If ū and ū do not have the same length, then ||ū|| ≠ ||u||. This means that the two formulas for the projection are not the same, and the projection of u onto ū may or may not have the same length as the projection of ū onto u. If the two vectors are not parallel, then the projection of one vector onto the other will be shorter than the first vector. However, if the two vectors are perpendicular, then the projection of one vector onto the other will be the same length as the first vector.
Learn more about vectors here:- brainly.com/question/24256726
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A park is in the shape of a right triangle with an area of 294 yd². The shortest side of the park (one of the legs) is 21 yds. The city council would like to add a path along the longest side of the park (the hypotenuse). How long would the path be? Show your work. Don’t forget to label your answer.
Answers
Answer: The length of the path along the longest side of the park would be 35 yds.
Step-by-step explanation: Area of triangle = (1/2) x base x height294 = (1/2) x 21 x heightMultiplying both sides by 2 and dividing by 21, we get:height = 28So the other leg of the triangle is 28 yds.Now we can use the Pythagorean theorem to find the length of the hypotenuse:hypotenuse² = shortest side² + other leg²hypotenuse² = 21² + 28²hypotenuse² = 441 + 784hypotenuse² = 1225Taking the square root of both sides, we get:hypotenuse = 35Therefore, the length of the path along the longest side of the park would be 35 yds.