As, we get the same results when we double a number and multiply the number by 2.
So, Yes doubling the number is same as multiplying by 2.
Given, the statement
Doubling is same as multiplying by 2.
we have to answer that, is doubling the same as multiplying by 2.
Let a number be, a
now to double the number, we have to add it to itself or to add it twice
= a + a
= 2a
So, on doubling a number we got 2a
Now, on multiplying a number by 2, we get
= a×2
= 2a
As, we can see that we got the same results when we double a number and multiply the number by 2.
So, Yes doubling the number is same as multiplying by 2.
Hence, Yes doubling the number is same as multiplying by 2.
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What is the magnitude of 3 4j?.
The magnitude of 3 4j is 5. This is because the magnitude of any complex number in the form a + bi is the square root of (a² + b²). In this case, a is 3 and b is 4, and the square root of (3² + 4²) is 5.
The magnitude of a complex number is the length of a line from the origin to the point on the complex plane that represents the number. The magnitude of 3 4j can be calculated using the Pythagorean theorem.
Using the theorem, the magnitude of 3 4j is 5. This is because 3 and 4 are the lengths of the sides of a right triangle and 5 is the length of the hypotenuse. The equation to calculate the magnitude of 3 4j is the square root of 3 squared plus 4 squared. This is written as the square root of (3² + 4²) = 5.
The magnitude of 3 4j is 5. This is because the magnitude of any complex number in the form a + bi is the square root of (a^2 + b^2). In this case, a is 3 and b is 4, and the square root of (3^2 + 4^2) is 5. This means that the magnitude of 3 4j is 5.
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(a) find the critical numbers of (if any), (b) find the open interval(s) on which the function is increasing or decreasing, (c) apply the First Derivative Test to identify all relative extrema, and (d) use a graphing utility to confirm your results.
The critical numbers of the function x³ - 6x² + 15 is 0 and 4
The given function is x³ - 6x² + 15
To find the critical value first we need to find the derivative, then set the derivative f'(x) to zero
The derivative of x³ - 6x² + 15 is
3x³⁻¹ - 2(6)x²⁻¹ = 0
3x² - 12x = 0
3x(x - 4) = 0
3x = 0
x = 0
x - 4 = 0
x = 4
so, x = 0 or 4
Therefore, the critical numbers of the function x³ - 6x² + 15 is 0 and 4
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fail 59 45 67 after running an independence test, can it be concluded that pass/fail rates are dependent on school?
The correct option is B
No, it cannot be concluded that pass/fail rates are dependent on school because the p-value = 0.9373.
What is meant by an alternative hypothesis?In statistical hypothesis testing, the alternative hypothesis is one of the suggested propositions in the hypothesis test. In general, the purpose of a hypothesis test is to demonstrate that, under the given conditions, there is sufficient evidence to support the believability of an alternate hypothesis rather than the test's exclusive statement (null hypothesis). Because it is based on a review of the literature and previous studies, it is usually congruent with the research hypothesis.
Null hypothesis : H₀ : pass/fail rates are independent on school
Alternative Hypothesis : H₁: pass/fail rates are dependent on school
Test Statistic is,
x²stat=∑(O-E)²/E
Here O is the observed frequency and E is the Expected frequency.
E=(Row total× Column total)/Grand total
O E O-E (O-E)² (O-E)² /E
40 41.4184 -1.4184 2.-118 0.0486
33 32.6327 0.3673 0.1349 0.0041
50 48.9490 1.0510 1.1046 0.0226
59 57.5816 1.4184 2.0118 0.0349
45 45.3673 -0.3673 0.1349 0.0030
67 68.0510 -1.0510 1.1046 0.0162
Total=0.1294
Degrees of freedom=(Number of rows-1)×(Number of columns-1)
=(2-1)×(3-1)
=2
p-value=P(x²>x²stat)=P(x²>0.1294)
For 3 degrees of freedom,
P(x²>0.1294)=0.9373
Level of significance α=0.10
As p-value is 0.9373>α:0.10
Fail to reject the null hypothesis.
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one cubic foot will hold 7.5 gallons of water. a rectangle-shaped tank is 10 feet by 8 feet by 8 feet. how many gallons of water will this tank hold?
The rectangle-shaped tank is 10 feet by 8 feet by 8 feet is 4800 gallons of water.
Cubic foot holds 7.5 gallons of water
We need to find the amount of gallons of water can a rectangle-shaped tank is 10 feet by 8 feet by 8 feet.
Vol = L*W*H
10 x 8 x 8
640 cubic feet
1 cubic feet hold 7.5 gallons of water
640 cubic feet hold 7.5 x 640 = 4800
Therefore, the amount of gallons of water can a rectangle-shaped tank is 10 feet by 8 feet by 8 feet is 4800 gallons of water.
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based on the central limit theorem, the sample mean can be used as a good estimator of the population mean, assuming that the sample size, , is sufficiently large.
According to the central limit theorem, the given statement is true.
In the given question we have to check the given statement is true or false.
The given statement is:
"Based on the central limit theorem, the sample mean can be used as a good estimator of the population mean, assuming that the sample size, is sufficiently large."
As we know that the average of set of data is known as a sample mean.
Regardless of the distribution of the population, the central limit theorem states that the distribution of sample means approaches a normal distribution as the sample size increases. The Central Limit Theorem is frequently thought to hold for sample sizes equal to or larger than 30.
So according to the central limit theorem, the given statement is true.
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Point DD is located at (2,1)(2,1) on the coordinate plane. Point DD is reflected over the yy-axis to create point D'D ′ . Point D'D ′ is then reflected over the xx-axis to create point D''D ′′ . What ordered pair describes the location of D''?D ′′ ?
Answer: (-2,-1)
Step-by-step explanation: First, plot the point. Then you go to the left 4 times. Then you plot your new point. Then go down 2 times. Plot your final point.
bethany and joseph are preparing budgets for a new product as well as finalizing plans for the full-scale marketing and manufacturing of the new utilibot. they are in the phase of the new-product development process.
The answer for the given statement is commercialization. Bethany and Joseph are in the commercialization phase of the new-product development process, since they are preparing budgets for a new product as well as finalizing plans for the full-scale marketing and manufacturing of the new UtiliBot.
What is Commercialization?Commercialization is the process of carrying new products or services to the market. Commercialization needs a correctly-developed three-tiered product roll-out and marketing strategy, which includes the ideation phase, the business process, and the stakeholder stage. The launch or commercialization of a new product is contemplated the final stage of new product development (NPD). Commercialization consists of stages such as production, distribution, marketing, sales, and customer support.
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I will give brainlest
The constant of proportionality of the equation y = 1 / 4 x is 1 / 4.
How to solve proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent.
A proportional relationship is one in which two quantities vary directly with each other. We say the variable y varies directly as x if:
y = k x
for some constant k , called the constant of proportionality.
Therefore, let's model the equation to the y = 1 / 4 x .
Therefore, the constant of proportionality is 1 / 4.
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cori races her friend heading south for 9 kilometers, east for 20 kilometers, then south for 6 more kilometers. how far is cori from where she started?
The required distance of Cori from where he started is 35km.
What is meant by distance?Distance is a quantitative or qualitative measurement of the distance between two objects or places. Distance can refer to a physical length or an estimation based on other criteria in physics or everyday usage. Because spatial cognition is a rich source of conceptual metaphors in human thought, the term is also used metaphorically to mean a measurement of the amount of difference between two similar objects or a degree of separation. The concept of a metric space is used to codify most such conceptions of distance, both physical and metaphorical.
Given,
Cori races her friend heading south for 9 kilometers, east for 20 kilometers, then south for 6 more kilometers.
The distance of Cori from starting point=9+20+6
=15+20
=35
Hence, the required distance of Cori from where he started is 35km.
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write the following expression in simplest form. the expression quantity negative two thirds times x minus 6 end quantity minus quantity negative 14 plus one sixth times x end quantity
The simplified form of the expression is, negative five sixths times x plus eight.
What is word problem?
A math word problem is a mathematical question that is stated as one sentence or more and asks students to use their arithmetic skills in a "real-life" situation. Therefore, in order for kids to understand the word problem, they need to be familiar with the terminology that goes along with the mathematical symbols that they are used to.
Given that: quantity negative two thirds times x minus 6 end quantity minus quantity negative 14 plus one sixth times x end quantity
It can be write in mathematical form as,
[tex](-\frac{2}{3}x-6) - (-14+\frac{1}{6}x)[/tex]
Simplifying the parenthesis,
[tex]= -\frac{2}{3}x-6+14-\frac{1}{6}x\\ = 8 - \frac{15}{18}x\\ = 8 - \frac{5}{6}x\\= -\frac{5}{6}x+8[/tex]
Hence, the simplified form of the expression is, negative five sixths times x plus eight
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Can you prove triangles congruent by SAS?.
The triangle ABC and XZY are proved to be congruent by SAS.
Explain the concept of congruence.Congruence of triangles: Two triangles are supposed to be harmonious assuming each of the three comparing sides are equivalent and every one of the three relating angle are equivalent in measure. These triangles can be slides, pivoted, flipped and went to be seemed to be indistinguishable.
By the rule of SAS which means, Two sides are equal thhen the angle between the two sides is also equal (SAS: side, angle, side)
Here in he given triangle,BC=YZ
AC=XZ
∠ACB=∠XZY
By SAS ΔABC≅ΔXYZ
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I went into a tore with a 70% off ign on the door. I found a pair of pant that were originally $49. 99 for $30. 00 I didn't think thi wa 70% off o I had to make ure. What were the real percentage off?
The real percentage off of pant in the store was 39.99% in the store, which was less than the stated 70% off sign present on the door of store.
The percentage off will be calculated by the formula -
Percentage off = change in cost/original cost × 100
Change in cost = original cost - new cost
Change in cost = 49.99 - 30.
Performing subtraction on Right Hand Side of the equation
Change in cost = 19.99
Keep the values in formula for calculation of percentage off -
Percentage off = 19.99/49.99 × 100
Performing division on Right Hand Side of the equation
Percentage = 0.3999 × 100
Performing multiplication on Right Hand Side of the equation
Percentage = 39.99%
Thus, there was 39.99% off.
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what is the probability that the wheel stops on a white slice, given that the wheel stops on a number less than 9?
The probability that the wheel stops on a white slice, given that the wheel stops on a number less than 9 is 1/2.
We have given that
A spinner with 8 equally size slices numbered 1 to 8 and some slices are white and other gray in colour .
Total possible outcomes = 8 = {1,2,3,4,5,6,7,8}
we have to calculate probability that the wheel stops on a white slice, given that the wheel stops on a number less than 9?
let consider two events
A : wheel stops at white
B: wheel stops on white slice and number less than 9
favourable cases for event A = 4
= { 8,4,2,1}
P( wheel stops at white colour)
= favourable cases/total possible outcomes
= 4/8 = 1/2
favourable cases for event B = 4
= {1,2,4,8}
Probability ( wheel stops white slice with numbered less than 9)= white slice with number less than 9/ total slices numbered less than 9
= 4/8 = 1/2
Hence, the required probability is 1/2.
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Complete question:
spinner has 8 equally sized slices numbered from to 1&8 Some are white and some are grey, as shown below. 1 2 3 4 5 6 7 8 . Answer the following questions Write each answer a fraction. The wheel will be spun and will stop on a slice at random (a) What Is the probabllity that the wheel stops on grey slice, glven that the (b) wheel stops on &n even-numbered slice?
a local bbq restaurants offers 2 side dishes with a lunch plate. there are 7 side dishes. how many choices of side dishes does a customer have? note: there is no requirement that the customer chooses different side dishes (i.e. he or she can choose say baked beans twice as their side dish).
The number of choice out of 7 that consumer have are 42.
What is permutation?The term permutation alludes to a numerical computation of the quantity of ways a specific set can be sorted out. Set forth plainly, a change is a word that depicts the quantity of ways things can be requested or organized. With stages, the request for the course of action matters.
According to given data:Number of choices of side dishes does a customer have,
total dishes(n)=7 , r = 2
ⁿP₂
⁷P₂
7×6 = 42
Thus required number of ways are 42.
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unoccupied seats on flights cause airlines to lose revenue. suppose a large airline wants to estimate its average number of unoccupied seats per flight over the past year. to accomplish this, the records of 225 flights are randomly selected and the number of unoccupied seats is noted for each of the sampled flights. the sample mean is 11.2 seats and the sample standard deviation is 4.3 seats. note: if you are using a student's t-distribution, you may assume that the underlying population is normally distributed. (in general, you must first prove that assumption, though.)
The confidence interval for the mean is (10.7485, 11.6515)
Given Data:
n = 225
×= 11.2
s = 4.1
Note that, Population standard deviation([tex]\alpha[/tex]) is unknown. So we use t distribution.
Our aim is to construct a 90% confidence interval.
c = 0.90
[tex]\alpha[/tex] = 1- c = 1- 0.90 = 0.10
[tex]\alpha[/tex]/2 = 0.10/2 = 0.05
Also, d.f = n - 1 = 225 - 1 = 224
t[tex]\alpha[/tex]/2.d.f- = t[tex]\alpha[/tex]/2.n-1 = t0.05,224 = 1.652
( use t table or t calculator to find this value..)
The margin of error is given by
E = t[tex]\alpha[/tex]/2,d.f. * (s / [tex]\sqrt{n}[/tex])
= 1.652 * (4.1/ √225)
= 0.4515
Now , confidence interval for mean(\mu) is given by:
(× - E ) < μ< x + E)
(11.2 - 0.4515) < μ < (11.2 + 0.4515)
10.7485 < μ< 11.6515
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How many Nadhs are needed for the reduction of one oxygen molecule?.
To reduce 1 molecule of oxygen 4 electron are required, which means 4 Nadhs are needed for the reduction of one oxygen molecule
NADH donates one electron to become NADH⁺ + e⁻
So, the number of Nadhs are needed for the reduction of one oxygen molecule is same as the number of electrons needed for the reduction of one oxygen molecule
Water has 2 hydrogen and each hydrogen needs only one electron. Hence, four electrons along with four hydrogen atoms are required to reduce one molecule of oxygen to two molecules of water.
Therefore, To reduce 1 molecule of oxygen 4 electron are required, which means 4 Nadhs are needed for the reduction of one oxygen molecule.
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Exercise statement: the life spans of car batteries are normally distributed, with a mean of 44 months and a standard deviation of 5 months. A car battery is selected at random. Find the probability that the life span of the battery is less than 36 months. What is the shortest life expectancy a car battery can have and still be in the top 5% of life expectancies
The shorted life expectancy to be in top 5% is 52.225
Given that.
Mean = 44
Standard Deviation = 5
a)
Z =36 – 44/5
Z =-8/5
Z =-1.6
P(z<-1.6)=normsdist(-1.6)=0.0548
b)
P(Z > 2) = 0.05
P(Z <=) = 1 -0.05 = 0.95
z=normsinv(0.95)=1.645
shorted life expentancy to be in top 5%=
= 44+1.645*5
Shorted life expentancy to be in top 5% = 52.225
For Minitab use:
Choose Calc > Probability Distributions > Normal.
Select Inverse cumulative probability.
In Mean, enter 44.
In Standard deviation, enter 5.
In Input column, enter Probability=0.95
Hence, The shorted life expectancy to be in top 5% is 52.225.
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What is the unit digit in 3 65 times6 59 times7 71 ))?.
4 is the unit digit in product .
What do Units digits mean?
The digit that goes in the place of one in a number is known as the units digit. It is the number's last digit on the right, for example.For instance, the units digit for 243 is 3 and for 39 it is 9.The Unit Place Digit refers to the digit placed in the one's position of the particular number.Unit digit in 3⁴ = 1
Unit digit in( 3⁴)¹⁶ = 1
Unit digit in 3⁶⁵ = Unit digit in( 3⁴)¹⁶ = 1 * 3 = 3
Unit digit in 6⁵⁹ = 6
Unit digit in 7⁴ = 1
Unit digit in (7⁴)¹⁷ = 1
Unit digit in 7⁷¹ = Unit digit in (7⁴)¹⁷ * 7³ = 1 * 3 = 3
Required digit= Unit digit in ( 3 * 6 * 3 ) = 4
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The complete question is -
What is the unit digit in the product (3⁶⁵ * 6⁵⁹ * 7⁷¹ ) = ?
rank these forces (a through f) on the basis of the magnitude of the torque they apply to the wrench, measured about an axis centered on the bolt.
D > B=E > F > A > C
The ranking is like, D (next to the end of the wrench, B=E (middle of the wrench), F next to the top of the wrench, A (top of the wrench), C (bottom of the wrench)
Given,
Forces;
D > B=E > F > A > C
We have to rank these forces (a through f) on the basis of the magnitude of the torque they apply to the wrench, measured about an axis centered on the bolt
Magnitude of torque;
The ratio of the force's and the lever arm's magnitudes yields the torque's magnitude. Force has a dimensional formula of [M1L1T2], whereas a lever arm has [L]. Consequently, [M1L2T]2 is the dimensional formula for torque.
Here,
The ranking is;
D (next to the end of the wrench, B=E (middle of the wrench), F next to the top of the wrench, A (top of the wrench), C (bottom of the wrench)
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determine the point estimate of the population mean and the margin of error for the given confidence interval. lower bound: 12 upper bound: 20
The required point estimate of the population mean and the margin of error are 16 and 4.
How to solve the point estimate of the population mean and the margin of error?The point estimate is the value of a statistic that estimate the value of the parameter.
According to given data in the question:
Given, lower point =12, upper point = 20
we know that
Population mean(x) = 12+20/2 = 16
And formula for margin o error,
x + E = upper point , x - E = lower point
Then, 16 + E = 20
E = 4
Similarly, 16 - E = 12
E = 4
Hence, population mean and margin of error are 16 and 4 respectively.
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Minimize the objective function p = 45x 48y for the given constraints.
Answer:
1640y
Step-by-step explanation:
the reason is y is known as variables constant is number 48y is a monomial that is why it is 26840y
A freeway has a capacity of 4000 vph. The normal flow rate on the freeway is 3000 vph. An incident blocks the freeway for 5 min. After 5 min, the freeway is opened to full traffic flow. Approximately how long does it take to dissipate the queue that resulted from the blockage? (4pts)
It will take 20 minutes to dissipate the queue that resulted from blockage if
the freeway has the capacity of 4000 vph.
Mean service rate(M) = 4000vph
Mean arrival rate(λ) = 3000vph
Block time duration of queue (r) = 5min
Time taken to dissipate the queue = t
t = (M * r)/(M-λ)
Substitute the given values
t = (4000*5)/(4000-3000)
t = 20000/1000
t = 20minutes.
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solve for the unknown, t
3e^9t = 100
Solving for the unknown variable t in the natural exponent expression 3e^9t = 100 gave
t = 0.3896175How to solve for tThe given expression is given in natural exponent and is solved as follows
3e^9t = 100
dividing through by 3
3e^9t / 3 = 100 / 3
e^9t = 100/3
take natural logarithm of both sides
In e^9t = In (100/3)
9t = In (100/3)
divide through by 9
9t / 9 = 3.5065578 / 9
t = 0.3896175
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MAJOR HELP !!!!! in a butcher shop, each slab of beef weighs6^7 pounds. if there are 6^3 containers filled with beef, how much does all the beef weigh ? Keep your answer in a^b form.
The weight of each beef will be 6⁴
What is an exponent?An exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.
From the information, in a butcher shop, each slab of beef weighs 6^7 pounds and there are 6^3 containers filled with beef, the weight of each beef will be:
= Total pounds / Container
= 6^7 / 6^3.
= 6^(7 - 3).
= 6^4
The weight is 6⁴.
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the local restaurant reported losses of $275 each day for three days. what was the loss for the three days?
Answer:
loss of $825
Step-by-step explanation:
$275 x 3 =$825
Answer: 825
Step-by-step explanation:
Just times 275 by 3 and you have the answer.
What is the slope of a line perpendicular to the line whose equation is 10x-12y=-24.
The slope of a line perpendicular to the line whose equation is 10x - 12y = -24 is 5/6
Given equation,
10x - 12y = -24
This line's parallel has the same slope as this line. Solve for y to alter the equation in order to calculate the slope.
y = mx + b
Where m is the slope and b is the y-intercept.
From the given equation,
10x - 12y = -24
-12y = -10x - 24
y = -10x/-12 + 24/12
y = 5x/6 + 2
Therefore, m = 5/6
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A population of insects increases at a rate of 290+8t+0.6t2 insects per day.
Find the insect population after 5 days, assuming that there are 70 insects at t=0. Round your answer to the nearest whole number.
The insect population after five days is 1645 in population of insects increases at a rate of 290+8t+0.6t2 insects per day.
A total of 290+8t+0.6t2 insects are added to the insect population per day. If there are P insects in the population,
then dP/dt = 290 + 8 + 0.6
since there are P insects at t=0, then
[tex]\int\limits^5_0[/tex][tex]{dP = (290 + 8 + 0.6) (290+8t+0.6t2)dt}[/tex] [after 5 days]
P(5) -V(0) = 290(5)+ 4t2 + t3/5)
P= 290t + 4t2 + t3/5) (5)
Insects: 2+ (5) 3/5 - 200 (0) + 5 (0) - 2+ (0) 3/5 P(5) - 70
= 1450 + 100 + 25-0 P(5)
= 70 + 1575 P(5) = 1645.
In the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations, calculus, also known as infinitesimal calculus or "the calculus of infinitesimals," is the study of continuous change in mathematics.
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In a solar system, two comets pass near the sun, which is located at the origin. Comet E is modeled by quantity y plus 16 end quantity squared over 400 plus x squared over 144 equals 1 and Comet H is modeled by quantity y plus 13 end quantity squared over 144 minus x squared over 25 equals 1 comma where all measurements are in astronomical units.
Part A: What are the vertices for the path of Comet E? Show your work. (4 points)
Part B: Which comet travels closer to the sun? Give evidence to support your answer. (5 points)
Part C: What key feature does the sun represent for both comets? Give evidence to support your answer. (6 points)
The evaluation of the paths of the ellipse and hyperbola are as follows;
Part A: The vertices are; (0, 36), (0, -4)
Part B: Comet H comes closest to the sun
Part C: The location of the Sun is the location of the x-coordinate of the path of both ellipse
What is an ellipse?An ellipse is the locus of a point that moves such that the sum of the distances from two points, known as the focal points, is a constant
Part A: The standard form of the equation of a hyperbola is presented as follows;
[tex]\dfrac{(x - h)^2}{a^2} -\dfrac{(y-k)^2}{b^2} =1[/tex]
Where;
(h, ,k) = The center of the ellipse
a = Vertex to center distance
c = The distance from center to foci
The equation of an ellipse is presented as follows
[tex]\dfrac{(x - h)^2}{a^2} +\dfrac{(y-k)^2}{b^2} =1[/tex]
The vertices of the ellipse are; a + h and k + b
The specified equation is presented as follows;
Comet E = [tex]\dfrac{(y+16)^2}{400} +\dfrac{x^2}{144} =1[/tex]
The vertices for the comet E are;
(0, 20 + 16) = (0, 36) and (0, 16 - 20) = (0, -4)
Part B: Comet H = [tex]\dfrac{(y+13)^2}{144} +\dfrac{x^2}{25} =1[/tex]
The vertex of the comet H = (0, -13 + 12) = (0, -1), and (0, -13 - 12) = (0, -25)
Based on the location of the comet H close to the origin, the comet that comes closest to the Sun is comet H
Part C; The location of the Sun at the origin is the location of the x-coordinate of the center of both comets
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MEASUREMENT
Paula stands on the side of a river and sights the opposite bank at an angle of depression of 7°. If Paula is 5. 5 feet tall,
approximately how wide is the river, to the nearest foot?
Answer:
45
Step-by-step explanation:
Based on the given conditions, formulate: [tex]5.5\div\text{tan}7^o[/tex]
Calculate the approximate value: [tex]\frac{5.5}{0.122785}[/tex]
Calculate: [tex]44.793745[/tex]
Find the closest integer: 45
Answer: 45
Please help me this is geometry
Answer: The last option, [tex]8\sqrt{2}[/tex]
Step-by-step explanation:
When looking at this triangle, there are two things we can note about it right away. First, it's a right triangle so we can use the Pythagorean theorem. Second, the two legs of the triangle are congruent (as shown by the dash lines) so both of them are equal to 8.
Using the Pythagorean theorem we will solve.
a² + b² = c²
(8)² + (8)² = c²
64 + 64 = c²
128 = c²
c = [tex]\sqrt{128}[/tex]
c = [tex]\sqrt{64*2}[/tex]
c = [tex]8\sqrt{2}[/tex]
