Answer:
some particle traveled through empty spaces between atoms and some particles were deflected by electrons
Step-by-step explanation:
The motion of particles will be
some particle traveled through empty spaces between atoms and some particles were deflected by electrons.
What was Rutherford Experiment?The vast majority of the alpha particles simply passed through the gold foil.Some of the alpha particles had a slight angle of deflection.Only a tiny fraction of the alpha particles rebounded.So, the observation made the stamement
He came to the conclusion that the majority of space in an atom was unoccupied since there was very little alpha particle deflection.The fact that very few particles were diverted from their course led him to the further conclusion that positive charge takes up very little space in an atom.Then, motion of particles will be
some particle traveled through empty spaces between atoms and some particles were deflected by electrons.
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What is the 50th term of the arithmetic sequence having u(subscript)1 = -2 and d = 5
Answer:
243
Step-by-step explanation:
The general term for this arithmetic sequence is:
a(n) = -2 + 5(n - 1).
Then a(50) = -2 + 5(49) = 243
Find the area of the region enclosed by the curves x=3y^2, x=0, and y=2
Answer:
8
Step-by-step explanation:
Hello,
[tex]x=3y^2<=>y=\sqrt{\dfrac{x}{3}} \ \ for \ x\geq 0[/tex]
And for y = 2, x = 3 * 2 * 2 = 12 so first, let's compute
[tex]\displaystyle \int\limits^{12}_0 {\sqrt{\dfrac{x}{3}}} \, dx =\dfrac{1}{\sqrt{3}} \int\limits^{12}_0 {\sqrt{x}} \, dx\\\\=\dfrac{1}{\sqrt{3}} \left[ \dfrac{2}{3}x^{3/2}\right]_0^{12}\\\\=\dfrac{1}{\sqrt{3}} *\dfrac{2}{3}*12*\sqrt{12}\\\\=\dfrac{2*12*2*\sqrt{3}}{3*\sqrt{3}}\\\\=2*4*2=16[/tex]
The area which is asked is 12*2 - 16 = 24 - 16 = 8
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Using integrals, it is found that the area of the region enclosed by the curves in the interval is of 27 units squared.
In this problem:
The curve is [tex]x = 3y^2[/tex], hence the integral is relative to y.The lower limit is when x = 0, hence [tex]0 = 3y^2 \rightarrow y = 0[/tex].The upper limit is when y = 2.Then, the integral for the area is:
[tex]A = \int_{0}^{2} 3y^2 dy[/tex]
[tex]A = y^3|_{y = 0}^{y = 3}[/tex]
[tex]A = 3^3 - 0^3[/tex]
[tex]A = 27[/tex]
The area of the region enclosed by the curves in the interval is of 27 units squared.
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Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. After 9 hours of burning, a candle has a height of 25.4 centimeters. After 23 hours of burning, its height is 19.8 centimeters. What is the height of the candle after 22 hours?
Answer:
Suppose that the height (in centimeters) of a candle is a linear function of
the amount of time (in hours) it has been burning.
After 11 hours of burning, a candle has a height of 23.4 centimeters.
After 30 hours of burning, its height is 12 centimeters.
What is the height of the candle after 13 hours?
:
Assign the given values as follows:
x1 = 11; y1 = 23.4
x2 = 30; y2 = 12
:
Find the slope using: m = %28y2-y1%29%2F%28x2-x1%29
m = %2812-23.4%29%2F%2830-11%29 = %28-11.4%29%2F19
:
Find the equation using the point/slope formula: y - y1 = m(x - x1)
y - 23.4 = -11.4%2F19(x - 11)
y - 23.4 = -11.4%2F19x + 125.4%2F19
y = -11.4%2F19x + 125.4%2F19 + 23.4
y = -11.4%2F19x + 125.4%2F19 + 23.4
y = -11.4%2F19x + 125.4%2F19 + 444.6%2F19
y = -11.4%2F19x + 570%2F19
y = -11.4%2F19x + 30, is the equation
:
What is the height of the candle after 13 hours?
x = 13
y = -11.4%2F19(13) + 30
y = -148.2%2F19 + 30
y = -7.8 + 30
y = 22.2 cm after 13 hrs
In designing an experiment involving a treatment applied to 4 test subjects, researchers plan to use a simple random sample of 4 subjects selected from a pool of 31 available subjects. (Recall that with a simple random sample, all samples of the same size have the same chance of being selected.) Answer the question below.
What is the probability of each simple random sample in thiscase?
Answer:
The probability is [tex]p(n ) = 3.18*10^{-5}[/tex]
Step-by-step explanation:
From the question we are told that
The population size is N = 31
The sample size n = 4
Generally the number of way by which the n can be selected from N is mathematically represented as
[tex]\left N} \atop {}} \right. C_n = \frac{N! }{(N-n)!n!}[/tex]
=> [tex]\left 31} \atop {}} \right. C_4 = \frac{31! }{(31-4)!4!}[/tex]
=> [tex]\left 31} \atop {}} \right. C_4 = \frac{31 * 30 * 29 * 28* 27! }{27! * 4*3 * 2 * 1 }[/tex]
=> [tex]\left 31} \atop {}} \right. C_4 = \frac{ 755160 }{ 24}[/tex]
=> [tex]\left 31} \atop {}} \right. C_4 = 31465[/tex]
The number of ways of selecting a particular sample size is is [tex]k = 1[/tex]
Therefore the probability of each simple random sample in this case is mathematically evaluated as
[tex]p(n ) = \frac{1}{31465}[/tex]
[tex]p(n ) = 3.18*10^{-5}[/tex]
Residents of four cities are able to vote in an upcoming regional election. A newspaper recently conducted a survey to gauge support for each of the two candidates. The results of the poll are shown in the two-way frequency table below.
Answer:
3 only
Step-by-step explanation:
Consider the statement, "The two cities with the highest number of respondents, both show more support for candidate A." In the total column, the two highest number of respondents are 471 and 463 which represent Carsonville and Appleton. For Carsonville, the number of respondents who prefer candidate A is 205, which is less than the number of respondents who prefer candidate B, 266. Therefore, this statement is not true.
Consider the statement, "The number of people who support candidate B in Carsonville is twice the number of people who support candidate B in New Thomas." In the table, the number of people who support candidate B in Carsonville is observed to be 266 and the number of people who support candidate B in New Thomas is 138. Since 266 is not equal to twice 138, this statement is not true.
Consider the statement, "More residents of Center City responded to the poll than the number who responded from New Thomas." In the total column, it can be observed that 350 people responded to the poll in Center City and 318 people responded to the poll in New Thomas. Since, 350 is greater than 318, this statement is true.
Consider the statement, "Overall, more residents support candidate A than candidate B." The bottom row of the table represents the total number of responses for each candidate. The number of people supporting candidate A is 797, which is less than the number of people supporting candidate B, 805. So, this statement is not true.
Therefore, the true statement is III only.
More residents of the center city responded to the pole than the number who responded from New Thomas, which is the only correct option. Option B. is correct.
Data given in the table shows the data of elections between two candidates among the different cities.
What is Statistic?
Statistics is the study of mathematics that deals with relations between comprehensive data.
I.The two cities with the highest number of respondents both show more support for candidate A. This statement is false because carsonville is the second highest support for A but it does not show more support for candidate A.
II.The number of people who support candidate B in Carsonville is twice the number of people who support candidate B in New Thomas. It is false
III. More residents of Center City responded to the pole than the number who responded from New Thomas. It is true.
IV. Overall, more residents support candidate A than candidate B. it is also false.
Thus, more residents of the center city responded to the pole than the number who responded from New Thomas, which is the only correct option. Option B. is correct.
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the angle theta is in the second quadrant and cos theta = -2/√29 determine possible coordinates for point P on the terminal arm of theta a. (2,5) b. (-2,√29) c. (-5,2) d. (-2,5)
[tex] \cos(\theta)=-\frac{2}{\sqrt{29}}[/tex] and $\theta$ lies in $2^{\text{th}}$ quadrant.
where, $x-$ coordinate is negative, and $y-$ coordinate is positive
so it can't a.
now, cosine means, side adjacent over the hypotenuse, in Cartesian plane, that will be $x-$ coordinate over the distance from origin.
Assume the triangle , with base $2$ units and hypotenuse $\sqrt{29}$ and it's in second quadrant. (so [tex] \cos(\theta)=-\frac{2}{\sqrt{29}}[/tex])
now, the leftmost point on $x-$ axis is , obviously $(-2,0)$
and by Pythagoras theorem, we can find the perpendicular side, that will be $y^2=(\sqrt{29})^2-(2)^2\implies y=5$
so the coordinates of the upper vertex is $(-2,5)$, each point lying on this "ray" should have equal ratio of respective coordinates. i.e. $\frac25=\left|\frac xy\right| $
and it should lie on second quadrant, so $x<0 \, y>0$
Option d satisfies this.
1+2x=6x+11 PLS HELP URGENT
Answer:
x = -5/2
Step-by-step explanation:
1+2x=6x+11
Subtract 2x from each side
1+2x-2x=6x-2x+11
1 = 4x+11
Subtract 11 from each side
1-11 = 4x
-10 =4x
Divide by 4
-10/4 = 4x/4
-5/2 =x
Answer:
[tex]\boxed{x=-\frac{5}{2}}\\[/tex]
Step-by-step explanation:
To begin, get the variable on one side of the equation - preferably the left for standard solution notation (for this equation, it is easier to place it on the right side to avoid negative values). Do this by subtracting 2x from both sides of the equation. Then, subtract 11. Finally, divide by 4 and get the answer in terms of x.
1 + 2x = 6x + 11
1 = 4x + 11
-10 = 4x
[tex]\boxed{x=-\frac{5}{2}}[/tex]
Quadrilateral RSTV is dilated with respect to the origin by a scale factor of 1.5 to produce quadrilateral R'S'T'V' . Vertex R is located at (6, -9). Which ordered pair represents R' after the dilation?
Answer:
(9, -13.5)
Step-by-step explanation:
It's given in the question that a quadrilateral RSTV is dilated with a scale factor of 1.5 with respect to the origin to form R'S'T'V'.
Rule for dilation is,
(x, y) → (kx, ky)
where 'k' is the scale factor.
If vertex R of the quadrilateral is (6, -9),
By the given rule of dilation,
R(6, 9) → R'[(1.5 × 6), -(1.5 × 9)]
→ R'(9, -13.5)
Therefore, Option given in bottom right (9, -13.5) will be the answer.
18x + 7, when x = 2
Answer:
43
Step-by-step explanation:
18x+7
=18×2+7
=36×9
=45
Answer:
43
Step-by-step explanation:
x=2
18x+7
18(2)+7
36+7
43
Hope this helps ;) ❤❤❤
I NEED HELP WITH THESE 4 ASAP
Answer:
I'm confused by this. What do they mean by prove?
Step-by-step explanation:
The sum of two positive number is 6 times their difference. what is the reciprocal of the ratio of the larger number to the smaller?
let the numbers be a and b, a>b
a+b=6(a-b)
we need to find reciprocal of ratio of larger to smaller , which will be same as ratio of smaller to larger or b/a, let's call it x
divide the equation by a.
1+x=6(1-x)
on solving, x=5/7
Kent Co. manufactures a product that sells for $60.00. Fixed costs are $285,000 and variable costs are $35.00 per unit. Kent can buy a new production machine that will increase fixed costs by $15,900 per year, but will decrease variable costs by $4.50 per unit. What effect would the purchase of the new machine have on Kent's break-even point in units?
0riginal break even point:
285000/ 60/35 = $166,250
New break even point = new fixed costs / ( selling price - variable cost/ selling price)
New break even point = 285,000 + 15,900. / ( 60-( 35-4.50)/60
300,900 / 60-30.50/60 = $612,000
The new break even point increases.
how many meters are in 250 centimeters
Answer:
2.5 meters
Step-by-step explanation:
The average score of all golfers for a particular course has a mean of 70and a standard deviation of 5.Suppose 100golfers played the course today. Find the probability that the average score of the 100golfers exceeded 71.Round to four decimal places.
Answer:
0.9773
Step-by-step explanation:
Here, we start by calculating the z-scores statistic
Mathematically;
z-score = (x-mean)/SD/√n
From the question, we have;
x = 71, mean = 70, SD = 5 and n = 100
Plugging these values in the equation above, we have;
z-score = (71-70)/5/√100 = 1/5/10 = 1/0.5 = 2
So the probability we want to calculate is that;
P(z > 2)
This is obtainable from the standard normal distribution table
P(z > 2) = 0.97725 which is 0.9773 to 4 decimal places
A manufacturer of paper coffee cups would like to estimate the proportion of cups that are defective (tears, broken seems, etc.) from a large batch of cups. They take a random sample of 200 cups from the batch of a few thousand cups and found 18 to be defective. The goal is to perform a hypothesis test to determine if the proportion of defective cups made by this machine is more than 8%.
Required:
a. Calculate a 95% confidence interval for the true proportion of defective cups made by this machine.
b. What is the sample proportion?
c. What is the critical value for this problem?
d. What is the standard error for this problem?
Answer:
a
The 95% confidence interval is [tex]0.0503 < p < 0.1297[/tex]
b
The sample proportion is [tex]\r p = 0.09[/tex]
c
The critical value is [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
d
The standard error is [tex]SE =0.020[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 200
The number of defective is k = 18
The null hypothesis is [tex]H_o : p = 0.08[/tex]
The alternative hypothesis is [tex]H_a : p > 0.08[/tex]
Generally the sample proportion is mathematically evaluated as
[tex]\r p = \frac{18}{200}[/tex]
[tex]\r p = 0.09[/tex]
Given that the confidence level is 95% then the level of significance is mathematically evaluated as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5\%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{ \alpha }{2}[/tex] from the normal distribution table, the value is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the standard of error is mathematically represented as
[tex]SE = \sqrt{\frac{\r p (1 - \r p)}{n} }[/tex]
substituting values
[tex]SE = \sqrt{\frac{0.09 (1 - 0.09)}{200} }[/tex]
[tex]SE =0.020[/tex]
The margin of error is
[tex]E = Z_{\frac{ \alpha }{2} } * SE[/tex]
=> [tex]E = 1.96 * 0.020[/tex]
=> [tex]E = 0.0397[/tex]
The 95% confidence interval is mathematically represented as
[tex]\r p - E < \mu < p < \r p + E[/tex]
=> [tex]0.09 - 0.0397 < \mu < p < 0.09 + 0.0397[/tex]
=> [tex]0.0503 < p < 0.1297[/tex]
Please help me with this question
Answer:
0 ≤ x ≤ 10
Step-by-step explanation:
The domain of f(x) is the set of values of x for which the function is defined. Here, the square root function is only defined for non-negative arguments, so we require ...
-x^2 +10x ≥ 0
x(10 -x) ≥ 0
The two factors in this product will both be positive only for values ...
0 ≤ x ≤ 10 . . . . the domain of f(x)
Evaluate the expresión 6c-d when c=2 and d=10 I need help?
Answer:
the answer is 18
Step-by-step explanation:
8 is the answer
I will be honest I'm having a major brain fart.. What's the line called and what's it do again? it's separating numbers.. Looks like this
29
---
3
I know I'm stupid for this one... I've been up for 30 hours studying and now I can't remember this.. I need sleep but can't till i figure this out now...
Answer:
fraction bar. separates numerator and denominator in a fraction
Answer:
basically a dividing symbol, but specifically used for fractions
Step-by-step explanation:
THE PRICE OF AN ITEM FROM $10 TO $17. WHAT WAS THE PERCENT INCREASE IN THE PRICE OF THE ITEM?
Answer:
70%
Step-by-step explanation:
The method to find out percentage increase is by subtracting the original price from the increased price and making it into a fractional form with the denominator as 10 (out of 100%). So it results to this.
(original price - increased price) / 10
(17 - 10) / 10 = 7/10
7/10 can be converted from its fractional form to 70% i.e.its percentage.
Hope this helps and please mark as the brainliest.
Point E lies within rectangle ABCD. If AE = 6, BE = 7, and CE = 8, what is the length of DE?
Answer:
[tex]\sqrt{51}[/tex] units.
Step-by-step explanation:
Point E is inside a rectangle ABCD.
Please refer to the attached image for the given statement and dimensions.
Given that:
Sides AE = 6 units
BE = 7 units and
CE = 8 units
To find:
DE = ?
Solution:
For a point E inside the rectangle the following property hold true:
[tex]AE^2+CE^2=BE^2+DE^2[/tex]
Putting the given values to find the value of DE:
[tex]6^2+8^2=7^2+DE^2\\\Rightarrow 26+64=49+DE^2\\\Rightarrow DE^2=100-49\\\Rightarrow DE^2=51\\\Rightarrow \bold{DE = \sqrt{51}\ units}[/tex]
determine the results of the following operations
Answer:
[tex]\sqrt[3]{4}\times (\sqrt[3]{16}-10 )[/tex]
Step-by-step explanation:
Let be [tex]\sqrt[3]{64}-\sqrt[3]{32} \times \sqrt[3]{125}[/tex], this expression is simplified as follows:
1) [tex]\sqrt[3]{64}-\sqrt[3]{32} \times \sqrt[3]{125}[/tex] Given
2) [tex]\sqrt[3]{4^{3}}-\sqrt[3]{2^{5}}\times \sqrt[3]{5^{3}}[/tex] Definition of power
3) [tex](4^{3})^{1/3}-(2^{2}\cdot 2^{3})^{1/3}\times (5^{3})^{1/3}[/tex] Definition of n-th root/[tex]a^{b+c}= a^{b}\cdot a^{c}[/tex]/[tex](a^{b})^{c} = a^{b\cdot c}[/tex]
4) [tex]4 - (2^{2})^{1/3}\times 2\times 5[/tex] [tex]a^{b+c}= a^{b}\cdot a^{c}[/tex]/[tex](a\cdot b)^{c} = a^{c}\cdot b^{c}[/tex]
5) [tex]4 - 10\times 4^{1/3}[/tex] Multiplication/Definition of power
6) [tex]4^{1/3}\cdot (4^{2/3}-10)[/tex] Distributive property/[tex]a^{b+c}= a^{b}\cdot a^{c}[/tex]
7) [tex]\sqrt[3]{4}\times [(4^{2})^{1/3}-10][/tex] [tex](a^{b})^{c} = a^{b\cdot c}[/tex]/Definition of n-th root
8) [tex]\sqrt[3]{4}\times (\sqrt[3]{16}-10 )[/tex] Definition of power/Result
Show that the set of functions from the positive integers to the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} is uncountable. [Hint: First set up a one-to-one correspondence between the set of real numbers between 0 and 1 and a subset of these functions. Do this by associating to the real number 0.d1d2 . . . dn . . . the function f with f(n).
Answer:
since the set of functions expressed are uncountable and they are a subset of real numbers starting from N therefore the set {0,1,2,3,4,5,6,7,8,9} is uncountable as well as its off functions
Step-by-step explanation:
set = {0,1,2,3,4,5,6,7,8,9}
setting up a one-to-one correspondence between the set of real numbers between 0 and 1
The function : F(n)= {0,1} is equivalent to the subset (sf) of (n) , this condition is met if n belongs to the subset (sf) when f(n) = 1
hence The power set of (n) is uncountable and is equivalent to the set of real numbers given
since the set of functions expressed are uncountable and they are a subset of real numbers starting from N therefore the set {0,1,2,3,4,5,6,7,8,9} is uncountable as well as its offfunctions
Given the graph, find an equation for the parabola.
Answer:
[tex]\Large \boxed{\sf \bf \ \ y=\dfrac{1}{16}(a-3)^2-2 \ \ }[/tex]
Step-by-step explanation:
Hello, please consider the following.
When the parabola equation is like
[tex]y=a(x-h)^2+k[/tex]
The vertex is the point (h,k) and the focus is the point (h, k+1/(4a))
As the vertex is (3,-2) we can say that h = 3 and k = -2.
We need to find a.
The focus is (3,2) so we can say.
[tex]2=-2+\dfrac{1}{4a}\\\\\text{*** We add 2. ***}\\\\\dfrac{1}{4a}=2+2=4\\\\\text{*** We multiply by 4a. ***}\\\\16a=1\\\\\text{*** We divide by 16. ***}\\\\a=\dfrac{1}{16}[/tex]
So an equation for the parabola is.
[tex]\large \boxed{\sf y=\dfrac{1}{16}(a-3)^2-2 }[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Please help me understand this question!
Answer:
C
Step-by-step explanation:
The first sentence basically sets up the equation which is given, so we can read it for knowledge but it is not crucial to solve the problem.
We start here:
we are given: $120 - 0.2($120)
= 120 - (0.2)(120) (factoring out 120)
= 120 (1 - 0.2)
= 120 (0.8)
= 0.8 (120) (answer c)
PLEASE HELP ASAP WILL GIVE BRAINLIEST
i need help asap please
Answer:
[tex]x = -\frac{3}{2}[/tex] or [tex]x = 1[/tex]
Step-by-step explanation:
Using the zero product property, first step is to set the given equation, [tex] 2x^2 + x - 1 = 2 [/tex] , to zero. Then factorise the left side.
Thus,
[tex] 2x^2 + x - 1 = 2 [/tex]
Subtract 2 from both sides
[tex] 2x^2 + x - 1 - 2 = 2 - 2 [/tex]
[tex] 2x^2 + x - 3 = 0 [/tex]
Factorise the left side
[tex] 2x^2 + 3x - 2x - 3 = 0 [/tex]
[tex] x(2x + 3) - 1(2x + 3) = 0 [/tex]
[tex] (x - 1)(2x + 3) = 0 [/tex]
Find the solution
[tex] x - 1 = 0 [/tex]
Or
[tex]2x + 3 = 0[/tex]
[tex] x = 1 [/tex]
Or
[tex]2x + 3 = 0[/tex]
[tex]2x = -3[/tex]
[tex]x = -\frac{3}{2}[/tex]
The answer is: [tex] x = 1 [/tex] or [tex]x = -\frac{3}{2}[/tex]
Which of the following statements is false?
If a number is an integer, then it is irrational.
If a number is a natural number, then it is rational.
If a number is a fraction, then it is rational.
If a number is a whole number, then it is rational.
Answer:
If a number is an integer, then it is irrational. ⇒ false statement
Step-by-step explanation:
Let's check:
If a number is an integer, then it is irrational.
- incorrect, as all integers are rational
If a number is a natural number, then it is rational.
- correct, natural numbers are subset of rational numbers
If a number is a fraction, then it is rational.
- correct, they can be shown as p/q
If a number is a whole number, then it is rational.
- correct, whole numbers are subset of rational numbers
The statement "If a number is an integer, then it is irrational" is false.
Which of the following statements is false?The statement "If a number is an integer, then it is irrational" is false. This is because not all integers are irrational.
The other statements are all true:
"If a number is a natural number, then it is rational." This is true because all natural numbers are integers, and all integers are rational.
"If a number is a fraction, then it is rational." This is true because a fraction is a number of the form p/q, where p and q are integers and q is not equal to 0. Any number of this form is rational.
"If a number is a whole number, then it is rational." This is true because all whole numbers are integers, and all integers are rational.
Therefore, the false statement is the first one: "If a number is an integer, then it is irrational."
Below is a table summarizing the statements:
Statement Truth value
If a number is an integer, then it is irrational False
If a number is a natural number, then it is rational True
If a number is a fraction, then it is rational True
If a number is a whole number, then it is rational True
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Help me please answer this, this will be my first grade for freshman year. The picture of the question is down below.
Answer:
D
Step-by-step explanation:
-0.81 is a high negative correlation, which means the y is decreasing with x increasing, which means y(the number of broken glass) decreases when x(amount of paper used) increased. So we can say that the toilet paper is surely helping.
make me brainly if you find it correct
If an image of a triangle is congruent to the pre-image, what is the scale factor of the dilation? 0.1 1 10
Answer:
1
Step-by-step explanation: diliation is like multiplilcation if you were to do 3*1 =3. simply congruent means all sides and angles are the same.
Given that the image and the preimage of the triangle are congruent, their
dimensions are the same.
The scale factor of dilation of an image of a triangle that is congruent to the pre-image is; 1Reasons:
Let ΔABC represent the preimage, and let ΔA'B'C' represent the image.
Given that the image and the preimage are congruent, we have;
AB ≅ A'B'
BC ≅ B'C'
AC ≅ A'C'
By definition of congruency, we have;
AB = A'B'
BC = B'C'
AC = A'C'
The scale factor of dilation is given as follows;
[tex]\displaystyle Scale \ factor = \mathbf{ \frac{A'B'}{AB}} = \frac{AB}{AB} = 1[/tex]Therefore;
If the image is congruent to the pre-image, the scale factor of dilation is; 1Learn more about dilation transformation here:
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A baseball is hit 3 feet above the ground at 80 feet per second and at an angle of with respect to the ground. Find the maximum height. Round your answer to the nearest integer.
Answer:
53
Step-by-step explanation:
i used an angle of 45 degrees.
Distance from ground = 3feets
Angle = 45⁰
U is the initial velocity = 80ft/sec
g = 32
The question wants us to vfind maximum height
We have
r(t) = (80cos45⁰)ti + [3 + 80sin45⁰]t - 0.5(32)t²
We know cos 45 is also sin45 = 1/√2
r(t) = (40√2)ti + [3+40√2]t - 16t²
When we differentiate with respect to t:
r'(t) = (40√2)i + (40√2 - 32t)
= 40√2 =32t
t = 40√2/32
t= 20√2/16
We put the value of t into (3 + 40√2)t -16t²
When we substitute and simplify this we have
3 + 56.57 + 1.77 -16 +8
= 53.34
Which is approximately 53.
