The movement of the ping pong ball follows a exponential progression.
The expression for the k-th bounce is: [tex]\mathbf{T_k = 235 \times (0.75)^k}[/tex]The height after the 6th bounce is 41.82 ftThe total distance after the 12th bounce is 1584.84ft.There will be 31457280 bacteria after a day and a half.1. Ping pong ball
The given parameters are:
[tex]\mathbf{a = 235}[/tex] --- the initial height
[tex]\mathbf{r = 75\%}[/tex] --- the common ratio
(a) The expression after bouncing k times
To do this, we make use of
[tex]\mathbf{T_n = a \times r^n}[/tex]
So, we have:
[tex]\mathbf{T_n = 235 \times (0.75)^n}[/tex]
In this case; k = n.
So, the equation becomes
[tex]\mathbf{T_k = 235 \times (0.75)^k}[/tex]
Hence, the expression for the k-th bounce is: [tex]\mathbf{T_k = 235 \times (0.75)^k}[/tex]
(b) The height after bouncing 6 times
This means that k = 6.
So, we have:
[tex]\mathbf{T_k = 235 \times (0.75)^k}[/tex]
[tex]\mathbf{T_6 = 235 \times (0.75)^6}[/tex]
[tex]\mathbf{T_6 = 41.82}[/tex]
Hence, the height after the 6th bounce is 41.82 ft
(c) The total distance after the 12th bounce
First, we calculate the total height after the 12th bounce using:
[tex]\mathbf{S_k = \frac{a(1 - r^k)}{1 - r}}[/tex]
So, we have:
[tex]\mathbf{S_k = \frac{235 \times (1 - 0.75^{12})}{1 - 0.75}}[/tex]
[tex]\mathbf{S_k = \frac{235 \times (0.968)}{0.25}}[/tex]
[tex]\mathbf{S_k = 909.92}[/tex]
So, the total distance is:
[tex]\mathbf{Distance = 2 \times S_k - a}[/tex]
[tex]\mathbf{Distance = 2 \times 909.92 - 235}[/tex]
[tex]\mathbf{Distance = 1584.84}[/tex]
Hence, the total distance after the 12th bounce is 1584.84ft.
(2) Cell division
The given parameters are:
[tex]\mathbf{r = 2/2hr}[/tex] --- rate
[tex]\mathbf{a = 120}[/tex] --- initial number of cells
[tex]\mathbf{t = 18}[/tex] --- number of 2 hours is a day and a half
So, the number of bacteria is:
[tex]\mathbf{T_t = ar^t}[/tex]
This gives
[tex]\mathbf{T_t = 120 \times 2^{18}}[/tex]
[tex]\mathbf{T_t = 31457280}[/tex]
Hence, there will be 31457280 bacteria after a day and a half.
Read more about exponential functions at:
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help plshddjjdhdjjdjdjdh
What are the slope and y-intercept of the linear function?
2
-3 -2 -1.
2
оа
Oь
slope:-2: y-intercept: 2
1
slope: 2 :y-intercept: 1
Ос
1
slope: 2 :y-intercept: 2
slope: 2; y-intercept: 1
Od
What is the value of W?
951 4 1404 393
Answer:
w = 17
Step-by-step explanation:
Altitude SU of isosceles triangle RST bisects base RT. This means ...
UR = UT
5w = w+68
4w = 68 . . . . . subtract w
w = 17 . . . . . . divide by 4
Thirty percent of all telephones of a certain type are submitted for service while under warranty. Of these, 70% can be repaired, whereas the other 30% must be replaced with new units. If a company purchases ten of these telephones, what is the probability that exactly four will end up being replaced under warranty
Answer:
40%
Step-by-step explanation:
Mikael has a loan of $40 000.
He pays 1.6% simple interest for six months
How much interest does he pay altogether?
Step-by-step explanation:
Based on the given conditions,
[tex] formulate: 1.6\% \times 40000 \times 12 \div 12
[tex] formulate: 1.6\% \times 40000 \times 12 \div 12Reduce the fraction: \dfrac{2 \times 40000}{125}
[tex] formulate: 1.6\% \times 40000 \times 12 \div 12Reduce the fraction: \dfrac{2 \times 40000}{125}[/tex]
[tex]Reduce the fraction: 2 \times320
[tex]Reduce the fraction: 2 \times320Calculate the product orquotient: 640[tex]
Answer 640
Answer:
[tex]\sf\longmapsto \: 640[/tex]
Step-by-step explanation:
Based on given cases:
[tex] \sf \: Formulate: 1.6\% \times 40000 \times 12 \div 12[/tex]
Reduce the fraction:
[tex] \sf \longmapsto \: \dfrac{2 \times 40000}{125}[/tex]
[tex] \sf \longmapsto \: 320 \times 2[/tex]
Calculate the product/quotient:
[tex] \sf\longmapsto \: 640[/tex]
ive been stuck for so long. pls help
Answer:
B
Step-by-step explanation:
Might be C, but I hope it helps
Show that: [tex]\sqrt[ab]{ \frac{ {x}^{a} }{ {x}^{b} } } . \sqrt[bc]{ \frac{ {x}^{b} }{ {x}^{c} } } . \sqrt[ca]{ \frac{ {x}^{c} }{ {x}^{a} } } = 1.[/tex]
Brainliest! Brainliest..ans.
Here we need to Prove that ,
[tex]\bf\implies \sqrt[ab]{ \frac{ {x}^{a} }{ {x}^{b} } } . \sqrt[bc]{ \frac{ {x}^{b} }{ {x}^{c} } } . \sqrt[ca]{ \frac{ {x}^{c} }{ {x}^{a} } } = 1.[/tex]
Lets start with LHS , which is ,
[tex]\bf\implies LHS = \sqrt[ab]{ \dfrac{ {x}^{a} }{ {x}^{b} } } . \sqrt[bc]{ \dfrac{ {x}^{b} }{ {x}^{c} } } . \sqrt[ca]{ \dfrac{ {x}^{c} }{ {x}^{a} } } [/tex]
We know that ,
[tex]\bf\implies \sqrt[n]{k^m }= k^{\frac{m}{n}}[/tex]
• So that ,
[tex]\bf\implies \sqrt[ab]{x^{a-b}} . \sqrt[bc]{x^{b-c}} .\sqrt[ac]{x^{c-a}} \\\\\bf\implies x^{\frac{a-b}{ab}} . x ^{\frac{b-c}{bc}} .x^{\frac{c-a}{ca}} \\\\\bf\implies x^{\frac{ ac - bc + ab - ac + bc - ba }{abc } }\\\\\bf\implies x^{\frac{0}{abc}} \\\\\bf\implies x^0 \\\\\bf\implies 1 = RHS [/tex]
Hence ,
[tex]\implies \boxed{\bf \red{ LHS = RHS }} [/tex]
[tex]\large\underline{\sf{Solution-}}[/tex]
Consider LHS:
[tex]\sf= \sqrt[\sf ab]{\dfrac{\sf x^{a}}{\sf x^{b}}}\cdot \sqrt[\sf bc]{\dfrac{\sf x^{b}}{\sf x^{c}}}\cdot \sqrt[\sf ac]{\dfrac{\sf x^{c}}{\sf x^{a}}}[/tex]
As we know that:
[tex]\sf\red\leadsto\dfrac{x^{a}}{x^{b}}=x^{a-b}[/tex]
We get:
[tex]\sf= \sqrt[\sf ab]{\sf x^{a-b}}\cdot \sqrt[\sf bc]{\sf x^{b-c}}\cdot \sqrt[\sf ac]{\sf x^{c-a}}[/tex]
We can also write it as:
[tex]\sf= x^{\dfrac{a-b}{ab}}\cdot x^{\dfrac{b-c}{bc}}\cdot x^{\dfrac{c-a}{ac}}[/tex]
We know that:
[tex]\sf \red\leadsto x^{a}\cdot x^{b}=x^{a+b}[/tex]
We get:
[tex]\sf= x^{\bigg(\dfrac{a-b}{ab}+\dfrac{b-c}{bc}+\dfrac{c-a}{ac}\bigg)}[/tex]
[tex]\sf= x^{\bigg(\dfrac{c(a-b)+a(b-c)+b(c-a)}{abc}\bigg)}[/tex]
[tex]\sf= x^{\bigg(\dfrac{ac-bc+ab-ac+bc-ab}{abc}\bigg)}[/tex]
[tex]\sf= x^{\bigg(\dfrac{0}{abc}\bigg)}[/tex]
[tex]\sf= x^{0}[/tex]
[tex]\sf=1[/tex]
[tex]\textsf{= RHS}\\[/tex]
1.0286 as a fraction
Answer:
1 143 /5000
Step-by-step explanation:
Scientists often write very large or very small numbers using exponents. How might a scientist write the number shown using exponents?
make it look like a seventh grader wrote it please
19. As part of a cookie recipe, you mix cup of chocolate chips for every 1 cups of
sugar. How much chocolate chips do you need if you use a whole cup of sugar?
Answer: 1 cup
Step-by-step explanation: they have a 1:1 ratio
Answer:
1
Step-by-step explanation:
If you have 1 cup of chocolate chips for every 1 cup of sugar, that is a 1:1 ratio
A whole cup of sugar is equal to 1 cup of sugar
Therefore, you will have 1 cup of choloate chips for the whole cup of sugar
Evaluate -8x+5-2x-4+5x
Answer:
The value of the expression is - 9.
Evaluating the expression before simplifying is preferred because you only have to substitute once instead of substituting three times.
Step-by-step explanation:
x = 2
- 8x + 5 - 2x - 4 + 5x
= - 8x - 2x + 5x + 5 - 4
= - 10x + 5x + 1
= - 5x + 1
= - 5 ( 2 ) + 1
= - 10 + 1
= - 9
Find the equation of the linear function represented by the table y 6 9 12 15 x 1 2 3 4
Answer: y = 3x + 3
Step-by-step explanation:
We know the linear function as following:
y = mx + b
m is the slope of the equation. b represents the y-intercept.
To find m, we divide the rate of change of y by the rate of change of x. We know that the rate of change y is +3 because we add three each time in order to find the next value. The rate of change of x is +1 because we add one each time to find the next value. So m would be:
m = 3/1
m = 3
Our linear equation is now as following:
y = 3x + b
In order to find b, we should first substitute a coordinate in the equation above.
y = 3x + b
6 = 3(1) + b
Then, we multiply 3 with 1
6 = 3 + b
Finally, we substract 3 on both sides. Now we've got our b value.
b = 3
Now our equation should look like this.
y = 3x + 3
To verify if the equation, we should substitute another coordinate, and verify if each side of the equation is equal.
y = 3x + 3
15 = 3(4) + 3
15 = 12 + 3
15 = 15
So we now know that the equation is indeed correct.
Answer:
y = 3x + 3Step-by-step explanation:
As per given table we have ordered pairs:
(1, 6), (2, 9), (3, 12), (4, 15)Find the slope and y- intercept to work out the equation.
y = mx + bThe slope:
m = (9 - 6)/(2 - 1) = 3/1 = 3The y -intercept:
6 = 3*1 + b6 = 3 + bb = 3The equation is:
y = 3x + 3The graph is attached
HW
Example 7: While chasing the Joker, the Batmobile was traveling at 120 miles per hour. The
Joker's get-away car was traveling at 176 feet per second. Who was traveling faster, Batman or the
Joker? Explain your answer.
Answer:
this is a trick question 176 fps is equal to 120 mph
so 120=120
3x^2-24x+48 pls help me
Answer:
This polynomial is either a function like f(x), or it's just =0 and it's solved by a quadratic equation.
Step-by-step explanation:
Let's say it's equal to 0, we can easily divide the whole expression with 3, as obviously 3,24,48 have the same divisor(3), then we are left with:
x²-8x+16=0, then we apply the quadratic equation, and we got only 1 solution and that's x=4
If it is a function f(x), than it will have roots(root of a quadratic function is the x-coordinate where y=0, basically when the parabola intersects the x-axis(y=0), as we'll get that the only root is x=4
HELP HURRY SUBTRACTION
Answer:
408, 250, and 4055 hope this helps
Which equation does NOT have like terms to collect?
Answer:
15t+9r=2
Step-by-step explanation:
the terms which are the variables are not the same on any part of the equation
[tex][ 1 1 1 -1\\ 2 0 3 1\\ 4 x 1 -1\\ 1 0 -1 2 ] = 0[/tex]
Answer:
5hg vb
Step-by-step explanation:
,hgbn
Answer:
−120314x − 11
Step-by-step explanation:
4% of 50
Percent of a quantity
M
Answer:
4% of 50 is 2
Step-by-step explanation:
I NEED HELP OR I WILL GET A FAT F!!! What Is 6.38 times 5.2 rounded product to the nearest whole number!!!
Answer:
33.176
Step-by-step explanation:
A salesperson earns an income of $600 per week aus an dditional 5% commission on her total sales for that weck a. Write an equation that models the Salespersons total weekly income. b. What would be the salespersons income if her total sales were $10.000 that week? c. How much would a salesperson have to sell to have a $2000 weekly
WILL GIVE BRAINLIEST!... whats the unit rate of the equation(HAVE TO SHOW HOW YOU GOT ANSWER)
y=-4x
Answer:
-4
Step-by-step explanation:
The form of a liner equation is y=mx+b. b is 0 in this example. So we are left with y=-4x
-4 is the m, the slope. It is also called the unit rate of change. It tells us how much y changes for each 1x unit.
y x
0 0
-4 1 One unit changes y by -4 : The unit rate of change.
-8 2
x cube + 1 ÷ x squared -x+1
What’s the greatest common factor of (280, 168)
Answer:
Greatest common factor of 280 and 168 is 56
-NULL
Brainliest will be appreciated thank you!
Student football game tickets cost $20 Adult tickets cost $30. Write a function that shows
the total cost for s student tickets and a adult tickets.
Answer:
Here are the answers for the whole QC for CA students.
1. C
2. A
3. no
4. c
5. A
Step-by-step explanation:
In 1995, the cost of tuition at a large Midwestern university was $146 per credit hour. In 2001, tuition had risen to $200 per credit hour.
Determine a linear equation to represent the cost, C, of tuition as a function of x, the number of years since 1990. (Assuming the cost increases by the same amount each year.)
Linear Equation:
In the year 2008, tuition will be ($ )per credit hour.
In the year( ) , tuition will be $317 per credit hour
Answer:
72 is the correct answer
Answer:
I believe 72 is the correct answer
Step-by-step explanation:
Hi ppl of brainly. I need some help with my math assignment. explain if u can (if u can't, that's okay ) if you dont know it. please dont answer it. if u have any questions about the question, please drop in a comment!
Answer:
17.156
Step-by-step explanation:
A rational number has has a terminating decimal expansion or a decimal expansion of non-terminating repeating digits. Here, the decimal expansion is terminating, so it is a rational number.
Answer:
C. 17.156
Step-by-step explanation:
A rational number is any number that can be expressed as a fraction. So for example, since [tex]\sqrt{2}[/tex] cant be expressed as a fraction, it isn't rational. A number like 1.25 on the other hand IS rational as it can be expressed as [tex]\frac{5}{4}[/tex] or [tex]\frac{125}{100}[/tex].
Option C can be expressed as [tex]\frac{17156}{1000}[/tex], so it must be rational.
- Note that if a number has a finite amount of digits after the decimal (ie it doesn't go on forever like option B), it can be represented as a fraction and thus is rational.
PLEASEE I NEEEDDD HELPPPPPP
Answer:
make a chart and it will be easy for you
lim┬(x→1)〖(1-√x)/(x^2-1)〗
Answer:
- 1/4
Step-by-step explanation:
[tex]\frac{1-\sqrt{x} }{x^{2}-1 } = \frac{(1-\sqrt{x})*(1+\sqrt{x} ) }{(x+1)(x-1)(1+\sqrt{x} )} \\= \frac{1-x}{-(1-x)(x+1)(1+\sqrt{x} )} \\= - \frac{1}{(x+1)(1+\sqrt{x} )} \\ \lim_{->1} - \frac{1}{(x+1)(1+\sqrt{x} )} \\ = -\frac{1}{(1+1)(1+\sqrt{1}) } = - 1/4[/tex]
Find cos 30 in terms of cos 0
Answer:
cos(30) = (sqrt(3)/2) * cos(0)
Step-by-step explanation:
cos(0) = 1
cos(30) = sqrt(3)/2
Thus, we can write that:
cos(30) = (sqrt(3)/2) * cos(0)
Evaluate the expression 6^2-(8–4^2+7
please mark this answer as brainlist
The value of given expression is 27.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
The given expression is 6²-(8-4)²+7.
Here, 6²-(8-4)²+7
= 6²-(4)²+7
= 36-16+7
= 20+7
= 27
Therefore, the value of given expression is 27.
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