Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. The height (in feet) of a rocket launched from the ground is given by the function f(t) = -16t2 + 160t. Match each value of time elapsed (in seconds) after the rocket’s launch to the rocket's corresponding instantaneous velocity (in feet/second).
Answers
Answer:
The pairs are;
t, v
2, 96
4, 32
5, 0
6, -32
7, -64
9, -128
Step-by-step explanation:
The given equation is f(t) = -16·t² + 160·t
We have, the velocity, v = d(f(t))/dt = d(-16·t² + 160·t)/dt = -32·t + 160
Which gives;
t, v
0, -32×(0) + 160 = 160
1, -32×(1) + 160 = 128
2, -32×(2) + 160 = 96
3, -32×(3) + 160 = 64
4, -32×(4) + 160 = 32
5, -32×(5) + 160 = 0
6, -32×(6) + 160 = -32
7, -32×(7) + 160 = -64
8, -32×(8) + 160 = -96
9, -32×(9) + 160 = -128
The given velocity values are;
96, -64, 32, 0, -128, -32 which correspond to 2, 7, 4, 5, 9, 6
The pairs are;
t, v
2, 96
4, 32
5, 0
6, -32
7, -64
9, -128
Related Questions
Select all transformations that carry rectangle
ABCD onto itself.
A. Rotate by 90 degrees clockwise using center P.
B. Rotate by 180 degrees clockwise using center P.
C. Reflect across line m.
D. Reflect across diagonal AC
.
E. Translate by the directed line segment from A to B.
Answers
Plot the image of quadrilateral ABCD under a reflection across the x-axis.
Answers
Answer:
The points for this will be:
A: (1, -4)
B: (-4, -2)
C: (-5, 4)
D: (-2, 1)
Step-by-step explanation:
If we reflect a shape over the x-axis, all of it’s points y values will be negated.
So, (1, 4) becomes (1, -4)
(-4, 2) becomes (-4, -2)
(-5, -4) becomes (-5, 4)
and (-2, -1) becomes (-2, 1)
Hope this helped!
New coordinates of the quadrilateral are A' is (1, -4), B' is (-4, -2), C' is (-5, 4) and D' is (-2, 1)
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The coordinates of quadrilateral ABCD are A is (1, 4), B is (-4, 2), C is (-5, -4) and D is (-2, -1)
After reflecting across the x-axis , the x-coordinates of the vertices will remain the same, but the signs of their y-coordinates will change.
Therefore, the new coordinates of the vertices will be:
A' is (1, -4)
B' is (-4, -2)
C' is (-5, 4)
D' is (-2, 1)
Hence, new coordinates of the quadrilateral are A' is (1, -4), B' is (-4, -2), C' is (-5, 4) and D' is (-2, 1)
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please helppp ill give brainliest the question is attached below
Answers
Answer: It is false, the diameter is not 16 m.
Step-by-step explanation:
P 4m are 8 m are 32 m away. The diameter= 32 m.
(I hope its rights!!!)
THIS HAS MULTIPLE QUESTIONS PLEASE ANSWER ASAP
Question 1 Solve the inequality. |d + 2| ≥ 6
Question 2 Solve the equation. If there is no solution, select no solution. 5|x+3/4|=10
Question 3 Solve the inequality. –2 < 4 x – 10 < 6
Answers
Answer:
Question 1: d ≥ 4 or d ≤ -8
Step-by-step explanation:
Question 1 Solve the inequality. |d + 2| ≥ 6
d + 2 ≥ 6 or d + 2 ≤ -6
d ≥ 4 or d ≤ -8
Find the GFC of 20 and 16
Answers
Pregunta N° 1: ¿Cuántas fracciones propias e irreductibles con denominador 24 existen? 1 punto A) 2 B) 4 C) 6 D) 8 E) 10 Pregunta N° 2: ¿Cuántas fracciones impropias e irreductibles con numerador 25 existen? 1 punto A) 19 B) 21 C) 25 D) 29 E) 33 Pregunta N° 3: La edad de Miguel es 4/5 de la edad de su novia. Si las edades de los dos suman 63 años, calcule la edad de la novia de Miguel. 1 punto A) 20 años B) 26 años C) 32 años D) 35 años E) 40 años Pregunta N° 4: Si son las 8 a. m., ¿qué fracción del día ha transcurrido? 1 punto A) 1 B) 2 C) 1/2 D) 1/3 E) 1/5
ayuden porfavor
Answers
Answer:
Pregunta 1: Opcion D. 8
Pregunta 2: Opción A. 19 (aunque lo correcto es decir que son 20)
Pregunta 3: 28 años (no está como opción)
Pregunta 4: Opción D. 1/3
Step-by-step explanation:
Las fracciones irreductibles son aquellas que después de dividirlas por un común divisor, una vez que no se pueden dividir más se dice que son irreducibles, por lo tanto no existe ningún número que sea divisor común del numerador y del denominador más que 1.
Fracciones irreductibles con común denominador 24.
Como máximo divisor tenemos el 24 y como mínimo el 1
entre 1/24 y 1 estarán nuestras fracciones o sea:
1/24 < x/24 < 1. Ahora convertimos el 1 en fracción de 24, lo que sería 24/24 para igualar el numerador en ambos lados de la ecuación, para poder determinar x
1/24 < x/24 < 24/24
Como vemos que x tiene que estar entre 1 y 24, las respuestas serán:
2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22 y 23
Eliminamos los números divisores de 24, aquellos pares, y nos focalizamos en los que no podriamos dividir por nada con 24, o sea los números primos
5, 7, 11, 13, 17, 19, 23. Como nos falta el 1, obtenemos un total de 8 fracciones: 1/24, 5/24, 7/24, 11/24, 13/24, 17/24, 19/24, 23/24
Mismo procedimiento para el 25:
1/25 es una de las fracciones irreductibles. Pensamos en los valores de x
1/25 < x/25 < 25/25
2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25
Los números divisibles por 25, son los multiplos de 5, asi que esas respuestas no irían. Las fracciones irreductibles son:
1/25, 2/25, 3/25, 4/25, 6/25, 7/25, 8/25, 9/25, 11/25, 12/25, 13/25, 14/25, 16/25, 17/25, 18/25, 19/25, 21/25, 22/25, 23/25 y 24/25 haciendo un total de
20. Por alguna razón está mal formulada la pregunta, son 20 pero no está como opción y como te piden fraccion impropia (numerador > denominador), contamos a partir de 26. FIjate que hasta el proximo entero que sería 50/25, también son 20 fracciones (irreductibles e impropias)
26/25, 27/25, 28/25, 29/25, 31/25, 32/25, 33/25, 34/25, 36/25, 37/25, 38/25, 39/25, 41/25, 42/25, 43/25, 44/25, 46/25, 47/25, 48/25, 49/25
Próxima pregunta:
Miguel tiene 4/5 de la edad de la novia, y ambas edades suman 63.
Plantiemos la siguiente ecuacion donde x es la edad de la novia
4/5x + x = 63
9/5x = 63
x = 63 . 5/9 (como 9/5 pasa al otro lado de la igualdad dividiendo, damos vuelta la fraccion multiplicandola)
x = 35
Si la novia tiene 35 años y la edad de Miguel es 4/5 de esa edad
4/5 .35 = (35 .4) /5 = 28
Es raro porque no está la respuesta como tal.
Próxima pregunta:
Al ser las 8 am, quiere decir que han pasado 8 horas de que empezó el día
y el día tiene 24 horas.
8 horas transcurridas / 24 horas totales = 1/3
Solve for y in the following system of equations: −x+y=0 −2x+y=−5 1. 5 2. 7 3. 6 4. 5
Answers
Answer:
y = 5
Step-by-step explanation:
−x+y=0 −2x+y=−5
Multiply the first equation by -2
-2(-x+y=0)
2x-2y =0
Add this to the second equation
2x-2y =0
−2x+y=−5
-------------------
0x -y = -5
-y =-5
Multiply by -1
y = 5
Given an angle of a triangle and the opposite side length; which trigonometric function would you use to find the hypotenuse? a TAN b COS c SIN d Not enough information
Answers
Answer:
Sin
Step-by-step explanation:
Sin < = opposite/hypotenuse
If 4SINB=3SIN(2A+B) :
Prove that:7COT(A+B)=COTA
Answers
Answer:
Step-by-step explanation:
Given the expression 4sinB = 3sin(2A+B), we are to show that the expression 7cot(A+B) = cotA
Starting with the expression
4sinB= 3sin(2A+B)
Let us re write angle B = (A + B) - A
and 2A + B = (A + B) + A
Substituting the derived expression back into the original expression ww will have;
4Sin{(A + B) - A } = 3Sin{(A + B)+ A}
From trigonometry identity;
Sin(D+E) = SinDcosE + CosDSinE
Sin(D-E) = SinDcosE - CosDSinE
Applying this in the expression above;
4{Sin(A+B)CosA - Cos(A+B)SinA} = 3{Sin(A+B)CosA + Cos(A+B)sinA}
Open the bracket
4Sin(A+B)CosA - 4Cos(A+B)SinA = 3Sin(A+B)CosA + 3Cos(A+B)sinA
Collecting like terms
4Sin(A+B)CosA - 3Sin(A+B)cosA = 3Cos(A+B)sinA + 4Cos(A+B)sinA
Sin(A+B)CosA = 7Cos(A+B)sinA
Divide both sides by sinA
Sin(A+B)CosA/sinA= 7Cos(A+B)sinA/sinA
Since cosA/sinA = cotA, the expression becomes;
Sin(A+B)cotA = 7Cos(A+B)
Finally, divide both sides of the resulting equation by sin(A+B)
Sin(A+B)cotA/sin(A+B) = 7Cos(A+B)/sin(A+B)
CotA = 7cot(A+B) Proved!
The length of a rectangle is 5/6 feet. The width is 3/8 feet. How much greater is the length of the rectangle than the width?
Answers
Answer:
0.46 feet
Step-by-step explanation:
Length = 5/6 feet (or 0.254 m)
Width = 3/8 feet (or 0.114 m)
(5/6 - 3/8) feet = 11/24 feet or 0.46 feet (0.140 m)
PLEaSE HELP!!!!!! will give brainliest to first answer
Answers
Answer:
The coordinates of A'C'S'T' are;
A'(-7, 2)
C'(-9, -1)
S'(-7, -4)
T'(-5, -1)
The correct option is;
B
Step-by-step explanation:
The coordinates of the given quadrilateral are;
A(-3, 1)
C(-5, -2)
S(-3, -5)
T(-1, -2)
The required transformation is T₍₋₄, ₁₎ which is equivalent to a movement of 4 units in the leftward direction and 1 unit upward
Therefore, we have;
A(-3, 1) + T₍₋₄, ₁₎ = A'(-7, 2)
C(-5, -2) + T₍₋₄, ₁₎ = C'(-9, -1)
S(-3, -5) + T₍₋₄, ₁₎ = S'(-7, -4)
T(-1, -2) + T₍₋₄, ₁₎ = T'(-5, -1)
Therefore, the correct option is B
Tricks for solving trigonometry proof question easily ??
Answers
Answer: do do that you need a firm understanding of trig. once you do, you can see all the steps and solve a trig proof problem easily. So go back to solving regular trig questions, and keep asking yourself why this formula works. once you have understanding of that, you can solve trig proof problems with ease.
Step-by-step explanation:
WILL GIVE BRAINLIEST!!!
Help Someone please!! Given the following perfect square trinomial, find the missing term: 4x2 + ___x + 49 7 14 28 36
Answers
Answer:
28
Step-by-step explanation:
[tex]4 {x}^{2} + - - x + 49 \\ this \: is \: the \: expanded \: form \: of \\ {(2x + 7)}^{2} = 4 {x}^{2} + 28x + 49[/tex]
Answer:
[tex]\huge \boxed{28}[/tex]
Step-by-step explanation:
The trinomial is a perfect square.
Take the square root of the first term and the last term.
[tex](\sqrt{4x^2}+\sqrt{49})^2[/tex]
[tex]\sqrt{4x^2}=2x\\ \sqrt{49} =7[/tex]
[tex](2x+7)^2[/tex]
Expand to find the second term of the trinomial.
[tex](2x+7)(2x+7)\\2x(2x+7)+7(2x+7)\\4x^2 +14x+14x+49\\4x^2 +28x+49[/tex]
The second term of the trinomial is 28x.
PLEASE ANSWER !! WILL GIVE BRAINLIEST! Consider the exponential functions f, g, and h, defined as shown. Place the three functions in order from the fastest decreasing average rate of change to the slowest decreasing average rate of change on the interval [0, 3].
Answers
Answer: g(x) f(x) h(x)
Step-by-step explanation:
The order of the three functions in order from the fastest decreasing average rate of change to the slowest decreasing average rate of change on the interval [0, 3] is is g(x) >f(x) > h(x)
What is Function?A function from a set X to a set Y assigns to each element of X exactly one element of Y.
What is Exponential function?A function whose value is a constant raised to the power of the argument, especially the function where the constant is e.
What is average rate of change?It is a measure of how much the function changed per unit, on average, over that interval.
Given,
[tex]f(x) = 16(\frac{1}{2})^{x}[/tex]
interval = [0,3]
[tex]f(0)= 16(\frac{1}{2})^{0} =16 \\f(3)= 16(\frac{1}{2})^{3} =2[/tex]
Average rate of change = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
Average rate of change= [tex]\frac{2-16}{3-0}=-4.67[/tex]
Consider the function g(x)
g(0)=21
g(3)=1
Average rate of change = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
Average rate of change =[tex]\frac{1-27}{3-0}=-8.67[/tex]
Consider the exponential function
at x=0 the exponential function h =4
at x=0 the exponential function h =-3
Average rate of change = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
Average rate of change =[tex]\frac{-3-4}{3-0}=-2.33[/tex]
Hence, the order of the three functions in order from the fastest decreasing average rate of change to the slowest decreasing average rate of change on the interval [0, 3] is g(x) >f(x) > h(x)
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For each function, determine if it intersects or is parallel to the line y = -1.5x. If it
intersects the line, find the intersection point.
y =0.5x +4
PLEASE ANSWER I HAVE 25 MINUTES LEFT PLEASE
Answers
Answer:
Intersects; intersection point: (-2,3)
Step-by-step explanation:
Substitute -1.5x for y into y=0.5x+4:
-1.5x = 0.5x +4
-1.5x - 4 = 0.5x
-4 = 2x
x = -2
Plug in -2 for x into y=-1.5x
y = -1.5(-2)
y = 3
Organize the x and y values into an ordered pair:
(-2,3)
Answer:
y=0.5x+4 intersects y=-1.5x.
The intersection point is (-2,3)
Step-by-step explanation:
First, note that if two lines are not parallel, then they must intersect eventually in one way or another. Note that since these are two lines, they will only have one intersection points.
So we have the equation:
[tex]y=-1.5x[/tex]
Parallel lines have the same slope. Therefore, a line parallel to this line also has a slope of -1.5
The equation given to us is:
[tex]y=0.5x+4[/tex]
As we can see, this does not have a slope of -1.5. Therefore, the given equation is not parallel to y=-1.5x. However, this does mean that it will intersect y=-1.5x.
To find the x-value of their intersection, simply set the equations equal to each other and solve for x.
[tex]-1.5x=0.5x+4\\-2x=4\\x=-2[/tex]
Now, plug -4 into either of the equations:
[tex]y=-1.5(-2)=3\\y=0.5(-2)+4=-1+4=3[/tex]
Therefore, the point of intersection is (2,3).
If x = 7, what is the value of 4(x - 5)
Answers
Answer:
8
Step-by-step explanation:
Because if x=7 then it would be 7-5 which equals 2 then you would times 2 and 4 together which equals 8 then you would have your answer which is 8.
Answer:
its 8
Step-by-step explanation:
x= 7
so replace the x with the value of 7
4(7-5)
7 minus 5 is 2
4·2
4 multipied by 2 is 8
so the answer is 8
5x -2 ( 2x-2)= 2(3x-1)+7/2
Answers
Answer:
x = 1/2 or 0.5
Step-by-step explanation:
5x - 2(2x-2) = 2(3x - 1) + 7/2
= 5x - 4x + 4 = 6x - 2 + 7/2
= 5x + 4 = 10x - 2 + 7/2
= 5x + 6 = 10x + 7/2
= 5x + 2.5 = 10x
= 2.5 = 5x
Thus, x = 1/2 or 0.5
Hope this helps!
Mele earned scores of 75, 70, 92,95, and 97 points (a
total of 429 points) on the first 5 tests in Economics II
Solving which of the following equations for s gives
the score he needs to earn on the 6th test to average
exactly 85 points for all 6 tests?
+5=85
F. 429
G. 429
H. + 429
+5 = 85
= 85
J. S+429
= 85
6
K. S+ 429
85
100
Answers
Answer:
The equation for S which gives the score he needs to earn on the 6th test to average exactly 85 points for all 6 tests is;
S + 429 = 85 × 6
Step-by-step explanation:
The parameters given are;
The scores earned by Mele on the first five test in Economics II are;
75, 70, 92, 95, and 97 points
The total test points = 429 points
Therefore, the score, S, Mele needs to earn on the 6th test for him to get an average of exactly 85 points for the 6 tests is found as follows;
From the definition of average, μ = (Sum of data values)/(Number of data)
Sum of data values = S + 429
The number of data = 5 test + 6th test = 6
μ = 85 = (S + 429)/6
Therefore;
S + 429 = 85 × 6
Therefore, the equation for S which gives the score he needs to earn on the 6th test to average exactly 85 points for all 6 tests is S + 429 = 85 × 6.
an equation uses the symbol
Answers
Answer:
The '=' sign.
Step-by-step explanation:
The equals sign ( = ). for example:
3x + 1 = 8.
The equals sign was invented by Robert Recorde of Tenby, South Wales, UK in the early part of the 16th century.
Bill spent $42 on fruit at the grocery store. He spent a total of $60 at the store. What percentage of the total did he
spend on fruit?
Answers
Answer:
70%
Step-by-step explanation:
To find the total percentage of his $60 dollars that he spent on fruit, we simply take the amount of money spent on fruit divided by the total spent.
% spent on fruit = 42 / 60
% spent on fruit = 0.7
% spent on fruit = 70 %
Cheers.
Answer:
70%
Step-by-step explanation:
so he spent 42/60
lets simplify by dividing on both sides by 2
21/30
then divide by 3
7/10
which is also 70/100
so 70%
yaaaaayyyy we r done!!!!!!!!!
HOPE I HELPED
PLS MARK BRAINLIEST
DESPERATELY TRYING TO LEVEL UP
✌ -ZYLYNN JADE ARDENNE
JUST A RANDOM GIRL WANTING TO HELP PEOPLE!
PEACE!
thank you theta upon sin theta cos cos theta + sin thank you theta + cos cube theta upon sin theta + cos theta + sin theta minus cos theta upon sin theta minus cos theta is equal to
Answers
Answer:
Hey... Ans is in the pic..
Hope it helped u if yes mark me mark me BRAINLIEST!
Tysm!
:)
What is the surface area of the sphere below?
Answers
Hey there! I'm happy to help!
To find the surface area of a sphere, here is what you do.
You square the radius.
4²=16
You multiply by 4.
16×4=64
And you multiply by pi!
64×π=64π
Therefore, the surface area of the sphere is A. 64π units². It's that easy!
Now you can find the surface area of a sphere! Have a wonderful day! :D
Question :-
What is the surface area of the sphere that has a radius of 4 units?Answer :-
The surface area of the sphere is 64π units².[tex] \rule{180pt}{3pt}[/tex]
Diagram :-
[tex]\setlength{\unitlength}{1.2cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\qbezier(-2.3,0)(0,-1)(2.3,0)\qbezier(-2.3,0)(0,1)(2.3,0)\thinlines\qbezier (0,0)(0,0)(0.2,0.3)\qbezier (0.3,0.4)(0.3,0.4)(0.5,0.7)\qbezier (0.6,0.8)(0.6,0.8)(0.8,1.1)\qbezier (0.9,1.2)(0.9,1.2)(1.1,1.5)\qbezier (1.2,1.6)(1.2,1.6)(1.38,1.9)\put(0.2,1){\bold{4 \: units}}\end{picture}[/tex]
Solution :-
As per the provided information in the given question, we have been given that the radius of the sphere is 4 units. We have been asked to find or calculate the surface area of the sphere.
To calculate the surface area of the sphere, we will use the formula below :-
[tex]\bigstar \:\:\:\boxed{\sf{\:\:Surface \: Area_{(Sphere)} = 4\pi r^2 \:\:}}[/tex]
Substitute the given values into the above formula and solve for surface area:
[tex]\sf:\implies Surface \: Area_{(Sphere)} = 4\pi r^2[/tex]
[tex]\sf:\implies Surface \: Area_{(Sphere)} = 4 \times \pi \times (4 \: units)^2[/tex]
[tex]\sf:\implies Surface \: Area_{(Sphere)} = (4 \: units)^2 \times 4 \times \pi[/tex]
[tex]\sf:\implies Surface \: Area_{(Sphere)} = 16 \: units^2 \times 4 \times \pi[/tex]
[tex]\sf:\implies \bold{Surface \: Area_{(Sphere)} = 64\pi \: units^2}[/tex]
Therefore :-
The surface area of the sphere is 64π units².[tex]\\[/tex]
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At a school carnival is the diameter of the map of a trampoline has 12 feet and the diameter of the metal frame is 14 feet what is the length in feet of the metal frame that's around the trampoline use 3.14 for pie and round the answer to the nearest 10th
Answers
Answer:
The length of the steel frame will be approximately 44 feet
Step-by-step explanation:
We can solve this problem by calculating the circumference of the steel frame. We are working with the fact that the steel frame was welded into a circular shape.
The circumference of the steel frame can be calculated using
[tex]circumference = \pi \times d[/tex]
where d diameter of the steel frame = 14 feet
[tex]circumference = 3.14 \times 14=43.96ft[/tex]
Therefore, the length of the steel frame will be approximately 44 feet
Solve the inequality 2x-5 is less than or equal to -x+12 . Give your answer as an interval.
Answers
Answer:
[tex]\Large \boxed{\mathrm{( - \infty, \frac{17}{3}) }}[/tex]
Step-by-step explanation:
[tex]2x-5\leq -x+12[/tex]
Add x and 5 on both parts.
[tex]2x+x\leq 12+5[/tex]
Combine like terms.
[tex]3x\leq 17[/tex]
Divide both parts by 3.
[tex]\displaystyle x \leq \frac{17}{3}[/tex]
Use the distributive property to rewrite the given expression without parentheses.
7(x+2)
7(x+2) =
Answers
Answer:
7x+14
Step-by-step explanation:
The distributive property is when you multiply the number on the outside of rhe parenthesis with the numbers on the inside.
In this case it will be 7×x and 7×2
7(x+2)=7x+14
Use distributive property to simplify the following expression. 2(4+9w)
Answers
Answer:
18w+8
Step-by-step explanation:
[tex]2(4 + 9w) \\ = 2(4) + 2(9w) \\ 8 + 18w \\ = 18w + 8[/tex]
Answer:
8+18w [tex]\huge\checkmark[/tex]
Step-by-step explanation:
Hi! Hope you are having an amazing day! :)
Distribute 2 by multiplying everything inside the parentheses by 2:
[tex]\huge\mathrm{2(4+9w)}[/tex]
[tex]\huge\mathrm{8+18w}[/tex] (Answer)
Hope you find it helpful.
Feel free to ask if you have any doubts.
[tex]\bf{-MistySparkles^**^*}\star[/tex]
What is the center of a circle with the equation (x - 6)2 + (y + 2)2 = 9?
A)
(6,2)
B)
(6,-2)
0)
(-6, 2)
D)
(-6, -2)
Answers
Answer:
B. (6,-2)
Step-by-step explanation:
The equation of a circle is (x-h)^2+(y-k)^2=r^2
The center of the circle is (h,k)
So, in this problem, h is 6 and k is -2, so the center of this circle is (6,-2).
equation y = (2x)/(x-1), how do I get -0.5 as the x intercept ???
Answers
Answer:
( 0,0) is the x intercept
Step-by-step explanation:
y = (2x)/(x-1),
To find the x intercept set y = 0 and solve for x
0 = (2x)/(x-1)
Multiply by x-1 on each side assuming x does not equal 1
0 = 2x
x = 0
The x intercept is 0
( 0,0) is the x intercept
What is the domain of F(x) = In(x)?
Answers
Answer as an inequality: [tex]x > 0[/tex]
Answer in interval notation: [tex](0, \infty)[/tex]
Answer in words: Set of positive real numbers
All three represent the same idea, but in different forms.
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Explanation:
Any log is the inverse of an exponential equation. Consider a general base b such that f(x) = b^x. The inverse of this is [tex]f^{-1}(x) = \log_b(x)[/tex]
For the exponential b^x, we cannot have b^x = 0. We can get closer to it, but we can't actually get there. The horizontal asymptote is y = 0.
Because of this, [tex]\log_b(x)[/tex] has a vertical asymptote x = 0 (recall that x and y swap, so the asymptotes swap as well). This means we can get closer and closer to x = 0 from the positive side, but never reach x = 0 itself.
The domain of [tex]\log_b(x)[/tex] is x > 0 which in interval notation would be [tex](0, \infty)[/tex]. This is the interval from 0 to infinity, excluding both endpoints.
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The natural log function Ln(x) is a special type of log function where the base is b = e = 2.718 approximately.
So,
[tex]\log_e(x) = \text{Ln}(x)[/tex]
allowing all of what was discussed in the previous section to apply to this Ln(x) function as well.
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In short, the domain is the set of positive real numbers. We can't have x be 0 or negative.
A rectangular prism has a height of 12 centimeters and a square base with sides measuring 5 centimeters. A pyramid with the same base and half the height of the prism is placed inside the prism, as shown in the figure
Answers
The answer is 200 cm³
The volume of the rectangular prism (V1) is:
V1 = l · w · h (l - length, w - width, h - height)
It is given:
h = 12 cm
w = l = 5 cm (since it has a square base which all sides are the same size).
Thus: V1 = 12 · 5 · 5 = 300 cm³
The volume of pyramid (V2) is:
V2 = 1/3 · l · w · h (l - length, w - width, h - height)
It is given:
h = 12 cm
w = l = 5 cm (since it has a square base which all sides are the same size).
V2 = 1/3 · 12 · 5 · 5 = 1/3 · 300 = 100 cm³
The volume of the space outside the pyramid but inside the prism (V) is a difference between the volume of the rectangular prism (V1) and the volume of the pyramid (V2):
V = V1 - V2 = 300 cm³ - 100 cm³ = 200 cm³
