Answer:
Step-by-step explanation:
I see you're in college math, so we'll solve this with calculus, since it's the easiest way anyway.
The position equation is
[tex]s(t)=-1.86t^2+15t[/tex] That equation will give us the height of the rock at ANY TIME during its travels. I could find the height at 2 seconds by plugging in a 2 for t; I could find the height at 12 seconds by plugging in a 12 for t, etc.
The first derivative of position is velocity:
v(t) = -3.72t + 15 and you stated that the rock will be at its max height when the velocity is 0, so we plug in a 0 for v(t):
0 = -3.72t + 15 and solve for t:\
-15 = -3.72t so
t = 4.03 seconds. This is how long it takes to get to its max height. Knowing that, we can plug 4.03 seconds into the position equation to find the height at 4.03 seconds:
s(4.03) = -1.86(4.03)² + 15(4.03) so
s(4.03) = 30.2 meters.
Calculus is amazing. Much easier than most methods to solve problems like this.
MY NOTES Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. (Enter your answers as a comma-separated list.) f(x) = 2x2 − 4x + 3, [−1, 3
Answer:
b) [tex]c=1[/tex]
Step-by-step explanation:
From the question, we are told that:
Function
[tex]F(x)=2x^2-4x+9[/tex]
Given
Rolle's theorem states that if a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b) such that f(a) = f(b), then f′(x) = 0 for some x with a ≤ x ≤ b.
Generally, the Function above is a polynomial that can be Differentiated and it is continuous
Where
-F(x) is continuous at (-1,3)
-F(x) Can be differentiated at (-1.3)
-And F(-1)=F(3)
Therefore
F(x) has Satisfied all the Requirements for Rolle's Theorem
Differentiating F(x) we have
[tex]F'(x)=4x-4[/tex]
Equating F(c) we have
[tex]F'(c)=0[/tex]
[tex]4(c)-4=0[/tex]
Therefore
[tex]c=1[/tex]
Frances bought a new dress that was discounted by 24%. she used the following expressions to find the price of the dress after the discount was applied
Answer:
[tex]0.76d[/tex]
Step-by-step explanation:
Given
[tex]Formula = d - (0.24)d[/tex]
Required
Equivalent expression
We have:
[tex]Formula = d - (0.24)d[/tex]
Open bracket
[tex]Formula = d - 0.24d[/tex]
[tex]Formula = 0.76d[/tex]
PLEASE HELP!!!
Find the equation of the line with an x intercept of 4 and a y intercept of -1.5
Answer:
y = 4x - 1.5
Step-by-step explanation:
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
y = 4x - 1.5
4. (08.02 MC)
Factor completely 2x3 + 10x2 + 14x + 70. (5 points)
(2x^2 + 14)(x + 5)
(x^2 + 7)(2x + 10)
2(x^3 + 5x2 + 7x + 35)
2[(x^2 + 7)(x + 5)]
Answer:
2[(x^2 + 7)(x + 5)]
Step-by-step explanation:
Note that the ratio of the first and second terms is the same as that between the third and fourth terms. So this cubic will factor by grouping, but first we can separate out the common scalar factor 2...
2x3+10x2+14x+70=
2(x3+5x2+7x+35)
2((x3+5x2)+(7x+35))
2(x2(x+5)+7(x+5))
2(x2+7)(x+5)
Answer:
The answer is D. 2[(x2 + 7)(x + 5)]
Step-by-step explanation:
Write an equation for the graph below in terms of x
Answer:
x = -2
Step-by-step explanation:
the line goes through -2 on the x-axis
the line also goes through -3 on the y-axis
Evaluate this |-2+3|
[tex]\displaystyle \Large \boldsymbol{} |-2+3| =|1|=1[/tex]
Find the area of the triangle with vertices (0,0,0),(−4,1,−2), and (−4,2,−3).
Answer:
0.5*sqrt33
Step-by-step explanation:
A(0,0,0) B(-4,1,-2), c(-4,2,-3)
Vector AB is (-4-0,-1-0, -2-0)= (-4,-1,-2) The modul of AB is sqrt (4squared+
+(-1) squared+ (-2) squared)= sqrt (16+1+4)=sqrt21
Vector AC is (-4,2,-3) The modul of vector AC is equal to sqrt ((-4)squared+ 2squared+(-3)squared)= sqrt(16+4+9)= sqrt29
Vector BC is equal to (-4-(-4), 2-1, -3-(-2))= (0,1,-1)
The modul of BC is sqrt (1^2+(-1)^2)=sqrt2
Find the angle B
Ac^2= BC^2+AB^2-2*BC*AB*cosB
29= 2+21-2*sqrt2*sqrt21*cosB
29= 2+21-2*sqrt42*cosB
cosB= -3/ sqrt42
sinB= sqrt( 1-(-3/sqrt42)^2)=sqrt33/42= sqrt11/14
s=1/2* (sqrt2*sqrt21*sqrt11/14)=1/2*sqrt(42*11/14)= 0.5*sqrt33
Người ta chiếu xạ liều 3000 Rơn ghen vào một quần thể ruồi dấm ở thế hệ F1: Chiếu xạ 1000 con ruồi dấm không cho ăn đường thì có 80 con bị đột biến và chiếu xạ 1000 con ruồi dấm có cho ăn đường thì có 120 con bị đột biến. Cho ăn đường có ảnh hưởng đến tỉ lệ đột biến của ruồi giấm không, với mức ý nghĩa 5%? Giá trị kiểm định là
Answer:
gggggggggggggggggggggrrrrrrrrrrrttyuuiiiii
A plot of land in the shape of a horizontal ellipse has a pole at each focus. The foci are 16 feet from the center. If the plot of land is 40 feet across one axis, how long is it across the other axis?
a. 34 feet
b. 46 feet
c. 24 feet
d. 30 feet
Answer: 24 feet
Step-by-step explanation: i just guessed it on pluto and got it right. please leave a like if it worked
The length of another axis for the given ellipse will be around 25.6125 feet so none of the options will be correct.
What is an ellipse?a regular oval form produced when a cone is cut by an oblique plane that does not intersect the base, or when a point moves in a plane so that the sum of its distances from two other points remains constant.
In another word, an ellipse is a curve that becomes by a point moving in such a way that the sum of its distances from two fixed points is a closed planar curve produced.
General equation of an ellipse
(x 2 / a 2 )+ (y2 / b 2 )= 1
Given that
the plot of land is 40 feet across one axis
so 2a = 40 feet
a = 20 feet
The foci are 16 feet from the center so
c = 16
Now we know that
c = √(b² - a²)
c² = b² - a²
16² = b² - 20²
b = 25.6125
So, the length of the minor axis will be around 25.6125 feet.
To learn more about ellipse,
https://brainly.com/question/14281133
#SPJ2
Please helpppppp i need help…
///..
ASAP!!!!
!!!,,!!!!!!
Answer:
True
Step-by-step explanation:
64 - x^2
Rewriting as
8^2 - x^2
(8-x)(8+x)
This is the difference of squares
What is the area of a square with a side length of 32 yards?
Answer:
A=1024 yd.^2
Step-by-step explanation:
A=s^2
Substitute,
A=32^2
So,
A=1024 yd.^2
Answer:
1024 yd²
Step-by-step explanation:
Since it's a square, the side lengths will all be the same length. Due to this, you can square the given value to find the area.
A(Square) = 32² = 1024
Find the slope of the line
Slope=m=_______
Answer:
[tex]\displaystyle m = \frac{3}{4}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Reading a coordinate planeCoordinates (x, y)Slope Formula: [tex]\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]Step-by-step explanation:
Step 1: Define
Identify points from graph.
Point (4, 0)
Point (0, -3)
Step 2: Find slope m
Simply plug in the 2 coordinates into the slope formula to find slope m
Substitute in points [Slope Formula]: [tex]\displaystyle m = \frac{-3 - 0}{0 - 4}[/tex]Simplify: [tex]\displaystyle m = \frac{3}{4}[/tex]muscle max gym charges a $30 fee to join plus $2 each day that you go workout. Capital cross-fit charges $10 to join and $4 each day you use the gym. After how many days of workouts would the two gyms have cost you the same amount of money?
Set up equations for each gym.
multiply daily cost by number of days(x) and add the fee:
Muscle max: 2x + 30
Capital: 4x + 10
Now set them
Equal to each other and solve for x:
2x + 30 = 4x + 10
Subtract 2x from both sides :
30 = 2x + 10
Subtract 10 from both sides :
20 = 2x
Divide both sides by 2:
X = 10
It will take 10 days
Use differentials to estimate the amount of paint needed to apply a coat of paint 0.07 cm thick to a hemispherical dome with diameter 50 m. (Round your answer to two decimal places.)
Answer:
2.75 m²
Step-by-step explanation:
From the information given:
the thickness of the paint = 0.07 cm = (0.07/100) m
= 0.0007 m thick
the diameter hemispherical dome = 50 m
∴
radius of the dome = 50m /2 = 25 m
The volume of a hemispherical dome is expressed as:
[tex]V = \dfrac{2}{3}\pi r^3[/tex]
Thus, the change in the volume now is:
[tex]\dfrac{dV}{dr} = \dfrac{2}{3}\pi *3 r^2[/tex]
[tex]{dV} = \dfrac{2}{3}\pi *3 r^2 (dr)[/tex]
[tex]{dV} = 2 \pi r^2 (dr)[/tex]
∴
dV = 2π × (25)² (0.0007)
where;
dr = 0.0007
dV = 2π × (25)² (0.0007)
dV = 2.75 m²
Find all real zeros of the function y = 2x - 4.
a.
2
C.
-4
b. 2, -4
d. -2
Answer:
x = 2
Step-by-step explanation:
To find the zeroes of the function, substitite 0 for y.
0 = 2x - 4
~Add 4 to both sides
4 = 2x
~Divide 2 to both sides
2 = x
Best of Luck!
List the stem numbers below!!
Answer:
see below
Step-by-step explanation:
The stems are in the middle and the leaves are on the left and right
Stems are 0,1,2,3,4,5
please help me
find x
9514 1404 393
Answer:
x = 6√2
Step-by-step explanation:
The side ratios in an isosceles right triangle are ...
1 : 1 : √2
These will be the same as ...
x : x : 12
so, ...
x = 12/√2
x = 6√2
A team wishes to purchase 10 shirts of the same color. A store sells shirts in 3 different colors. What must the inventory of the store be in order to conclude that there are at least 10 shirts in one of the three colors?
Answer:
30
Step-by-step explanation:
What is the simplified form of the following expression? Assume x > 0.
3
2x
16x
2x
4/24x²
2x
4/2443
16x4
124²
Answer:
fourth root of 24 x cubed/16x to the power four
Venn diagrams: unions, intersections, and complements
Attached is the photo reference
Answer:
a) 0
b) 2,3,4,5,6,7
c)3,4,6,7
Step-by-step explanation:
Question 6 of 10
The domain of a function f(x) is x = 0, and the range is ys -1. What are the
domain and range of its inverse function, '(x)?
Answer: y = 0 and x = -1
Please explain the answer
Answer:
3.5
Step-by-step explanation:
in order to find the maximum, we are basically solving to find the vertex of the graph. to find the vertex use :
-b/2a
the 'b' is 112
the 'a' is -16
so :
-112/-32 = 3.5
the answer is B, 3.5
What is the image point of (4, -6) after a translation right 5 units and up 4 units?
Answer:
(9,-2)
Step-by-step explanation:
5 is the x coordinate, and 4 is the y coordinate. When you go right a certain amount of units, you add those units to your x coordinate. If you were to go left a certain amount of units, you'd subtract them. Since we're going right, 5 + 4 = 9. When you go up a certain amount of units, you add those units to you y coordinate. If you were to go down a certain amount of units, you'd subtract them. Since we're going up, -6 + 4 = -2. So, x = 9 and y = -2, or (9,-2)
If x/4-y/6=1/6 and y/z=1/2, then what is the value of 3x-z?
A. 4
B.6
C. 3
D. 2
E. None
A certain freezing process requires that room temperature be lowered from 35oC at the rate of 6oC every hour. What will be the room temperature 8 hours after the process begins?
Answer:
-13 degrees celcius.
Step-by-step explanation:
6 degrees are lowered every hour. 6*8 = 48 degrees, 48 degrees are lowered.
35-48 is -13. The room temperature will be -13 eight hours after the process begins.
1% defective parts. 100,00 parts made in total. The number of defects made should equal?
Answer:
1,000 defects
Step-by-step explanation:
Find how many defects that should be made by finding 1% of 100,000:
100,000(0.01)
= 1000
So, there should be 1,000 defects
Consider the given statement. Determine whether its is equivalent to the given statement, a negation, or neither. Attached is the photo reference.
Answer:
1. Negation
2. Equivalent
3. Neither
4. Neither
Step-by-step explanation:
p ^ ~q
~q → p~
~q ∨ p
~p ∨q
You measure 49 turtles' weights, and find they have a mean weight of 80 ounces. Assume the population standard deviation is 6.1 ounces. Based on this, construct a 99% confidence interval for the true population mean turtle weight. Round your answers to 2 decimal places.
Answer:
The 99% confidence interval for the true population mean turtle weight is between 77.76 and 82.24 ounces.
Step-by-step explanation:
We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.99}{2} = 0.005[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a p-value of [tex]1 - 0.005 = 0.995[/tex], so Z = 2.575.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 2.575\frac{6.1}{\sqrt{49}} = 2.24[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 80 - 2.24 = 77.76 ounces.
The upper end of the interval is the sample mean added to M. So it is 80 + 2.24 = 82.24 ounces.
The 99% confidence interval for the true population mean turtle weight is between 77.76 and 82.24 ounces.
When a 0.42 tax was added to the price of a ticket, the total bill come to $7.03. Describe the above situation as a linear equation.
Answer:
P = 7.03 - 0.42T
Step-by-step explanation:
Let the price of a ticket be P.
Let the ticket be T.
A linear equation can be defined as an algebraic equation that's typically written for two (2) independent variables, in which each of them has an exponent of one (1) and they make a straight line when plotted on a graph.
Given the following data;
Tax = 0.42
Total bill = $7.03
Translating the word problem into an algebraic expression, we have;
0.42T + P = 7.03
P = 7.03 - 0.42T
hi plz help ASAP tyyy ^^
Answer:
26.75 units²
Step-by-step explanation:
This shape can be split into 3 triangles and a square. Find the area of each shape then add them all up.
[tex]A(Square)=2(2)=4\\\\A(Triangle)=\frac{1}{2}(2)(2)=2\\\\A(Triangle)=\frac{1}{2}(5)(2)=5\\\\A(Triangle)=\frac{1}{2}(9)(3.5)=15.75\\\\A(Shape)=4+2+5+15.75=26.75[/tex]
Therefore, the area of the shape is 26.75 units².
