Answer:
It’s A took test
Step-by-step explanation:
Answer: I'm pretty sure it's A!
Step-by-step explanation: It's on Edge, hope this helped :)
The cubic function p(x) = ax^3 + bx^2 + cx + d has a tangent equation y = 3x + 1 at the point (0, 1) and has a turning point at (-1, -3). Find the values of a, b, c and d. ( Show all ways of solving this math) btw the answer is a = -5, b = -6, c = 3, d = 1. show me the clearest workout
Answer:
[tex]p(x) = -5x^3 -6x^2 + 3x + 1[/tex]
Step-by-step explanation:
Given cubic function:
[tex]p(x) = ax^3 + bx^2 + cx + d[/tex]
As point (0, 1) is on the curve, substitute x = 0 into the function, set it to 1, and solve for d:
[tex]\begin{aligned} p(0) & = 1\\ \implies a(0)^3 + b(0)^2 + c(0) + d & = 1\\ \implies d & = 1 \end{aligned}[/tex]
Differentiate the function:
[tex]\begin{aligned} p(x)& = ax^3 + bx^2 + cx + d\\\implies p'(x)&=3 \cdot ax^{3-1}+2 \cdot bx^{2-1}+1 \cdot cx^{1-1}+0 \\p'(x)&=3ax^2+2bx+c\end{aligned}[/tex]
The tangent equation at the point (0, 1) is y = 3x + 1.
Therefore, the gradient of the tangent equation when x = 0 is 3.
To find the gradient of the function at a given point, substitute the x-value of that point into the differentiated function. Therefore, substitute x = 0 into the differentiated function, set it to 3, and solve for c:
[tex]\begin{aligned}p'(0) & =3 \\ \implies 3a(0)^2+2b(0)+c & =3\\ \implies c & = 3\end{aligned}[/tex]
Substitute the found values of c and d into the function:
[tex]p(x) = ax^3 + bx^2 + 3x + 1[/tex]
Substitute point (-1, -3) into the function and solve for b:
[tex]\begin{aligned}p(-1) & = -3\\\implies a(-1)^3 + b(-1)^2 + 3(-1) + 1 & = -3\\-a+b-3+1&=-3\\-a+b&=-1\\b&=a-1\end{aligned}[/tex]
To find the turning points of a function, set the differentiated function to zero and solve for x.
As there is a turning point of function p(x) when x = -1, substitute x = -1 into the differentiated function and set it to zero (remembering to substitute the found value of c = 3 into the differentiated function):
[tex]\begin{aligned} p'(-1) & =0\\\implies 3a(-1)^2+2b(-1)+3 & = 0\\3a-2b+3&=0\end{aligned}[/tex]
Substitute the found expression for b into the equation and solve for a:
[tex]\begin{aligned}3a-2b+3&=0\\\implies 3a-2(a-1)+3&=0\\3a-2a+2+3&=0\\a+5&=0\\a&=-5\end{aligned}[/tex]
Finally, substitute the found value of a into the found expression for b and solve for b:
[tex]\begin{aligned}b & = a-1\\\implies b & = -5-1\\b & = -6\end{aligned}[/tex]
Therefore:
a = -5b = -6c = 3d = 1Differentiation Rules
[tex]\boxed{\begin{minipage}{4.8 cm}\underline{Differentiating $ax^n$}\\\\If $y=ax^n$, then $\dfrac{\text{d}y}{\text{d}x}=nax^{n-1}$\\\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{4cm}\underline{Differentiating a constant}\\\\If $y=a$, then $\dfrac{\text{d}y}{\text{d}x}=0$\\\end{minipage}}[/tex]
The height, above the ground, of a block on a vertical spring is a sinusoidal (trigonometric) function of time. In the interval from time 2.1 seconds to time 2.7 seconds, the block's height decreases from its maximum of 48 inches to its minimum of 30 inches. Which function h(t) could model the block's height in inches above the ground at time t seconds?
The sinusoidal function for the given conditions can be written as h(t) = 9cos(1.67π(x - 2.1)) + 39.
What is sinusoidal function?The term sinusoidal refers to a curve, also known as a sine wave or a sinusoidal, that shows smooth, periodic oscillation. It is named after the function y=sin (x). Sinusoidal appear often in mathematics, physics, engineering, signal processing, and many other fields.
A general form of a cosine function is given as shown below,
g(x) = a cos(bx+c) + d
Where the values of the given constant is,
a = amplitude
b = The period is of 2pi/B
c = phase shift
d = vertical shift
Since for the given condition the greatest value is 48 and the smallest value is 30 (a difference of 18), therefore, the amplitude is of the function can be written as,
2a = 18
a = 9
Further, a conventional cosine function with amplitude 9 would fluctuate between -9 and 9, while this one ranges between 30 and 48, resulting in d = 39 vertical shift.
Also, The minimum and maximum values form half the period, therefore, we can write,
π/B = 2.7 - 2.1
B = π/0.6
B = 1.67π.
Furthermore, The maximum value in the normal function is at x = 0, but the greatest value in this function is at x = 2.1, thus, the phase shift is 2.1 units to the right, or c = -2.1.
Hence, the sinusoidal function for the given conditions can be written as h(t) = 9cos(1.67π(x - 2.1)) + 39.
Learn more about Sinusoidal Function here:
https://brainly.com/question/12060967
#SPJ1
John buys a phone for $4 500 and sells it to his brother who pays him in three instalments of $1 200.
(a) Determine with the appropriate working if John made a profit or a loss. [2] (b) What was his percentage profit/loss?
Maricopa's Success scholarship fund receives a gift of $ 115000. The money is invested in stocks,
bonds, and CDs. CDs pay 3.75 % interest, bonds pay 4.8 % interest, and stocks pay 7.2 % interest.
Maricopa Success invests $ 45000 more in bonds than in CDs. If the annual income from the
investments is $ 6322.5, how much was invested in each account?
stock=
bonds=
cds=
The value invested in each security will be:
stock= $38000 ,
bonds= $46000
cds= $3000
How to calculate the value?Let the money invested in stocks be 'x', bonds be 'y' and CDs be 'z'.
Total money received as fund = x+y+z = $115000 -(Eqn 1)
$15000 more is invesed in bonds as compared to CDs i.e y = z + $15000 - (Eqn2)
Stocks pay 6.8%, bonds pay 3.6% and CDs pay 4% interest
Interest earned from stocks = 6.8% of x = 0.068x
Interest earned from bonds = 3.6% of x = 0.036x
Interest earned from CDs = 4% of x = 0.04x
Total interest earned = 0.068x + 0.036y + 0.04z = $5840 - (Eqn 3)
x + y + z =$115000 ----(1)
y = z + $15000 -----(2)
0.068x + 0.036y + 0.04z = $5840 ------(3)
Putting y = z+$15000 in Eqn 1 gives us:
x + (z+$15000) + z = $115000 ==> x = $100000 - 2z ----(Eqn 4)
Similarly,
Putting y = z+$15000 in Eqn 3 gives us:
0.068x + 0.036(z+$15000) + 0.04z = $5480 ==> 0.068x + 0.076z = $4940 ----(Eqn 5)
Putting Eqn 4 in Eqn 5,
0.068($100000 - 2z) + 0.076z = $4940
Hence, 0.06z = $1860
z = $31000
Put z = $31000 in Eqn 4 and get x = $100000 - 2z = $38000
Put z = $31000 in Eqn 2 and get y = z + $15000 = $46000
Hence final answer: x = $38000 , y = $46000, z = $31000
where x is the money invested in stocks, y in bonds and z in CDs.
Learn more about bonds on:
https://brainly.com/question/25965295
#SPJ1
Identify the terms for the simplified expression:
21x^3+3x^2-14x+9x^2+15x
Answer: 21x^3 + 3 + 12x^2 + x
Step-by-step explanation:
Figure LMNO is dilated to form figure L'M'NO'.
Where is the center of dilation located?
inside figure LMNO
outside figure LMNO
on a vertex of figure LMNO
L
M
L'
M'
O
-0'-
The location of a center of dilation in the figure is at the point where the corresponding vertex of the pre–image and image overlaps, which is point N, the correct option is therefore;
On a vertex of figure LMNOHow can the center of dilation be found?The given pre–image = Parallelogram LMNO
The image obtained from the pre–image = Parallelogram L'M'N'O'
Required: The location of the center of dilation
Solution:
The center of dilation is the point about which the figure or image is dilated.
It is the point that does not change following the dilation.
A vertex on the pre–image that gives an image vertex at the same point, is at the center of dilation which does not change in both the pre–image and image.
Therefore, given that point N and N' coincides, which indicates that the distance the pre–image point N is dilated to get the image point, N is 0. The center of dilation is at the vertex N.
The correct option is therefore;
On a vertex of figure LMNOLearn more about the center of dilation of a dilation transformation here:
https://brainly.com/question/9659751
#SPJ1
Answer:
On a vertex of figure LMNO
Step-by-step explanation:
The height above ground of a cannon is a function of the time since it was shot.
Question: When time equals 0, why is the height of the cannon ball not equal to 0? Describe the domain of this function. Describe the range.
The height of the cannonball not equal to 0 when time equals 0 because initial height of the cannonball is above the ground
When time equals 0, why is the height of the cannonball not equal to 0?From the graph, we have the y-intercept to be
y-intercept = (0, y), where y > 0
This means that the graph starts above the origin
This in other words mean that the initial height of the cannonball is above the ground (e.g. it could be on a building)
Hence, the height of the cannonball not equal to 0 when time equals 0 because initial height of the cannonball is above the ground
Describe the domain and the range of this functionIn this case, the domain is from t = 0 till the ball lands on the floor, while the range is from the initial height of the cannonball till the maximum height
Read more about domain and range at
https://brainly.com/question/2264373
#SPJ1
(05.01)Which statement best describes the area of the triangle shown below?
It is one-half the area of a rectangle of length 4 units and width 2 units.
It is one-half the area of a square of side length 4 units.
It is twice the area of a rectangle of length 4 units and width 2 units.
It is twice the area of a square of side length 4 units.
A statement that best describes the area of the triangle is It is one-half the area of a square of side length 4 units.
What is the area of the triangle?The area of a triangle can be found by the formula:
= 1/2 x base x height
The base is 4 units and the height if 4 units.
Area of the triangle is:
= 1/2 x 4 x 4
= 8 units²
The area of a square of side length 4 units. is:
= 4 x 4
= 16 units²
In conclusion, option B is correct.
Find out more on the area of a triangle at https://brainly.com/question/17335144
#SPJ1
What is the answer for this question 2 (6² +2²)÷4-10
Step-by-step explanation:
2 . (6² + 2²) ÷ 4 - 10
= 2 . (36 + 4) ÷ 4 - 10
= 2 . 40 ÷ 4 - 10
= 80 ÷ 4 - 10
= 20 - 10
= 10
Standing on the roof of a (42.0+A) m tall building, you throw a ball straight up with an initial speed of (14.5+B) m/s. If the ball misses the building on the way down, how long will it take from you threw the ball until it lands on the ground below? Give your answer in seconds and round the answer to three significant figures.
The time it would take from when you threw the ball until it lands on the ground below is equal to 2.16 seconds.
Given the following data:
Height of building = (42.0+A) m = (42.0+9) m = 51 m.
Initial speed of ball = (14.5+B) m/s = (14.5+8) m/s = 22.5 m/s.
Scientific data:
Acceleration due to gravity = 9.8 m/s²
How to determine the time?Generally speaking, when this ball is thrown straight up at a certain speed, it begins to slow down as a result of the effect of downward gravitational acceleration. Consequently, the ball reaches a maximum height where it can't go higher anymore and then starts to fall down due to gravity.
In order to determine the time it would take from when you threw the ball until it lands on the ground below, we would apply the second equation of motion:
S = ut + ½gt²
½gt² + ut - S = 0
Substituting the given parameters into the formula, we have;
0.5(9.8)t + 22.5t - 51 = 0.
4.9t + 22.5t - 51 = 0.
Next, we would solve the quadratic equation by using the quadratic formula:
[tex]t = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}\\\\t = \frac{-22.5\; \pm \;\sqrt{22.5^2 - 4(0.5)(-51)}}{2 \times 0.5}\\\\t = \frac{-22.5\; \pm \;\sqrt{506.25 + 102}}{2}\\\\t = \frac{-22.5\; \pm \;\sqrt{608.25}}{2}[/tex]
t = 2.16 or -47.16
Since the time cannot be negative, the value of t to three significant figures is equal to 2.16 seconds.
Read more on time here: https://brainly.com/question/27740756
#SPJ1
Complete Question:
Standing on the roof of a (42.0+A) m tall building, you throw a ball straight up with an initial speed of (14.5+B) m/s. If the ball misses the building on the way down, how long will it take from when you threw the ball until it lands on the ground below? Give your answer in seconds and round the answer to three significant figures.
A=9, B=8
the angle bisector bisect the opposite side inti the two length ,2 and 4 unit long. the length of the height on that side is 225 units. determine the length of the other two sides of a triangle.
The lengths of the other two sides of the triangle is 8√6 units.
What will be the length?
Given that,
AD is the angle bisector of ∠A .
BD = 2 units .
DC = 4 units .
AE ⟂ BC and √15 units .
So, AB / AC = BD / DC { By angle bisector theorem }
AB / AC = 2/4
AB / AC = 1/2 ......... Eqn.(1)
Also, BC = BD + DC = 2 + 4 = 6 units .
Now let BE = x units .
So, in right-angled ∆AEB ,
AB = √(15 + x²) { By pythagoras theorem }
In right angled ∆AEC ,
AC = √{15 + (x - 6)²} { By pythagoras theorem }
Putting both values in Eqn.(1),
AB/AC = 1/2
√(15 + x²)/√(15 + x² + 36 - 12x) = 1/2
Squaring both sides,
(15 + x²) / (x² - 12x + 51) = 1/4.
4(15 + x²) = x² - 12x + 51.
60 + 4x² = x² - 12x + 51.
4x² - x² + 12x + 60 - 51 = 0.
3x² + 12x + 9 = 0.
3x² + 3x + 9x + 9 = 0.
3x(x + 1) + 9(x + 1) = 0.
(3x + 9)(x + 1) = 0.
x = (-3) and (-1) .
Taking x = (-1),
AB = √(15 + x²) = √(15 + 1) = 4 units .
So, AC = 4 * 2 = 8 units .
Taking x = (-3),
AB = √(15 + 9) = √24 = 4√6 units.
So, AC = 2 * 4√6
= 8√6 units .
Hence, the lengths of the other two sides of the triangle is 8√6 units.
Learn more about triangle on:
https://brainly.com/question/1058720
#SPJ1
7.) Given 9x-27y = 81
D.) Does the line RISE or fall?
E.) Why?
Answer: rises; your slope is positive
Every single time your slope is positive, your line goes upward.
Every time your slope is negative, however, your line goes downward.
Rearrange 9x - 27y = 81 to -27y = -9x + 81 because we want to put our equation into slope intercept so that we can eventually get our 'y' all by itself.
Divide by -27 for every variable.
Your slope intercept form should now look like this; y = 1/3x - 3
Now that we're completely done or that we have 'y' by itself, it's safe to say that our answer is 1/3, which is, also, positive.
Hope this helps, dawg.
g(x)=−5x+1, find g(1)
Answer:
-4
Step-by-step explanation:
keep value of x as 1 in 5x+1
g(1)=-5×1+1
=-4
SLOVE FOR X , really need help it’s due tmrw thanks
Answer:
3.5
Step-by-step explanation:
21x+6
21/21 6/21
x=3.5
Find the LCM and
GCF of: 25 and 100
Answer:
Look below
Step-by-step explanation:
The LCM of 25 and 100 is 100
The GCF of 25 and 100 are 25.
Which of the following Statements are true?
Statement 1: A right triangle can be an equilateral triangle.
Statement 2: An equilateral triangle can be a right triangle.
Step-by-step explanation:
both statements are wrong.
a right (or right-angled) triangle has a 90° angle. that is all.
an equilateral triangle has 3 equally long sides.
but that also implies that the 3 angles must be equal too.
the sum of all angles in a triangle must be 180°.
if all angles are equally large, that means
180 = 3×angle
angle = 180/3 = 60°.
that means none of the angles can be 90°, so, no right-angled triangle can be equilateral.
and no equilateral triangle can be right-angled.
Assume the statements below are true. If exactly two of the students went to the movies, who did NOT go to the movies?
If Catherine goes to the movies, then Jessika will go.
If Jessika goes to the movies, then Jorge will go.
If Jorge goes to the movies, then Mike will go.
Answer:Jorge and Mike
Step-by-step explanation:
Nobody goes if Mike goes
You are recording intake and output for your patient who has fluid restrictions of 1,000 milliliters per day. During the past 24 hours, the patient has consumed 3 fluid ounces of milk. 725 milliliters of IV fluid and 4 fluid ounces of juice with the potassium supplement. If one fluid ounce is equal to 30 milliliters, how many milliliters of fluids did the patient consume in 24 hours?
The patient consumed 935 milliliters of fluids in 24 hours.
Restrictions of fluid per day = 1000 milliliters
Consumption of fluid by patient in past 24 hours are :
Milk = 3 ounces
IV fluid = 725 Milliliters
Juice = 4 ounces
As we know that,
One fluid ounce = 30 milliliters
Then, Milk = 3 × 30 = 90 milliliters
Juice = 4 × 30 = 120 milliliters
To determine the total amount of fluids we will add the total amount of Milk, IV fluids and Juice.
Fluids consume by patient = 90 + 725 + 120
= 935 milliliters
To learn more about Fluid Consumption visit :
https://brainly.com/question/15382158
#SPJ9
an angle measures 101.4 less then the measure of supplementary angles. what is the measure of each angle
Answer:
39.3°, 140.7°
Step-by-step explanation:
supplementary angles means that together they have 180°.
so, when we have 2 angles, x and y.
x + y = 180
x = y - 101.4
using the second equation in the first
y - 101.4 + y = 180
2y - 101.4 = 180
2y = 281.4
y = 281.4/2 = 140.7°
x = y - 101.4 = 140.7 - 101.4 = 39.3°
so, the starting angle is 39.3°, and every supplementary angle is then 140.7°.
The speed of an object is given by the following formula: where s is the speed of the object, d
is the distance traveled in miles, and t is the time traveled in hours. If a car travels 312 miles at a
rate of 52 mph, how long did it take?
Find an equation for the line graphed below:
Answer: y = -1/5x -3
Step-by-step explanation:
Answer:
Answer given by bryc31 is correct: [tex]y = -\frac{1}{5}x -3[/tex] is correct
I am simply providing an explanation in case you need it
Step-by-step explanation:
The slope-intercept form equation of a straight line in 2D coordinates is given by y = mx + b
where m is the slope(rise/run) and b the y-intercept i.e. the y value where the line intersects the y axis
Given two points (x₁, y₁) and (x₂, y₂) on the straight line, we can compute the slope as follows
m = [tex]\frac{y_2 - y_1}{x_2-x_1}[/tex]
Two distinct points on the line are at (0, -3) and (5,-4)
[tex]m = \frac{-4 -(-3)}{5-0} = \frac{-4 + 3)}{5-0} = \frac{-1}{5} = - \frac{1}{5}[/tex]
So we know the equation to be
[tex]y = - \frac{1}{5}x + b[/tex]
To find b, take any point on the straight line, plug in y and x values in the above equation and solve for b
However, looking at the graph we see that the line crosses the y axis at
y = -3. So this is the value for the y intercept i.e. b
The equation of the line is therefore
[tex]y = - \frac{1}{5}x - 3[/tex]
Find the average rate of change of
The average rate of change of f(x)=[tex]8x^{2} -5[/tex] on the interval [4,b] is [tex]\frac{128-8b^{2} }{4-b}[/tex]
Given,
The function f(x) =[tex]8x^{2} -5[/tex]
The intervals = [4,b]
The average rate of change = [tex]\frac{f(a)-f(b)}{a-b}[/tex]
Where a and b are the interval
f(4)= [tex]8(4)^{2}-5[/tex]
=123
f(b)= [tex]8b^{2}-5[/tex]
The average rate of change = [tex]\frac{123-(8b^{2}-5) }{4-b}[/tex]
[tex]=\frac{123-8b^{2}+5 }{4-b} \\=\frac{128-8b^{2} }{4-b}[/tex]
Hence, The average rate of change of f(x)=[tex]8x^{2} -5[/tex] on the interval [4,b] is [tex]\frac{128-8b^{2} }{4-b}[/tex]
Learn more about average rate of change of function here
brainly.com/question/23715190
#SPJ1
f(x)=2x^2-6
Find f(7)
Answer:
f(7) = 92
Step-by-step explanation:
f(7) means what is the value of f(x) when x = 7
substitute x = 7 into f(x)
f(7) = 2(7)² - 6 = 2(49) - 6 = 98 - 6 = 92
a decimal point is used when working with dollars but the decimal point is not necessary when working with cent for each dollar amount give the equivalent amount expressed as cents $5.74 and $0.16
A decimal point is used when working with dollars but the decimal point is not necessary when working with cent for each dollar amount, the equivalent amount expressed as cents of $5.74 is 574 cents and $0.16 is 16 cents
We know that 1 dollar is equal to 100 cents
So, x dollar = x(100) cents
For $5.74 = 5.74(100) cents
= 574 cents
For $0.16 = 0.16(100) cents
= 16 cents
What is a decimal point?Integer and non-integer numbers are represented using the decimal numeral system, also known as the base-ten positional numeral system, denary, or decanary. The Hindu-Arabic numeral system has been expanded to include non-integer values. Decimal notation is the term used to describe how numbers are represented using the decimal system.
It is indicated by a '.', for instance, 3.14
Learn more about decimal point
https://brainly.com/question/26090574
#SPJ9
how many liters make a kilogram
Answer:
One litre of water has a mass of almost exactly one kilogram.kilograms = liters × density of a liquid.
construct a triangle ABC with line AB= 10cm BC=6cm and AC=11cm. Hence measure the values of the angle
Hence , the construction of the triangle is given below.
AB = 10 cm BC = 6 cm AC = 11 cm
We have to find ∠A, ∠B, and ∠C.
To construct a triangle,
Firstly draw a line segment AB = 10 cm
From A we need a point C at a distance of 6 cm. So with A as the center, draw an arc of 6cm in length from point A.
From B we need a point C at a distance of 11 cm. So with B as the center, draw an arc of 11cm in length from point B.
Mark the point of intersection of the arcs as C.
Meet points C to A and B respectively.
By using a protractor measure the angles of A, B, and C.
To learn more about the construction of triangles refer here : https://brainly.com/question/26262748
#SPJ9
2. Find the roots of the polynomial equation (point)
2x³ + 2x2-19x+ 20 = 0
Answer:
x=-4
Step-by-step explanation:
this is if by roots, the problem is asking for the zeros of the equation
The functions fand g are defined as follows.
g(x)=2x³ +6
f(x)=-4x-1
Find f(7) and g (-3).
Simplify your answers as much as possible.
f(7)=
g(-3)=
The probability of rain in Nevada is 0.3.
If it rains, the probability of the school bus being late is 0.4.
If it does not rain, the probability of the school bus being late is 0.15.
What is the probability that it will not rain?
If it does not rain, the probability of the school bus bring on time is?
What is the probability that it will rain and the school bus will be on time?
Based on the probability of rain in Nevada, the probability that it will not rain is 0.7.
The probability that if it does not rain, the school bus will be on time is 0.85.
The probability that it will rain and the school bus will still be on time is 0.6.
How to find the probability?The probability that it will not rain in Nevada can be found by the formula:
= 1 - probability of rain in Nevada
= 1 - 0.3
= 0.7
The probability that if it does not rain, the school bus will be on time is:
= 1 - probability of the school bus being late if it does not rain
= 1 - 0.15
= 0.85
The probability that it will rain and the school bus will still be on time is:
= 1 - probability of the school bus being late if it rains
= 1 - 0.4
= 0.6
Find out more on probability at https://brainly.com/question/25870256
#SPJ1
For the function f(x) = (2e)5, find
ƒ−¹(x).
Answer:
no
Step-by-step explanation:
89382