a. The acceleration of P at time t is a(t) = 12t - 30.
b. The indefinite integral of 5 + 2sin^2(x) dx is 6x - (1/2)sin(2x) + C, where C is the constant of integration.
(a) To find the velocity and acceleration of point P at time t, we need to differentiate the position function x(t) = 2t^3 - 15t^2 + 36t + 4 with respect to time.
Given:
x(t) = 2t^3 - 15t^2 + 36t + 4
Velocity:
The velocity of P is given by the derivative of the position function, which is the first derivative of x(t).
v(t) = dx/dt
Differentiating x(t) with respect to t:
v(t) = d/dt(2t^3 - 15t^2 + 36t + 4)
= 6t^2 - 30t + 36
Therefore, the velocity of P at time t is v(t) = 6t^2 - 30t + 36.
Acceleration:
The acceleration of P is given by the derivative of the velocity function, which is the second derivative of x(t).
a(t) = dv/dt
Differentiating v(t) with respect to t:
a(t) = d/dt(6t^2 - 30t + 36)
= 12t - 30
Therefore, the acceleration of P at time t is a(t) = 12t - 30.
(b) The indefinite integral of 5 + 2sin^2(x) dx:
∫(5 + 2sin^2(x)) dx
Using the identity sin^2(x) = (1/2)(1 - cos(2x)):
∫(5 + (2/2)(1 - cos(2x))) dx
∫(5 + (1 - cos(2x))) dx
∫(6 - cos(2x)) dx
Integrating term by term:
∫6 dx - ∫cos(2x) dx
Integrating each term:
6x - (1/2)sin(2x) + C
Therefore, the indefinite integral of 5 + 2sin^2(x) dx is 6x - (1/2)sin(2x) + C, where C is the constant of integration.
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what is the solution to the inequality below? b+1 > -8
Answer:
from my point of view the solution should be 36
Answer:
b > -9
Step-by-step explanation:
Fill in the blank to make the two fractions equivalent.
7/8=?/48
I’m confused can someone help me ASAP
Answer:
42 should be in the blank.
Step-by-step explanation:
If you multiply 7/8 by 6, watch what happens...
7/8 *6 = 42/48
The denominators are the same, which shows how the equations are probably equal.
I know it might seem confusing because I'm not great at explaining, but I hope it helps! Have an awesome day c:
Find the unknown number 18/8 = 24/x
Answer:
[tex] \huge{ \boxed{ \bold{ \tt{10.6}}}}[/tex]
Step-by-step explanation:
[tex] \rm{ \frac{18}{8} = \frac{24}{x} }[/tex]
Use cross product property
⇢ [tex] \rm{18 \times x = 24 \times 8}[/tex]
⇢ [tex] \rm{18x = 192}[/tex]
Divide both sides by 18
⇢ [tex] \rm{ \frac{18x}{18} = \frac{192}{18}} [/tex]
⇢ [tex] \rm{x = 10.6}[/tex]
We're done !
Hope I helped!
Best regards! :D
~TheAnimeGirl
Three consecutive integers are such that three times the smallest is 14 more than the largest.Find the integers.
Answer:
8, 9, 10Step-by-step explanation:
x ← the smallest integer
x+1 ← the middle integer
x+2 ← the largest integer
3x ← three times the smallest
x+2 + 14 ← 14 more than the largest
3x = x+2 + 14
-x -x
2x = 16
÷2 ÷2
x = 8
x+1 = 8+1 = 9
x+2 = 8+2 = 10
Check: 3×8 = 24; 24-14 = 10
Can someone help me plsss
Answer:
The slope of the line is [tex]\frac{-1}{2}[/tex]
Step-by-step explanation:
The rule of the slope of a line is
m = [tex]\frac{y2-y1}{x2-x1}[/tex] (x1, y1) and (x2, y2) are two points lie on the line→ Let us solve the question
∵ The line contains the points B (-4, 4) and R (0, 2)
∴ x1 = -4 and y1 = 4
∴ x2 = 0 and y2 = 2
→ Substitute them in the rule of the slope above to find it
∵ m = [tex]\frac{2-4}{0--4}=\frac{-2}{4}=\frac{-1}{2}[/tex]
∴ m = [tex]\frac{-1}{2}[/tex]
∴ The slope of the line is [tex]\frac{-1}{2}[/tex] .
5+7-2+5=? Please help me out
The answer of 5+7-2+5=15
Find the value of the discriminant. Then describe the number and type of roots for the equation. 3x^2\:+\:4x\:-7=0
The given equation has two real and distinct roots.
The formula for the discriminant is b² - 4ac. For the given equation, 3x² + 4x - 7 = 0,
the value of a = 3, b = 4 and c = -7.Substituting these values in the formula for discriminant, we get:$$\begin{aligned}b^2-4ac&=4^2-4\times3\times(-7) \\&=16+84 \\&=100 \end{aligned}$$
Hence, the value of discriminant is 100.Using the value of the discriminant, we can determine the nature of roots. If the discriminant is positive, then the roots are real and distinct.
If the discriminant is zero, then the roots are real and equal.
If the discriminant is negative, then the roots are imaginary and conjugate.In this case, the discriminant is positive (100), so the roots will be real and distinct.
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WILL GIVE BRAINLIEST- In this diagram, is ZHCS (on the right) a scaled copy of XNYJ (on the left)? Explain why or why not.
Answer:
No, they are not copies of each other.
Step-by-step explanation:
<XNY and <ZHC are not the same sized angles. The shapes would have the same angles if they were just scaled down copies.
A uniform distribution is defined over the interval from 2 to 5.
What is the range of the random variable, x?
Over the range, what is the probability of the random variable, x?
What is the area of this uniform distribution?
The probability of x within this range is constant and equal to 1/3. The area under the uniform distribution curve is 1.
The range of the random variable, x, in a uniform distribution from 2 to 5 is [2, 5]. It represents the entire interval of possible values for x.
The probability of the random variable, x, in a uniform distribution is constant over the range. Since it is a uniform distribution, the probability density function is equal for all values within the range. Therefore, the probability of x taking any specific value within the range [2, 5] is the same, and it is given by 1 divided by the length of the range:
Probability of x = 1 / (length of range)
= [tex]P(x) = \frac{1}{5 - 2} = \frac{1}{3}[/tex]
The area of the uniform distribution is represented by the probability density function over the range. Since it is a uniform distribution, the probability density is constant within the range. Therefore, the area under the curve is equal to the length of the range multiplied by the constant probability density:
Area = (length of range) * (probability density) = (5 - 2) * (1 / (5 - 2)) = 3 * (1 / 3) = 1.
Hence, the area of the uniform distribution is 1.
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find value of each of the following 11+(-33)-(-7)
Answer:
= 11-33+7
= 11+7-33
= 18-33
= -15
Step-by-step explanation:
if we multiple + by - then it becomes -
if we multiple - by - then it becomes +
by this way I have done
I hope this will help u .
water runs into a conical tank at the rate of 26 cubic inches per second. the tank stands point down and has a height of 11 inches and a base radius of 7 inches. how fast is the water level rising when the water is 5 inches deep?
The water level is rising at a rate of approximately 0.017 inches per second when the water is 5 inches deep.
Let's start with the formula for the volume of a cone.V= 1/3πr²h
Here, h is the height of the water level at a given time. We are given that water is flowing in at a rate of 26 cubic inches per second. Therefore, we can calculate the rate of change of volume as dV/dt = 26.The tank stands point down, which means that the apex of the cone is at the bottom and the base is at the top. The height of the tank is 11 inches, so when the water level is 5 inches deep, the remaining height of the tank that is empty is 11 - 5 = 6 inches.The radius of the tank at the base is 7 inches, which means that the radius of the top of the water level is proportional to the height of the water level. Therefore, the radius of the top of the water level when the water level is 5 inches deep is: r = (5/11) x 7 = 3.18 inches.Now we can use the formula for the volume of a cone to find the volume of water in the tank when the water level is 5 inches deep.
V= 1/3πr²h= 1/3 x π x (3.18)² x 5= 53.4 cubic inches
Now we can find the rate of change of height with respect to time using the formula
dV/dt = A dh/dt, where A is the area of the base of the tank.
A = πr² = π(7)² = 49π square inches.
Therefore, we have:
26 = 49π dh/dt
dh/dt = 26 / (49π)
dh/dt ≈ 0.017
The water level is rising at a rate of approximately 0.017 inches per second when the water is 5 inches deep.
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Solve 4 −6
s −83
Thank you in advance
Answer:
Alright, so we have 4 - 6 = s - 83.
This means
-2 = s - 83
Add 83 to both sides to get:
81 = s
s = 81 :)
The probabilities of it landing on sections A, B and
C are shown in the table below.
What is the probability, as a percentage (%), of the
spinner landing on section D?
Section
A
B
с
Probability
1
20
0.23
37%
Answer:
.05 + .23 + .37 + P(D) = 1
.65 + P(D) = 1
P(D) = .35 = 35%
Solve by quadratic formula:
8a2 + 6a + 5=0
Answer:
[tex]x = \frac{-3 \pm i\sqrt{31}}{8}[/tex]
Step-by-step explanation:
Quadratic Formula: [tex]x = \frac{-b \pm \sqrt{b^2-4ac} }{2a}[/tex]
√-1 is imaginary number i
Step 1: Define Quadratic
8a² + 6a + 5 = 0
a = 8
b = 6
c = 5
Step 2: Plug into Quadratic Formula
[tex]x = \frac{-6 \pm \sqrt{6^2-4(8)(5)} }{2(8)}[/tex]
Step 3: Solve
[tex]x = \frac{-6 \pm \sqrt{36-160} }{16}[/tex]
[tex]x = \frac{-6 \pm \sqrt{-124} }{16}[/tex]
[tex]x = \frac{-6 \pm \sqrt{124} (\sqrt{-1} )}{16}[/tex]
[tex]x = \frac{-6 \pm i\sqrt{124}}{16}[/tex]
[tex]x = \frac{-6 \pm 2i\sqrt{31}}{16}[/tex]
[tex]x = \frac{2(-3 \pm i\sqrt{31})}{16}[/tex]
[tex]x = \frac{-3 \pm i\sqrt{31}}{8}[/tex]
Evaluate each expression.
1) 2 x 6+1+1
A) 13
B) 10
C) 14
D) 19
Answer:
c) 14
Step-by-step explanation:
2*6 + 1 + 1
following PEMDAS, the multiplication comes first.
2 * 6 = 12
12 + 1 + 1
14
Two similar triangles are shown below:
Which two sets of angles are corresponding angles? (4 points)
w and v;
w and y;
w and z;
w and z;
Answer:
it's w and y
Step-by-step explanation:
i am no good with explaining sorry
I need helps with this please its due tmr :(
1. 17x - 3
2. 5m + 4n
3.-11x + 11
4. 6k + 1
5. 5xy + 7x
6. 7x - 19
7. 14a - 3b + 4
8. 6m - n
9. -a + 2n + 7
10. 6a
(c) A different television costs $330.
(1) Ben buys one in a sale when this cost is reduced by 15%.
How much does Ben pay?
Which of the following are remote interior angles of angle 1? Check all that apply.
Answer:
3 and 4
Step-by-step explanation:
3 and 4 because you have to find two angles(in the triangle) that are far away of angles 1
which are 3 and 4
Answer: 3 and 4
Step-by-step explanation:
How do you spell 63 in word form
Answer:
Hey mate here is ur answer.....
Step-by-step explanation:
63
Sixty Three
hope it helps you,
follow me.....
Answer:
sixty three
Step-by-step explanation:
What is 829×2929-(920)×0
Answer:
0
Step-by-step explanation:
Use the remainder Theorem to find the remainder for (x2- 2)/(x - 1) and state whether or not the binomial is a factor of
the polynomial.
Answer:
The remainder is -1
The binomial is not a factor of the polynomial
Step-by-step explanation:
In the algebraic division, there are 4 terms
Dividend ⇒ the term before the division signDivisor ⇒ the term after the division signQuotient ⇒ the answerRemainder ⇒ appear when the dividend not divisible by the divisor (the divisor is not a factor of the dividend)The remainder theorem:
If you divide a polynomial f(x) by (x - h), then the remainder is f(h).You do not need to use the long division to find the remainder, just evaluate the polynomial when x = h to find the remainder.If h(h) = 0, then (x - h) is a factor of f(x)Let us use it to solve the question
∵ The dividend is x² - 2
∴ f(x) = x² - 2
∵ The divisor is x - 1
∴ (x - h) = (x - 1)
∴ h = 1
Let us find f(1)
∵ f(1) = (1)² - 2 = 1 - 2 = -1
∴ f(1) = -1
∴ The remainder is -1
∵ f(1) ≠ 0
∴ x - 1 is not a factor of x² - 2
∴ The binomial is not a factor of the polynomial
Earth’s diameter is approximately 12,760,000 meters.
What is that number in scientific notation?
1.276 × 10-7
12.76 × 10-6
1.276 × 107
0.1276 × 108
Answer: C. 1.276 x 107
Step-by-step explanation:
Correct on e d g e n u i t y!
Answer:
C
Step-by-step explanation:
I just took the asignment.
What is -115/12 as a mixed number?
Answer:
Since − 115 /12
is a proper fraction, it cannot be written as a mixed number.
Cannot be written as a mixed number
Step-by-step explanation:
Which value from the set (2 14, 16, 63} makes the equation n - 7 = 9 true?
63
16
2
14
Answer:
16
Step-by-step explanation:
16-7=9 so 16 makes the equation n-7=9 true
which equation in a standar form has a grpah that passes through the point (-4,2) and has a slope 9/2
Equation in standard form that has a graph that passes through point (-4, 2) and has slope of 9/2 is calculated to be as equal to -40.
The equation in standard form that has a graph that passes through the point (-4, 2) and has a slope of 9/2 is given by :
Step 1: Recall the standard form of a linear equation
The standard form of a linear equation is Ax + By = C, where A, B, and C are constants.
Step 2: Substitute given values
The equation should pass through the point (-4, 2) and should have a slope of 9/2.
Therefore, the slope-intercept form of the equation is given by:
y - 2 = (9/2)(x + 4)
Multiplying through by 2, we have: 2y - 4 = 9(x + 4)2y - 4
= 9x + 36
Rearranging, we get: 9x - 2y
= -40
Therefore, the equation in standard form that has a graph that passes through the point (-4, 2) and has a slope of 9/2 is 9x - 2y
= -40.
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how do you write a paragraph proof
Evaluate.
4/7+3/4
A. 3/7
B. 37/56
C. 7/11
D. 19/28
Answer:
its
1.32142857143
Step-by-step explanation:
if its not im sary
If f(x) = 4x4 + 5x2 + 4, then what is the remainder when f(x) is divided by
2 + 2?
Step-by-step explanation:
16+10+4
26+4
30
30÷(2+2)
30÷4
7 1/2
In the diagram below AB is parallel to CD what is the value of y
Answer:
y=60 due to adjacent angle
Answer:
Option - A. 60°
Step-by-step explanation:
AB is parallel to CD and given angle is alternate interior angle to y
∴ y = 60°
