The line contains the point (-7,0) and is parallel to the line defined by 4x=3y. What is the equation of the line
A student is trying to remember some formulas from geometry. in what follows, assume a is area, v is volume, and all other variables are lengths. determine which formulas are dimensionally consistent.
Find the coordinates of point p which divides the line segment from A=(0,4)to B=(6,8)in a ratio of 1:2
Simplify 13 + 2 - 5 - 15
13 +2 = 15 -5= 10 -15 = -5
For what values of r does the function y = erx satisfy the differential equation y'' − 6y' + 2y = 0? (enter your answers as a comma-separated list.)
The values of [tex]r[/tex] is [tex]\boxed{r = 3 - \sqrt7 }[/tex] and [tex]\boxed{r = 3 + \sqrt 7 }.[/tex]
Further explanation:
Given:
The function is [tex]y = {e^{rx}}.[/tex]
The differential equation is [tex]y'' - 6y' + 2y = 0\,\,\,\,\,or\,\,\,\,\dfrac{{{d^2}y}}{{d{x^2}}} - 6\dfrac{{dy}}{{dx}} + 2y = 0[/tex]
Explanation:
The given function can be expressed as follows,
[tex]y = {e^{rx}}[/tex]
Differentiate the above equation with respect to [tex]x[/tex].
[tex]\begin{aligned}\frac{{dy}}{{dx}} &= \frac{d}{{dx}}\left( {{e^{rx}}} \right)\\&= {e^{rx}} \times \frac{d}{{dx}}\left( {rx} \right)\\&= {e^{rx}} \times r\\&= r{e^{rx}}\\\end{aligned}[/tex]
Again differentiate with respect to [tex]x[/tex].
[tex]\begin{aligned}\frac{{{d^2}y}}{{d{x^2}}} &= \frac{d}{{dx}}\left( {r{e^{rx}}} \right)\\&= r\frac{d}{{dx}}\left( {{e^{rx}}} \right)\\&=r\times {e^{rx}} \times\frac{d}{{dx}}\left( {rx} \right)\\&= {r^2}{e^{rx}}\\\end{aligned}[/tex]
Now solve the differential equation.
[tex]\begin{aligned}y'' - 6y' + 2y &= 0\\{r^2}{e^{rx}} - 6r{e^{rx}} + 2{e^{rx}} &= 0\\{e^{rx}}\left( {{r^2} - 6r + 2} \right) &= 0\\{r^2} - 6r + 2 &= 0\\\end{aligned}[/tex]
Solve the quadratic equation [tex]{r^2} - 6r + 2 = 0.[/tex]
[tex]\begin{aligned}D&= {b^2} - 4ac\\&={\left( { - 6} \right)^2} - 4\left( 1 \right)\left( 2 \right)\\&= 36 - 8\\&= 28\\\end{aligned}[/tex]
The value of [tex]r[/tex] can be obtained as follows,
[tex]\begin{aligned}r&= \frac{{ - b \pm \sqrt D }}{{2a}}\\r&=\frac{{ - \left( { - 6} \right) \pm \sqrt {28} }}{{2 \times 1}} \\ r &= \frac{{6 \pm 2\sqrt7 }}{2}\\r&= 3 \pm \sqrt7\\r&= 3 - \sqrt 7 \,\,\,\,\,\,\,or\,\,\,\,\,\,\,r = 3 + \sqrt7 \\\end{aligned}[/tex]
The values of [tex]r[/tex] is [tex]\boxed{r = 3 - \sqrt7 }[/tex] and [tex]\boxed{r = 3 + \sqrt 7 }.[/tex]
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Derivatives
Keywords: Derivative, value of x, function, differentiate, minimum value, dy, compute, given value of [tex]x, y=6x, x=4, x=1[/tex]
How do I find slope?
Which is 10^-5 written in standard form?
A. 0.00001
B. 0.0001
C. 10.000
D. 100.000
A 1-ounce serving of cream cheese contains 7.8
grams of saturated fat. How much saturated fat is in 12
ounces of cream cheese?
To find the total grams of saturated fat in 12 ounces of cream cheese, multiply the grams per ounce (7.8) by the total ounces (12), which equals 93.6 grams.
Explanation:To answer this question, we need to multiply the amount of saturated fat in one ounce of cream cheese by the total number of ounces you have. Since one ounce of cream cheese contains 7.8 grams of saturated fat, you would multiply 7.8 by 12 (the total number of ounces) to get the total amount of saturated fat.
7.8 grams of saturated fat per ounce × 12 ounces = 93.6 grams
So, 12 ounces of cream cheese contains 93.6 grams of saturated fat.
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What is the lateral area of a pyramid with base edges 5 ft and surface area 55 ft2?
In the solution to this system, what is the value of y?
x+y+z=1x+y+z=1
2x+y−z=82x+y-z=8
x−y+z=−5
A turtle walks 7/8 mile in 50 minutes. What is the unit rate in miles per hour? (Hint: 50 minutes=5/6 of an hour.)
URGENT!: Which property justifies this statement?
If x + y = z and z = x + 4, then x + y = x + 4.
A.
symmetric
B.
distributive
C.
transitive
D.
associative
Find all values of x in the interval [0, 2π] that satisfy the equation. (enter your answers as a comma-separated list.) 3|tan(x)| = 3 g study
The values of x in the interval [0, 2π] that satisfy the equation 3|tan(x)| = 3 are π/4, 3π/4, 5π/4, and 7π/4.
Explanation:The given equation is 3|tan(x)| = 3. This means the absolute value of the tangent of x times 3 is equal to 3. We can remove the 3 from both sides to simplify to |tan(x)| = 1. The absolute value operator denotes the non-negative value of a number. So, we need to find the values of x such that tan(x) equals 1 or -1.
The solutions for tan(x) = 1 in the interval [0, 2π] are π/4 and 5π/4. The solutions for tan(x) = -1 in the same interval are 3π/4 and 7π/4.
Thus, the values of x that satisfy the equation are π/4, 3π/4, 5π/4, and 7π/4.
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Daniela finds the sum of two addenda. The sum is odd. Which statement is true about the addenda
Through any three noncollinear points, there is exactly one plane containing them. Points W, X, and Y are noncollinear.
Answer:
There is exactly one plane containing points W, X, and Y
Step-by-step explanation:
Estimate the square root to the nearest integer. Square root of 48
The equation y = 6.3x + 67.4 is the equation of a linear model in a scatter plot comparing the ages of boys between 2 and 10 years old open (x) and their average heights in centimeters open (y).
What is the average height of a 5-year-old boy?
98.9 cm
78.7 cm
67.4 cm
62.4 cm
The average height of a 5 year old baby can be obtained by substituting the x and y values into the regression equation ; Hence, the average height of the baby is 98.9 cm
Given the linear regression equation :
y = 6.3x + 67.4 x = age of baby = 5 ; y = height of babyThe average height of a 5 year old baby is thus :
y = 6.3(5) + 67.4
y = 31.5 + 67.4
y = 98.9
Hence, the average height a 5 year old baby will be 98.9cm
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We can use the right outside diagonal of the empty Lacsap's triangle as the coefficients of a polynomial: $$t^3 + 6t^2 + 12t + 8.$$ If we replace every $t$ with $t-1,$ we get $$(t-1)^3 + 6(t-1)^2 + 12(t-1) + 8.$$Expand and simplify this polynomial. Enter the polynomial as your answer.
To expand the given polynomial $(t-1)^3 + 6(t-1)^2 + 12(t-1) + 8$, we can apply the binomial theorem to each term and then combine like terms.
Explanation:To expand the polynomial $$(t-1)^3 + 6(t-1)^2 + 12(t-1) + 8,$$ we can start by applying the binomial theorem to each term:
$$(t-1)^3 = t^3 - 3t^2 + 3t - 1$$
$$6(t-1)^2 = 6(t^2 - 2t + 1) = 6t^2 - 12t + 6$$
$$12(t-1) = 12t - 12$$
$$8$$
Now, we can combine like terms:
$$t^3 - 3t^2 + 3t - 1 + 6t^2 - 12t + 6 + 12t - 12 + 8$$
Cancelling out terms that add up to zero, we are left with:
$$t^3 + 6t^2 + 12t + 8$$
Divide 300 in a ratio of 3:7
To divide 300 by a ratio of 3:7, calculate the value of each part by dividing 300 by the sum of the ratio parts (10) and then multiply by each part of the ratio to get 90 and 210, respectively.
Explanation:To divide 300 in a ratio of 3:7, first add the parts of the ratio together to determine how many parts you will split 300 into.
In this case, 3 + 7 equals 10 parts.
Then, you divide 300 by 10 to find out how much one part is worth.
This gives 300 ÷ 10 = 30. Now, to find the amounts corresponding to the ratio, multiply the single part value by the numbers in the ratio. For the first part (ratio 3), multiply 30 by 3 to get 90.
For the second part (ratio 7), multiply 30 by 7 to get 210.
So, 300 divided in a ratio of 3:7 gives us 90 and 210, respectively.
the vega family has a cell phone plan that costs $75 per month including taxes and fees. the plan lets the 5 members of the vega family share 1000 minutes of talk time per month and 400 text messages per month. any minutes over 1000 cost $1 per minutes and any text over 400 cost $2 per text. because of a family emergency the family uses 1050 minutes and 415 texts in march. write an expression you could use to find the amount of the vega cell phone bill for march. evaluate the expression show the work
theses two questions are together
Which sign makes this number sentence true? |78| __ |-222|
Curly used a shovel to dig his own swimming pool. He figured he needed a pool because digging it was hard work, and he could use it to cool off after working on it all day. He also planned to build a rectangular concrete deck around the pool that would be 6 feet wide at all points. The pool is rectangular and measures 14 feet by 40 feet. What is the area of the deck?
The area of the deck that is built around the pool is 1352 ft².
What is the area of the deck?A rectangle is a 2-dimensional quadrilateral with four right angles.
Area of a rectangle = length x width
Length = 14 + 6 + 6 = 26 Width = 40 + 6 + 6 = 52Area = 26 x 52 = 1352 ft²
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The movement of the progress bar may be uneven because questions more on your answer. The price of a CD decreased from $15 to $12. What is the percent of decrease? 3% 20% 33% 75%
15 -12 = 3
3/15 = 0.2 = 20% decrease
What are the factors of the trinomial x^2+6x-7
The distance between the two islands shown on the map is 210 miles. A ruler measures the distance on the map is three 1/2 inches how many miles would be represented by one 3/4 inches on the map?
Let g(x) = 5x -2 and h(x)= x^2-16
1. (h"Composition"g) (-1)
This is the best I can do with explaining this. If anyone could please help and explain this to me, I would really appreciate it. The composition thing is just an open circle between the two..
6,000 is 10 time as much as
the second angel im a triangle is 2° less the 3 times the first angle the third Angle is 14° more than twice the first angle find the measure of all three angles I'm the triangle (plz show step by step)
Suppose m<3 = 105. find m<6
To find the measure of angle 6, we can use the fact that angles 3 and 6 are vertical angles (opposite angles formed by the intersection of two lines). Therefore, their measures are equal.
Given that[tex]\( m\angle 3 = 105^\circ \), we have \( m\angle 6 = m\angle 3 = 105^\circ \).So, the measure of angle 6 is \( \boxed{105^\circ} \).[/tex]
The measure of angle 6 is 105 degrees. This is because angles 3 and 6 are vertical angles, meaning they are formed by intersecting lines and are opposite each other. According to the Vertical Angles Theorem, vertical angles are congruent, meaning they have the same measure. Therefore, if angle 3 measures 105 degrees, angle 6, being its vertical angle, also measures 105 degrees. This principle holds true regardless of the specific configuration of lines or shapes, as long as the angles are formed by intersecting lines. Hence, in this case, the measure of angle 6 directly corresponds to the measure of angle 3 due to their relationship as vertical angles, resulting in both having a measure of 105 degrees.