We are given the following differential equation:
[tex]\frac{dy}{dx}=\frac{x(y-1)}{4}[/tex]Since this equation gives the value of the slope of the tangent line at any point (x,y). To determine the equation of such line we need to use the general form of a line equation:
[tex]y=mx+b[/tex]Since in a tangent line the slope is equivalent to the derivative we may replace that into eh line equation like this:
[tex]y=\frac{dy}{dx}x+b[/tex]Now we determine the value of dy/dx at the point (1,3):
[tex]\frac{dy}{dx}=\frac{(1)(3-1)}{4}=\frac{2}{4}=\frac{1}{2}[/tex]Replacing into the equation of the line:
[tex]y=\frac{1}{2}x+b[/tex]Now we replace the point (1,3) to get the value of "b":
[tex]3=\frac{1}{2}(1)+b[/tex]Solving for "b":
[tex]\begin{gathered} 3=\frac{1}{2}+b \\ 3-\frac{1}{2}=b \\ \frac{5}{2}=b \end{gathered}[/tex]Replacing into the line equation:
[tex]y=\frac{1}{2}x+\frac{5}{2}[/tex]And thus we get the equation of the tangent line.
To approximate the value of f(1.4) we replace the value x = 1.4 in the equation of the tangent line:
[tex]y=\frac{1}{2}(1.4)+\frac{5}{2}[/tex]Solving the operation:
[tex]y=3.2[/tex]Therefore, the approximate value of f(1.4) is 3.2
The mean life of a television set is 97 months with the variance of 169. If a sample of 59 televisions is randomly selected what is the probability that the sample mean would be less than 100.9 months? Round your answer to four decimal places if necessary
Given that the mean life of a television set is 97 months, you can set up that:
[tex]\mu=97[/tex]You also know that the variance is:
[tex]\sigma^2=169[/tex]You can find the standard deviation by taking the square root of the variance. Then:
[tex]\sigma=\sqrt{169}=13[/tex]You need to find:
[tex]P(X<100.9)[/tex]You need to find the z-score with this formula:
[tex]z=\frac{\bar{X}-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]Knowing that:
[tex]\bar{X}=100.9[/tex]You can substitute values into the formula and evaluate:
[tex]z=\frac{100.9-97}{\frac{13}{\sqrt{59}}}\approx2.30[/tex]You have to find:
[tex]P(z<2.30)[/tex]Using the Standard Normal Distribution Table, you get:
[tex]P(z<2.30)\approx0.9893[/tex]Then:
[tex]P(X<100.9)\approx0.9893[/tex]Hence, the answer is:
[tex]P(X<100.9)\approx0.9893[/tex]A quadratic equation is shown below:x^2 + 18x + 76 = 0Which of the following is the first correct step to write the above equation in the form (x-p)^2 = q, when p and q are integers? A. Add 9 to both sides of the equationB. Add 5 to both sides of the equationC. Subtract 5 from both sides of the equationD. Subtract 9 from both sides of the equation.
SOLUTION:
[tex]\begin{gathered} x^2\text{ + 18x + 76 = 0} \\ To\text{ make left hand p}\operatorname{erf}ect\text{ square, we add 5 to both sides} \\ x^2\text{ + 18x + 76 + 5 = 0 + 5} \\ x^2\text{ + 18x + 81 = 5} \\ x^2\text{ }+18x+9^2\text{ = 5} \\ (x+9)^2\text{ = 5} \end{gathered}[/tex]The correct option B, that is, add 5 to both sides of the equation.
can you please help me before I get on error message and get kicked out
We have the following:
What we must do is calculate the total rate, that is, add all of them and then calculate each part, that is:
[tex]4+5+5+8+9+9=40[/tex]Now we calculate each angle like this
[tex]\begin{gathered} 720\cdot\frac{4}{40}=72 \\ 720\cdot\frac{5}{40}=90 \\ 720\cdot\frac{8}{40}=144 \\ 720\cdot\frac{9}{40}=162 \\ we\text{ add} \\ 72+90+90+144+162+162=720 \end{gathered}[/tex]then we can affirm that the smallest angle is 72 °
Using the drawing find y: MzBDJ = 7y + 2, mZJDR = 2y + 7 * HRT O 25 O 19 O O TY
A box can be formed by cutting a square out of each corner of a piece of cardboard and folding the sides up. If the piece of cardboard is 78 cm by 78 cm and each side of the square that is cut out has length x cm, the function that gives the volume of the box is V=6084x−312x2+4x3. Complete parts (a) and (b) below.
a) Notice that:
1)
[tex]6084x-312x^2+4x^3=4x(1521-78x+x^2)=4x(x-39)^2\text{.}[/tex]Therefore V(x)=0 at x=0 and it has a double root at x=39.
2)
[tex]\begin{gathered} V(-1)=6084(-1)-312(-1)^2+4(-1)^3, \\ V(-1)=-6084-312-4<0. \end{gathered}[/tex]Therefore, V(x)<0 when x is in the following interval:
[tex](-\infty,0).[/tex]3)
[tex]V(1)=6084(1)-312(1)^2+4(1)^3>0.[/tex]Therefore, V(x)>0 when x is in the following set:
[tex](0,39)\cup(39,\infty).[/tex]b) Since x is a length, then it must be greater than zero, also 2x must be smaller than 78, therefore the values of x that makes sense in the context are in the interval:
[tex](0,39)\text{.}[/tex]Answer:
a) Option B) The values of x that makes V>0 are in the set:
[tex](0,39)\cup(39,\infty).[/tex]b) Option A) The values of x that give squares that can be cut out to construct a box are the interval:
[tex](0,39)\text{.}[/tex](0,39).
A figure is made up of two triangles and a square. The trianglesand the square have the same base length of 9 feet. Thetriangles have a height of 12.3 feet. What is the total area of thefigure?
Hay e escalones desde el pedestal hasta la cabeza de la Estatua de la Libertad. La cantidad de escalones que hay en el Monumento a Washington es 27 menos que 6 veces la cantidad de escalones que hay en la Estatua de la Libertad. ¿Qué expresión representa la cantidad de escalones que hay en el Monumento de Washington en función de e? 27 < 6e 6(e-27) 6e-27 They 6e
Let
e -----> number of steps from the pedestal to the head of the Statue of Liberty
f ----> number of steps on the Washington Monument
we have that
f=6e-27
therefore
teh answer is
6e-27
Do you understand my explanation?escalones que hay en el Monumento a Washington
we have that
f=6e-27
What are the coordinates of the y- intercept of this function y 6 -5 1 2
The coordinates of the y-intercept of the function can be obtained if we follow the steps below
Step 1: we can get the equation of the graph using the equation below
[tex]\frac{y_2-y_1}{x_2\text{ -}x_1}\text{ = }\frac{y\text{ -}y_1}{x\text{ -}x_1}[/tex]Step 2: Select two coordinates that will be substituted into the equation
Selecting the points
(-2, -6) and (-1, -5)
[tex]\frac{-5\text{ -(-6)}}{-1\text{ -(-2)}}\text{ =}\frac{y-(-6)}{x\text{ -(-2)}}[/tex][tex]\frac{1}{1}=\frac{y+6}{x+2}[/tex]Cross multiplying
y + 6 = x + 2
y = x + 2 - 6
y = x -4
The equation of the line is y = x - 4
The next step is to obtain the y-intercept which is obtained by substituting x = 0 into the equation of the line.
If x = 0
then y = 0 - 4
Hence y = -4
Therefore the coordinates of the y-intercept are (0, -4)
What is the average rate of change of the equation f(x)^2+3x-5 from x=2 to x=4?Type your numerical answer below. Use the hyphen (-) to represent a negative sign if necessary.
Given:
The equation is,
[tex]f\mleft(x\mright)=x^2+3x-5,x=2\text{ to x = 4}[/tex]To find: The average rate of change
Explanation:
The average rate of the change formula is,
[tex]A\left(x\right)=\frac{f\mleft(b\mright)-f\mleft(a\mright)}{b-a}[/tex]Here, we have
[tex]\begin{gathered} a=2 \\ b=4 \end{gathered}[/tex]Substituting we get,
[tex]\begin{gathered} A\lparen x)=\frac{f\mleft(4\mright)-f\mleft(2\mright)}{4-2} \\ =\frac{\left\lbrack4^2+3\left(4\right)-5\right?-\left\lbrack2^2+3\left(2\right)-5\right?}{2} \\ =\frac{16+12-5-\left\lbrack4+6-5\right\rbrack}{2} \\ =\frac{23-5}{2} \\ =\frac{18}{2} \\ =9 \end{gathered}[/tex]Final answer:
The average rate of change of the given equation is 9.
I need help find the answer to number 10 and 11
10. We need to identify the value of b in the function:
[tex]f(x)=b^x[/tex]so that it produces the graph given.
Observing the graph, we see that the point (1,2) lies on it. Thus, we have:
[tex]\begin{gathered} 2=b^1 \\ \\ \Rightarrow2=b \end{gathered}[/tex]Therefore, the value of the base b is: 2
At a food drive, afood bank has a goal to collect 24,000 cans.If the food bank collects 100 fewer cansthan its goal, how many cans did it collect?
Given:
• Expected number of cans to collect = 24,000 cans.
,• The food bank collects 100 fewer cans.
Let's find the number of cans it collected.
Since the food bank collected 100 fewer cans, to find the number of cans it collected, let's subtract 100 from the expected goal which is 24000 cans.
Hence, we have:
Number of cans collected = expected goal - 100
Number of cans collected = 24000 - 100 = 23900
Therefore, the number of cans the food bank collected was 23,900 cans.
ANSWER:
23900 cans
What number should be added to both sides of the following equation to solve for g?g - 18 1\3 = 2543 1\36 2\318 1\325 2\3
Answer
[tex]18\frac{1}{3}[/tex]Explanation
Given:
[tex]g-18\frac{1}{3}=25[/tex]What to find:
The number that should be added to both sides of the following equation to solve for g.
Solution:
To solve for g 18 1/3 should be added to both sides as shown below
[tex]\begin{gathered} g-18\frac{1}{3}=25 \\ \\ Add\text{ }18\frac{1}{3}\text{ }to\text{ }both\text{ }sides \\ \\ g-18\frac{1}{3}+18\frac{1}{3}=25+18\frac{1}{3} \\ \\ g=25+18\frac{1}{3} \end{gathered}[/tex]The answer is 18 1/3
How do I solve for x? Would my answer be 27?
Given:
[tex]\angle ABC=(4x+2)^o,\angle ACB=(2x-9)^o,\angle XAC=(5x+13)^o[/tex][tex]We\text{ know that }\angle BAC\text{ and }\angle XAC\text{ are supplementary angles.}[/tex]The sum of the supplementary angles =180 degrees.
[tex]\angle BAC+\angle XAC=180^o[/tex][tex]\text{ Substitute }\angle XAC=(5x+13)^o\text{ in the equation.}[/tex][tex]\angle BAC+(5x+13)^o=180^o[/tex][tex]\angle BAC=180^o-\mleft(5x+13\mright)^o[/tex]We know that the sum of all three angles of the triangle is 180 degrees.
[tex]\angle ABC+\angle ACB+\angle BAC=180^o[/tex][tex]\text{ Substitute }\angle ABC=(4x+2)^o,\angle ACB=(2x-9)^o,\angle BAC=180^o-(5x+13)^o\text{.}[/tex][tex](4x+2)^o+(2x-9)^o+180^o-(5x+13)^o=180^o[/tex][tex](4x+2)^o+(2x-9)^o-(5x+13)^o=180^o-+180^o[/tex][tex](4x+2)^o+(2x-9)^o-(5x+13)^o=0[/tex][tex]4x+2+2x-9-5x-13=0[/tex]Adding like terms that have the same variable with the same powers.
[tex]4x+2x-5x+2-9-13=0[/tex][tex]x-20=0[/tex][tex]x=20[/tex]Hence the value of x is 20.
I am having trouble trying to figure out letter B
The confidence level is [0.1883, 0.3866] and the 95% confidence interval for the cost is [0.25x 564.9, 0.25x1160.1] = [141.23, 290]
n = 80
a) p = 23/80 = 0.2875
% = 95
Standard error SE = √(p(1 - p)/n = √(0.2875(1 - 0.2875)/80)
z - score = 1.9599
Width of the confidence level = z x SE = 1.95996 x 0.05060 = 0.0991
Lower level of the confidence level = p - width = 0.2875 - 0.099177 = 0.1883
upper level of the confidence level = p + width = 0.2875 + 0.099177 = 0.3866778
The confidence level is [0.1883, 0.3866]
b) The 95% confidence level for the number of such customers = [0.1883 x 3000, 0.3866 x 3000] = [564.9, 1160.1]
The 95% confidence interval for the cost = [0.25x 564.9, 0.25x1160.1] = [141.23, 290]
Therefore, the confidence level is [0.1883, 0.3866] and the 95% confidence interval for the cost is [0.25x 564.9, 0.25x1160.1] = [141.23, 290]
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Shaan and anita are married and have two children, ages 3 and 9. anita is a "nonworking" spouse who devotes all of her time to household activities. estimate how much life insurance shaan and anita should carry.
The cost of life insurance that shaan and anita should carry would be = $150,000
What is life insurance policy?A life insurance policy is defined as the type of insurance an individual contracts so as to enable their beneficiaries a stipulated amount of money after the individual dies.
The number of children owned by shaan and anita = 2
The age of the youngest child = 3
The age of the eldest child = 9
The insurance policy need = Number of years until the youngest child is 18 × $10,000
The number of years until the youngest child is 18 = 18-3= 15
15× 10,000 = $150,000
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Joey buys a home for $205,900. His home is predicted to increase in value 4% each year. What is the predicted value of his home in 22 years? Round answer to thenearest whole number
Since every year the value of the house increase by 4%, the new value will be the previous value plus 4% of the previous value. To find 4% of a quantity, we just have have to multiply it by 4 and then divide by 100(or, written as a decimal, multiply the number by 0.04).
If we call the previous value of the house as P and the new value as N, the new value after one year will be
[tex]N=P+0.04P=(1+0.04)P=1.04P[/tex]Every year that passes, to get the new value we multiply again by 1.04. The expression for the predicted value after t years is
[tex]N(t)=P_0(1.04)^t[/tex]Where P0 represents the initial value of the house. Evaluating t = 22 on this expression, we have
[tex]N(22)=205,900(1.04)^{22}=487,966.279171\ldots\approx487,966[/tex]The predicted value of his home in 22 years is $487,966.
simplifying with like terms; a + 2a -7
In the expression like terms are a and 2a.
Simplify the expression
[tex]a+2a-7=3a-7[/tex]So answer is 3a - 7.
1 point 3 John ran 3 les in of an hour Marlon ran s 4 miles in of an hour How lar did Marlon run in one hour?
Answer:
6.2 miles per hour
Explanation:
Marlon ran 8 1/4 miles in 4/3 of an hour.
So, we first need to transform the mixed number 8 1/4 into a fraction using the following equation:
[tex]\begin{gathered} A\frac{b}{c}=\frac{A\cdot c+b}{c} \\ 8\frac{1}{4}=\frac{8\cdot4+1}{4}=\frac{32+1}{4}=\frac{33}{4} \end{gathered}[/tex]Then, we need to divide 33/4 miles by 4/3 hour as:
[tex]\begin{gathered} \frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot d}{b\cdot c} \\ \frac{\frac{33}{4}}{\frac{4}{3}}=\frac{33\cdot3}{4\cdot4}=\frac{99}{16}=6.2\text{ miles per hour} \end{gathered}[/tex]So, Marlon ran 6.2 miles per hour.
if m<10=77 ,m<7=47 and m<16=139, find the missing measure of m<2=?
Note that a and b are parallel lines with a transversal line of c.
<10 is congruent to <8
so :
<8 = 77
<2 and <8 are supplementary (sum of 180 degrees)
<2 + <8 = 180
<2 + 77 = 180
<2 = 103
The answer is :
<2 = 103 deg
given triangle CAT is congruent to triangle DOG. Solve for x
Answer:
The value of x is 2 or -5.5.
Explanation:
Given that triangle CAT is congruent to triangle DOG, then we have that:
[tex]\angle T\cong\angle G[/tex]Step 1: We determine the value of angle T.
[tex]\begin{gathered} \angle T=180^0-(87^0+75^0) \\ =180^0-162^0 \\ =18^0 \end{gathered}[/tex]Step 2: Since angle T is congruent to angle G, then:
[tex](x+4)(2x-1)=18[/tex]Step 3: We solve the equation above for x.
[tex]\begin{gathered} 2x^2-x+8x-4-18=0 \\ 2x^2+7x-22=0 \\ 2x^2-4x+11x-22=0 \\ 2x(x-2)+11(x-2)=0 \\ (2x+11)(x-2)=0 \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} 2x+11=0\text{ or x-2=0} \\ 2x=-11\text{ or x=2} \\ x=-5.5\text{ or x=2} \end{gathered}[/tex]The value of x is 2 or -5.5.
Leo is 5 years older than Pat. In 10 years leo will be twice pat's present age. How old is leo
Answer:
20
Step-by-step explanation:
Pat is 15.
Leo is 5 years older(20)
Leo will be 30 in 10 years.
15 x 2 = 30
Roberto bought a new graduated cylinder for his chemistry class. it holds 650 mililiters of liquid. if the cylinder has a radius of 5 cm, then how tall is the cylinder.
8.27 cm
Explanation
Step 1
the volume of a cylinder is given by:
[tex]\begin{gathered} \text{Volume}=\text{ area of the circle}\cdot\text{ height} \\ \text{Volume}=(\pi\cdot raidus^2)\cdot\text{height} \end{gathered}[/tex]then
Let
Heigth=unknown=h
volume=650 ml
radius= 5 cm
also
1 mililiter= 1 cubic centimeter
so,replacing
[tex]\begin{gathered} \text{Volume}=(\pi\cdot raidus^2)\cdot\text{height} \\ \text{650 }=(\pi\cdot(5cm)^2)\cdot\text{h} \\ 650=25\pi\cdot h \\ \text{divide both sides by 25 }\pi \\ \frac{650}{25\pi}=\frac{25\pi h}{25\pi} \\ h=\frac{650}{25\pi}=8.27\text{ cm} \end{gathered}[/tex]so, the cylinder is 8.27 cm tall.
I hope this helps you
I have a pentagon that 8 and 8 and 6 and 6 and 10 whats the perimeter?
The perimeter of any closed figure is equal to sum of all sides of the figure.
Determine the perimeter of pentagon by addition of measure of sides of pentagon.
[tex]\begin{gathered} P=8+8+6+10+6 \\ =38 \end{gathered}[/tex]So answer is 38 cm.
is 1,000 feet greater than 300 yards
hello
to solve this question, we have to know the the dimensions or
Question 5 of 10 Which of the segments below is a secant? B D O A. CD O B. AB O C. ÃO D. BC
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
Diagram
secant = ?
Step 02:
We must analyze the diagra,m to find the solution.
Secant ===> straight line that cuts a curve in two or more parts
Segments:
CD: FALSE
AB: FALSE
AO: FALSE
BC: TRUE
The answer is:
Segment BC is a secant
For each coefficient choose whether it is positive or negative. Choose the coefficient with the greatest value. Choose the coefficient closest to zero.
First we need to find if the coefficients are negative or positive. The function:
[tex]\lvert x\rvert[/tex]Is always positive which means that its graph must be over the x axis. If this function is multiplied by a positive coefficient then the graph remains over the x axis. On the other hand, if it's multiplied by a negative number then the graph is now under the x axis. A and B graph are over the x axis so they are positive whereas C and D graphs are under the x axis and they are negative and that's the answer for a.
Then we must find the coefficient with the greatest value. Since a positive number is greater than any negative number we can discard C and D. Now we have two options, A and B which we know are different numbers since their graph are different. Both are V shaped but graph B is sharper than graph C. This means that B is greater than C. Then, the answer to part b is coefficient B.
In part c we must choose the coefficient that is closest to 0. Using the same argument as before, the sharper the V shaped graph is the greatest absolute value its coefficient has. This means that the least sharp graph is that of the coefficient that is closer to 0. Looking at the four graphs you can see that the least sharp V is that of coefficient A. Then, the answer to part c is coefficient A.
2. Line ( has a slope of -7 and a y-intercept of 12. What is the equation for line in slope-intercept form? y =12x-7 y=-7x+12 --7x+12y=0which one of those equations are true
The general form of a straight line graph is: y = mx + c
where m and c are the slope and slope-intercept respectively.
from the question given, the slope (m) = -7
and the intercept (c) = 12
substituting the values into y = mx + c
then y = -7x + 12
A plant is already 42 centimeters tall, and it will grow one centimeter every month.Let H be the plant's height (in centimeters) after M months.Write an equation relating H to M. Then use this equation to find the plant's helght after 35 months.Equation:D-ORХ5?Plant's height after 35 months: centimeters
write the height of the plant after m months as a linear function in which the y-intercept is the plant's initial height (42 cm) and the slope is the growth the plant experiences after each month (1 cm)
[tex]H=M+42[/tex]then, after 35 months
[tex]\begin{gathered} H=35+42 \\ H=77 \end{gathered}[/tex]The plant's height after 35 months is 77 cm.
17the leading term is-6x² +The expression represents aterm ispolynomial withterms. The constantand the leading coefficient is
0. quadratic
,1. two
,2. 1/7
,3. -6x²
,4. -6
1) Examining this polynomial, we can tell that:
[tex]-6x^2+\frac{1}{7}[/tex]This expression represents a quadratic polynomial with two terms. The constant term is 1/7, the leading term is -6x², and the leading coefficient is -6
2) Note that a constant term is always a number without a variable, the leading term is the one with the highest exponent, and a coefficient is a number that accompanies the leading variable.
What is the domain of the rational function f of x is equal to the quantity x squared plus x minus 6 end quantity over the quantity x cubed minus 3 times x squared minus 16 times x plus 48 end quantity question mark
To solve this problem, we have to find the zeros of the expression in the denominator, to do it, factor the expression:
[tex]\begin{gathered} x^3-3x^2-26x+48=0 \\ (x-3)(x-4)(x+4)=0 \\ x-3=0 \\ x=3 \\ x-4=0 \\ x=4 \\ x+4=0 \\ x=-4 \end{gathered}[/tex]The zeros of the function are x=3,4,-4.
Since these values make the expression be zero, they are not included in the domain of the function. This is because the expression in the denominator can not be zero, otherwise, the function would be undefined.
The correct answer is B:
[tex]\mleft\lbrace x\in R\mright|x\ne-4,3,4\}[/tex]