Answer:
a acute angle
Findf '(3), where f(t) = u(t) · v(t), u(3) =1, 2, −2, u'(3) =8, 1, 4,andv(t) =t, t2, t3.
Answer:
[tex]f'(3)=100[/tex]
Step-by-step explanation:
Given:
[tex]f(t)=u(t)\cdot v(t)\\u(3)=\left ( 1,2,-2 \right )\\u'\left ( 3 \right )=\left ( 8,1,4 \right )\\v(t)=\left ( t,t^{2},t^{3} \right )[/tex]
To find: [tex]f'(3)[/tex]
Solution:
[tex]v(t)=\left ( t,t^{2},t^{3} \right )[/tex]
At [tex]t=3;[/tex]
[tex]v(3)=(3,3^{2},3^{3} )=(3,9,27)[/tex]
Differentiate with respect to t
[tex]v'(t)=\left ( 1,2t,3t^{2} \right )[/tex]
At [tex]t=3;[/tex]
[tex]v'(3)=\left ( 1,2(3),3(3)^{2} \right )=\left ( 1,6,27 \right )[/tex]
Using product rule, differentiate [tex]f(t)=u(t)\cdot v(t)[/tex] with respect to [tex]t[/tex]
[tex]f'(t)=u'(t)\cdot v(t)+u(t)\cdot v'(t)[/tex]
At [tex]t=3;[/tex]
[tex]f'(3)=u'(3)\cdot v(3)+u(3)\cdot v'(3)\\=\left ( 8,1,4 \right )\cdot \left ( 3,9,27 \right )+\left ( 1,2,-2 \right )\cdot \left ( 1,6,27 \right )\\=24+9+108+1+12-54\\=100[/tex]
The product of two whole number is 462 and their sum is 43. What are the two numbers?
Answer:
21 and 22
Step-by-step explanation:
Let the two whole numbers be a and b.
Their product is 462. Hence, we can write that:
[tex]ab=462[/tex]
Likewise, because their sum is 42:
[tex]a+b=43[/tex]
This yields a system of equations:
[tex]\displaystyle \begin{cases} ab = 462 \\ a + b = 43 \end{cases}[/tex]
We can solve the system using substitution.
Isolating one variable in the second equation yields:
[tex]a=43-b[/tex]
From substitution:
[tex](43-b)(b)=462[/tex]
Distributing yields:
[tex]-b^2+43b=462[/tex]
Solve for b by factoring:
[tex]\displaystyle \begin{aligned} b^2 - 43d & = -462 \\ \\ b^2 - 43d + 462 & = 0 \\ \\ (b-21)(b-22) &= 0 \\ \\ b = 21 \text{ or } b & = 22 \end{aligned}[/tex]
Solve for a:
[tex]\displaystyle \begin{aligned} a& =43-(21) & \text{ or } a& =43-(22) \\ a&=22&\text{ or } a&=21\end{aligned}[/tex]
In conclusion, the two whole numbers are 21 and 22.
Find the midpoint of the segment with the following endpoints.
(-2, 1) and (6,-3)
Answer:
The midpoint is ( 2,-1)
Step-by-step explanation:
To find the x coordinate of the midpoint, add the x coordinates and divide by 2
(-2+6)/2 =4/2 =2
To find the y coordinate of the midpoint, add the y coordinates and divide by 2
( 1+-3)/2 = -2/2 = -1
The midpoint is ( 2,-1)
Answer:
(2, -1)
Step-by-step explanation:
Let M is the midpoint of that segment with the endpoints A(-2,1) and B(6,-3)
x-coordinate of M:
xM = (xA + xB) / 2 = (-2 + 6) / 2 = 4 / 2 = 2
y-coordinate of M:
yM = (yA + yB) / 2 = ( 1 + -3) / 2 = -2 / 2 = -1
Answer: M(2, -1)
What is the equation of the line parallel to 3x + 5y = 11 that passes through the point (15, 4)?
Answer:
The answer is
[tex]y = - \frac{3}{5} x + 13[/tex]Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
To find the equation of the parallel line we must first find the slope of the original line
The original line is 3x + 5y = 11
We must first write the equation in the general equation above
So we have
5y = - 3x + 11
Divide both sides by 5
[tex]y = - \frac{ 3}{5} x + \frac{11}{5} [/tex]Comparing with the general equation above
Slope = - 3/5
Since the lines are parallel their slope are also the same
Slope of parallel line = - 3/5
So the equation of the line using point
(15, 4) and slope - 3/5 is
[tex]y - 4 = - \frac{3}{5} (x - 15) \\y - 4 = - \frac{3}{5} x + 9 \\ y = - \frac{3}{5} x + 9 + 4[/tex]We have the final answer as
[tex]y = - \frac{3}{5} x + 13[/tex]Hope this helps you
Answer:D
Step-by-step explanation:Edge
Identify the nonlinear graph A) B) C) D)
A linear function makes a straight line
A nonlinear graph is any curve that isn't a straight line. In this case, graph C is a parabola (from a quadratic function).
Graph A is a straight line.
Graph B is a straight line.
Graph C is not a straight line
Graph D is a straight line.
The non-linear graph is option D.
Option D is the correct answer.
What are coordin2ates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
Graph A
Graph B
Graph C
Graph D
A linear graph is a graph that is a straight line.
A non-linear graph is a graph that is not a straight line.
Now,
With the given coordinates on each graph, we see that,
Graph A is a straight line.
Graph B is a straight line.
Graph C is not a straight line
Graph D is a straight line.
Thus,
The non-linear graph is option D.
Option D is the correct answer.
Learn more about coordinates here:
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The height off the ground, in feet, of a certain baseball that travels through the air is given by the equation h = 3.5 + 68t - 16t^2, where t is measured in seconds. Find the height off the baseball, to the nearest foot, when t = 4 seconds.
Answer:
20 feet
Step-by-step explanation:
Plug in 4 as t in the equation:
h = 3.5 + 68t - 16t^2
h = 3.5 + 68(4) - 16(4²)
h = 3.5 + 272 - 256
h = 19.5
So, the height of the basketball is 20 feet
Can someone explain this to me?
Answer:
120/7
Step-by-step explanation:
You cross multiply120=7xDivide both sides x= 120/7PLEASE HELP
Consider the equation: 1/4x + 3y − 23 = 42
The variables are:
The coefficients are:
The constants are:
Answer:
The variables are x and y.The coefficients are 1/4 and 3.Lastly the constants are -23 and 42
Step-by-step explanation:
Variables are letters used to represent an unknown number.Coefficients are the numbers in front of the variables.Constants are numbers by themselves they can be positive and negative.
For the equation: 1/4x + 3y − 23 = 42 the variables are x, y the coefficients 1/4 , 3are the constants are -23 , 42
What is a variable?A quantity that may assume any one of a set of values or in simple words a quantity whose value changes may vary.
What is a coefficient?A numerical or constant quantity placed before and multiplying the variable in an algebraic expression
What is a constant?A constant is a value or number that never changes in expression
in the given equation: 1/4x + 3y − 23 = 42
x and y are variables as the changes for different set of values.
1/4 and 3 are coefficient as they are placed before and multiplying the variable.
-23, 42 is a constant as its value never changes in expression.
Thus for the equation: 1/4x + 3y − 23 = 42 the variables are x, y the coefficients 1/4 , 3are the constants are -23 , 42
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Solve the inequality 9y+5(y+3)<4y−35 and write the solution in interval notation.
Answer:
( −∞,−5) interval notation, and inequality solution y < -5 ,
Step-by-step explanation:
Answer:
y<-5
Your Interval Notation would be an open circle and the arrow would be pointing to the left. (<-- (-6) --- (-5) --- (-4) -->) This will be your # line.
Step-by-step explanation:
9y+5(y+3) < 4y-35
1) Distribute the 5 in 5(y+3).
9y+5y+15 < 4y-35
2) Combine like terms. 9y and 5y.
9y+5y= 14y
14y+15 < 4y-35
3) MY TIP is to keep the variables on the left side, bc if you don't at the end you will have to flip the sign. so.. Subtract 4y from both sides
14y+15 < 4y-35
-4 -4
10y+15 < -35
3) Then you will subtract 15 from both sides
10y+15 < -35
-15 -15
10y < -50
4) Last is to divide to get your variable by itself.
10y < -50
÷10 ÷10
Answer : y < -5
Interval Solution: Open circle, -5 in the middle of the line and you will shade in the numbers to the left. .
Write an equation in slope-intercept form (y = mx + b).
Passing through (2, -3) with a slope of 5/3.
Answer:
Step-by-step explanation:
y + 3 = 5/3(x - 2)
y + 9/3 = 5/3x - 10/3
y = 5/3x - 19/3
What is the value of the expression below when y = 5?
4y2 – 7y - 6
Answer: 371
Step-by-step explanation:
Answer:59
Step-by-step explanation:
A bag contains 26 tiles, each with a different letter of the alphabet written on it. You choose 3 tiles from the bag without looking. What is the probability that you chose tiles with the letters A,B,C?
Answer:
1/26
Step-by-step explanation:
Total no. of tiles = 26
In each tile , a different alphabet is written.
And we need 3 tiles (in which A , B & C are written in it) in one try.
So the probability of choosing tiles with letters A , B & C ( in one try ) = 1/26
Question text
A recipe calls for 5 cups of flour to make 20 biscuits, how many cups of flour do you need to make 100 biscuits.
Plz help 7th grade math
Answer:
9feet
Step-by-step explanation:
B= -34 M=-25
-34-(-25)=-34+25=9
Answer:
9 feet
Step-by-step explanation:
Brett is -34 feet and Max is -25 feet from sea level.
In order to find how many feet Max is above Brett, we can change the numbers to be positive and subtract Brett's distance - Max's distance
34-25=9
Max is 9 feet above Brett
Please help. I don’t understand this math problem.
Answer:
(7) The value of -j is 9.
(8) The value of -(-j) is -9.
(9) The value of (-j)(-j) is 81.
Step-by-step explanation :
Part 7:
Given algebraic expression is:
j = -9
Now we have to determine the value of (-j).
-j = - (-9) = 9
The value of -j is 9.
Part 8:
Given algebraic expression is:
j = -9
Now we have to determine the value of -(-j).
- (-j) = - [-(-9)] = -9
The value of -(-j) is -9.
Part 9:
Given algebraic expression is:
j = -9
Now we have to determine the value of (-j)(-j).
(-j)(-j) = [- (-9)] × [- (-9)] = 9 × 9 = 81
The value of (-j)(-j) is 81.
If f (x) = 3x − 4, Find f (−1) Helpp
Answer:
f(x) = 3x-4
f(-1)= 3(-1) -4
f(-1) = -3-4
= -7
hope this helps uh!
Answer:
f(-1)= -7
Step-by-step explanation:
We are given the function:
f(x)=3x-4
We want to find f(-1). We must plug -1 in for x and solve.
f(-1)= 3(-1)-4
Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction.
Multiply 3 and -1.
f(-1)= -3 -4
Subtract 4 from -3.
f(-1)= -7
f(-1) is equal to -7.
Each day Tania decides to do something nice
for 2 strangers. What is the relationship
between the number people helped and days.
Write a Recursive and Explicit equation.
Answer:
Recursive:
[tex] a_1 = 2; a_n = a_{n-1} [/tex]
Explicit:
[tex] a_n = 2 [/tex]
Step-by-step explanation:
She helps the same number of people every day, 2.
Recursive:
[tex] a_1 = 2; a_n = a_{n-1} [/tex]
Explicit:
[tex] a_n = 2 [/tex]
Math 1 3/8 1/4 a c= 2 5/8 11/16 a c= 3 4/6 6/9 a c=
Wen can turn both fractions into decimals.
1 1/3 = 1.333...
1/4 = 0.25
As we can see 1 1/3 is greater than 0.25.
Therefore, the answer is [ 1 1/3 > 1/4 ]
Best of Luck!
2 Blood sugar levels are normally distributed with a mean of 100 milligrams per deciliter and a standard deviation of 10 milligrams per deciliter. Sam's blood sugar is 85 milligrams per deciliter. What is his Z-score? * (2 Points) O 1.5 0 -1.5 O 15 010
c(a + b)- d = f, for a
Answer:
Step-by-step explanation:
C(a + b) = f + d
a + b = (f + d)/C
a = (f + d)/C - b
5-1 + (-3) = 3 + (-1)
Answer: 1=2 so your answer would be false.
Step-by-step explanation:
Answer:
The answer is 1=2 which is false.
Step-by-step explanation:
5-1+(-3)= 3+(-1)
or, 5-1-3 = 3-1
or, 5-4 = 2
or, 1=2
The area can be found by multiplying the side lengths that are 6 units & 4 units
Answer:squares area is. 24
Step-by-step explanation:
6×4 = 24
Given the vectors shown, find the sum (P+Q+R).
The sum of 2 composite numbers is never a prime number. Explain your answer.
Answer:
Step-by-step explanation:
Composite numbers are positive numbers that have factors, This means that they are divisible by numbers other than 1 and itself provided that number is a factor of the composite number. They possess at the bearest minimum level, a divisor other than 1 and itself. They are a natural number that is expressible as the product of two(or more) numbers other than 1 and itself.
For example:
4 is a composite number because its factors are 1, 2 and 4 which have another divisor apart from 1 and itself (4). That divisor is 2.
We all know that prime numbers are numbers that can be only be divided by 1 and itself.
Therefore, the sum of two composite number, for example:
4 + 6 = 10, We can now see that 10 is never a prime number.
Determine if the following relations represent y as a function of x. x=y^4
Answer:
x = y⁴ does not represent y as a function of x
Step-by-step explanation:
Let's first isolate this equation for the 'y' value :
[tex]\mathrm{Switch\:sides} : y^4=x,\\\mathrm{For\:}x^n=f\left(a\right)\mathrm{,\:n\:is\:even,\:the\:solutions\:are\:}x=\sqrt[n]{f\left(a\right)},\:-\sqrt[n]{f\left(a\right)} : y=\sqrt[4]{x},\:y=-\sqrt[4]{x}[/tex]
So as you can tell, we have two functions. However, they can be rewritten as one function, y = ± ⁴√x. As we have two values of x that correspond to one value of y, this relation is not a function.
Solution: x = y⁴ does not represent y as a function of x
Determine the exponential regression of the data below using either a calculator or spreadsheet program. Round the values in the regression equation to two decimals.Then, estimate the y value when the x value is 100. Round your answer to one decimal place. (14,500),(23,320),(37,150),(41,87),(56,40),(70,21)
Answer:
Y = 1148.92(0.94^x) ; Y = 2.4
Step-by-step explanation:
Given the following data :
(14,500),(23,320),(37,150),(41,87),(56,40),(70,21)
X:
14
23
37
41
56
70
Y:
500
320
150
87
40
21
The exponential regression equation is expressed in the form :
Y = AB^x
A = Initial value
B = rate ; x = time
Using the online exponential regression calculator on the data provided :
Y = 1148.92(0.94^x)
Y = prediction
Estimate y, when x = 100
Y = 1148.92(0.94^100)
Y = 1148.92(0.0020548)
Y = 2.360800816
Y = 2.4
Answer:
2.4
Step-by-step explanation:
Solve the equation –4 In(6x) = 2.
O A. 0.101
B. 0.275
C 3.639
D. 67.238
Isolate the variable using algebraic manipulation.
[tex]-4 ln(6x)=2[/tex]
[tex]ln(6x)=-\frac{1}{2}[/tex]
[tex]6x=e^{-\frac{1}{2}}[/tex]
[tex]x=\frac{e^-\frac{1}{2}}{6}[/tex]
[tex]x=0.101[/tex]
Hope this helps.
頑張って!
Answer:
A) 0.101
Step-by-step explanation:
[tex]ln(6x) = -1/2[/tex] [tex]6x = e^(^-^1^/^2^)[/tex] [tex]6x = 1/\sqrt{e}[/tex] [tex]x = 1/(6\times \sqrt{e})[/tex]Using the calculator [tex]x = 0.101[/tex]
The data below were obtained from an experiment were participants were given drinks with or without caffeine and then asked to tap their fingers. The data for 20 participants are below. Assume the number of taps per minute is normally distributed. The variance is unknown. Find a 95% CI for μ number of taps. Identify the pivot function used. 246 242 248 245 250 244 252 248 248 247 250 248 246 242 248 244 245 246 250 242
Answer:
The 95% confidence interval is [tex]244.26 < \mu < 246.95[/tex]
The pivot function used is
[tex]t = \frac{\=x - \mu}{ \frac{\sigma}{\sqrt{n} } }[/tex]
Step-by-step explanation:
From the question we are told that
The data given is 246 242 248 245 250 244 252 248 248 247 250 248 246 242 248 244 245 246 250 242
The sample size is [tex]n= 20[/tex]
Given that the confidence level is 95% then the level of significance is
[tex]\alpha = (100 - 95)\%[/tex]
[tex]\alpha = 0.05[/tex]
The degree of freedom is mathematically represented as
[tex]df = 20 -1[/tex]
[tex]df = 19[/tex]
From the student t-distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]t_{\frac{\alpha }{2} , 19 } = 2.093[/tex]
The mean is mathematically represented as
[tex]\= x = \frac{\sum x_i}{ n}[/tex]
[tex]\= x = \frac{246+ 242 +248+245+ 250+ 244+252+ 248 +248 +247+ 250+ 248+ 246+ 242 +248 +244 +245 +246+ 250+ 242}{20}[/tex][tex]\= x = 246.6[/tex]
The standard deviation is mathematically represented as
[tex]\sigma = \sqrt{\frac{\sum (x_i - \= x )^2)}{n} }[/tex]
[tex]\sigma = \sqrt{\frac{(246- 246.6)^2 +(242- 246.6)^2 +(248- 246.6)^2 + (248- 245)^2+}{20} } \ ..[/tex]
[tex]\ ...\sqrt{\frac{(250-246.6 )^2+ (244- 246.6)^2+(252- 246.6)^2+ (248- 246.6)^2+ (248- 246.6)^2+}{20} } \ ...[/tex]
[tex]\ ..\sqrt{\frac{(247- 246.6)^2+ (250- 246.6)^2+ (248-246.6)^2+ (246-246.6)^2+ (242-246.6)^2+ (248-246.6)^2+ (244-246.6)^2+}{20} } \ ...[/tex] [tex]\sqrt{\frac{ (245-246.6)^2+ (246-246.6)^2+ ( 246-246.6)^2 + ( 250-246.6)^2+ ( 242-246.6)^2 +( 246-246.6)^2+ ( 242-246.6)^2 }{20} }[/tex][tex]\sigma = 2.87411[/tex]
The margin of error is mathematically represented as
[tex]E = t_{\frac{\alpha }{2} , 19} * \frac{\sigma }{\sqrt{n} }[/tex]
[tex]E = 2.093 * \frac{2.87411 }{\sqrt{20} }[/tex]
[tex]E = 1.345[/tex]
The 95% confidence interval is mathematically represented as
[tex]\= x - E < \mu < \= x + E[/tex]
=> [tex]245.6 - 1.345 < \mu <245.6 + 1.345[/tex]
=> [tex]244.26 < \mu < 246.95[/tex]
The pivot function used is
[tex]t = \frac{\=x - \mu}{ \frac{\sigma}{\sqrt{n} } }[/tex]
When a number is increased by 26, the result is tripled. Then the result is increased by 72. If the final result is 1/2 of the number, what is the value of this number?
Answer:
-60.
Step-by-step explanation:
Let the unknown number be x.
Number is increased by 26 = x+26
Then result is tripled = 3(x+26)
Then the result is increased by 72 = 3(x+26)+72
Final result is [tex]\dfrac{1}{2}[/tex] of the number = [tex]\dfrac{1}{2}x[/tex]
[tex]3(x+26)+72=\dfrac{x}{2}[/tex]
[tex]3x+78+72=\dfrac{x}{2}[/tex]
[tex]3x+150=\dfrac{x}{2}[/tex]
Isolate variable terms.
[tex]3x-\dfrac{x}{2}=-150[/tex]
[tex]\dfrac{6x-x}{2}=-150[/tex]
Multiply both sides by 2.
[tex]5x=-300[/tex]
Divide both sides by 5.
[tex]x=-\dfrac{300}{5}[/tex]
[tex]x=-60[/tex]
Therefore, the required number is -60.
Compare the function ƒ(x) = –x2 + 4x – 5 and the function g(x), whose graph is shown. Which function has a greater absolute maximum (vertex)? Question 16 options: A) There isn't enough information given. B) g(x) and ƒ(x) have equal absolute maximums. C) g(x) D) ƒ(x)
Answer:
Answer C: g(x)
Step-by-step explanation:
I used a graphing calculator to graph f(x) = -x^2 + 4x - 5, and by doing so I immedately saw that the vertex of f(x) is at (2, -1).
The absolute max of g(x) is approximately (3.25, 6.1).
The absolute max of f(x) is approximately (2, -1).
Since the y-coordinate of the absolute maximum of g(x) is greater than the y-coordinate of the absolute maximum of f(x), we conclude that Answer C is correct: g(x) has the greater absolute maximum