PLEASE HELP OMG calculate the slope of the graph below at the point (-1,5)
f(x) = x^5 + 1/x^3 +7
Answer:
The slope of the graph at x=-1 is 2
Step-by-step explanation:
Instant rate of change
Given a real function f(x), the instant rate of change with respect to x is defined as the derivative of f which coincides with the instant value of the slope of the tangent line in the point (x,y).
We have the function:
[tex]\displaystyle f(x) = x^5+\frac{1}{x^3}+7[/tex]
Prepare the function to apply the power rule of the derivative:
[tex]\displaystyle f(x) = x^5+x^{-3}+7[/tex]
Recall the power rule:
[tex](x^n)' = nx^{n-1}[/tex]
Also, the derivative of a constant is zero.
Taking the derivative:
[tex]\displaystyle f'(x) = 5x^4-3x^{-4}[/tex]
Evaluating for x=-1:
[tex]\displaystyle f'(-1) = 5(-1)^4-3(-1)^{-4}[/tex]
[tex]\displaystyle f'(-1) = 5*1-3*1=2[/tex]
The slope of the graph at x=-1 is 2
an arts academy requires there to be 6 teachers for every 132 students and 3 tutors for every 27 students . how many students does the academy have per teacher ? per tutor ? how many tutors does the academy need if it has 72 students ?
Answer:
3
Step-by-step explanation:
The number of necessary tutors when you divide 27 into 72, is 2.6; therefore the necessary number of tutors is 3 because you can’t have .6 of a tutor. Hope this helps!
Joey's Cafe has regular coffee and decaffeinated coffee. This morning, the cafe served 35
coffees in all, 7 of which were regular. What percentage of the coffees were regular?
Write your answer using a percent sign (%).
Answer:
20%
Step-by-step explanation:
Step 1:
7/35 Divide
Step 2:
1/5 Simplify
Step 3:
20/100 Multiply
Answer:
20%
Hope This Helps :)
Answer:
Joey's Cafe sold 20% regular coffee and 80% decaffeinated coffee.
Step-by-step explanation:
We are given that the cafe served 35 coffees. We are also told that of those 35 coffees, 7 coffees were regular.
Therefore, we can divide the number of regular coffees by the total number of coffees sold to get the percentage of regular coffees.
Our ratio will be set up as 7 regular coffees : 35 total coffees. We can also represent this as a fraction.
[tex]\displaystyle\frac{7}{35}=\frac{1}{5}\\\\\frac{1}{5}=0.2\\\\0.2 \times 100 = 20\%[/tex]
Therefore, of the coffees sold at the cafe, 20% of those coffees were regular.
Additionally, we can subtract this percentage from 100 to find out how much of the sales were decaffeinated coffee.
[tex]100\% - 20\% = 80\%[/tex]
Joey's Cafe sold 80% decaffeinated coffee.
Vance used the associative property to write (4.5 m + StartFraction 7 Over 8 EndFraction) minus 9 as the equivalent expression 4.5 m (StartFraction 7 Over 8 EndFraction minus 9). Did Vance apply the associative property correctly? Why or why not?
Yes, the terms with variables should be written first.
Yes, the terms can be regrouped and still be equivalent.
No, the order of the terms should have been changed.
No, the addition symbol was dropped in the second expression.
Answer: D
Step-by-step explanation:
No, the addition symbol was dropped in the second expression is not correct.
What is Expression?An expression is combination of variables, numbers and operators.
No, Vance did not apply the associative property correctly.
The associative property states that the grouping of terms in an expression can be changed without affecting the value of the expression.
However, in this case, Vance changed the order of the terms, but did not actually group them in a different way.
Additionally, Vance dropped the subtraction symbol in the second expression, which is incorrect.
The correct equivalent expression using the associative property would be:
(4.5 m + 7/8) - 9 = 4.5 m + (7/8 - 9)
From there, we could simplify the expression further, if needed.
Hence, No, the addition symbol was dropped in the second expression.
To learn more on Expressions click:
https://brainly.com/question/14083225
#SPJ3
How do you do these questions?
I'll do the first problem to get you started.
Part (a)
We have a separable equation. Get the y term to the left side and then integrate to get
[tex]\frac{dy}{dt} = ky^{1+c}\\\\\frac{dy}{y^{1+c}} = kdt\\\\\displaystyle \int\frac{dy}{y^{1+c}} = \int kdt\\\\\displaystyle \int y^{-(1+c)}dy = \int kdt\\\\\displaystyle -\frac{1}{c}y^{-c} = kt+D\\\\\displaystyle -\frac{1}{c*y^{c}} = kt+D\\\\[/tex]
I'm using D as the integration constant rather than C since lowercase letter c was already taken.
Let's use initial condition that [tex]y(0) = y_0[/tex]. This means we'll plug in t = 0 and [tex]y = y_0[/tex]. After doing so, solve for D
[tex]\displaystyle -\frac{1}{c*y^{c}} = kt+D\\\\\displaystyle -\frac{1}{c*(y_0)^{c}} = k*0+D\\\\\displaystyle D = -\frac{1}{c*(y_0)^{c}}\\\\[/tex]
Let's plug that in and isolate y
[tex]\diplaystyle -\frac{1}{c}y^{-c} = kt+D\\\\\\\diplaystyle -\frac{1}{c}y^{-c} = kt-\frac{1}{c*(y_0)^{c}}\\\\\\\diplaystyle y^{-c} = -ckt+\frac{1}{(y_0)^{c}}\\\\\\\diplaystyle y^{-c} = \frac{1-c*(y_0)^{c}kt}{(y_0)^{c}}\\\\\\\diplaystyle \frac{1}{y^{c}} = \frac{1-c*(y_0)^{c}kt}{(y_0)^{c}}\\\\\\\diplaystyle y^{c} = \frac{(y_0)^{c}}{1-c*(y_0)^{c}kt}\\\\\\\diplaystyle y = \left(\frac{(y_0)^{c}}{1-c*(y_0)^{c}kt}\right)^{1/c}\\\\\\\diplaystyle y = \frac{y_0}{\left(1-c*(y_0)^{c}kt\right)^{1/c}}\\\\\\[/tex]
-------------------------
We end up with [tex]\displaystyle y(t) = \frac{y_0}{\left(1-c*(y_0)^{c}kt\right)^{1/c}}\\\\[/tex] as our final solution. There are likely other forms to express this equation.
========================================================
Part (b)
We want y(t) to approach positive infinity.
Based on the solution in part (a), this will happen when the denominator approaches 0 from the left.
So [tex]y(t) \to \infty[/tex] as [tex]1-c*(y_0)^{c}kt \to 0[/tex] in which we can effectively "solve" for t showing that [tex]t \to \frac{1}{c*(y_0)^{c}k}[/tex]
If we define [tex]T = \frac{1}{c*(y_0)^{c}k}[/tex] , then approaching T from the left side will have y(t) approach positive infinity.
This uppercase T value is doomsday. This the time value lowercase t approaches from the left when the population y(t) explodes to positive infinity.
Effectively t = T is the vertical asymptote.
========================================================
Part (c)
We're told that the initial condition is y(0) = 5 since at time 0, we have 5 rabbits. This means [tex]y_0 = 5[/tex]
Another fact we know is that y(3) = 35 because after three months, there are 35 rabbits.
Lastly, we know that c = 0.01 since the exponent of dy/dt = ky^(1.01) is 1.01; so we solve 1+c = 1.01 to get c = 0.01
We'll use y(3) = 35, c = 0.01 and [tex]y_0 = 5[/tex] to solve for k
Doing so leads to the following:
[tex]\displaystyle y(t) = \frac{y_0}{\left(1-c*(y_0)^{c}kt\right)^{1/c}}\\\\\\\displaystyle y(3) = \frac{5}{\left(1-0.01*(5)^{0.01}k*3\right)^{1/0.01}}\\\\\\\displaystyle 35 \approx \frac{5}{\left(1-0.0304867k\right)^{100}}\\\\\\\displaystyle 35\left(1-0.0304867k\right)^{100} \approx 5\\\\\\\displaystyle \left(1-0.0304867k\right)^{100} \approx \frac{1}{7}\\\\\\[/tex]
[tex]\displaystyle \left(1-0.0304867k\right)^{100} \approx 7^{-1}\\\\\\\displaystyle 1-0.0304867k \approx \left(7^{-1}\right)^{1/100}\\\\\\\displaystyle 1-0.0304867k \approx 7^{-0.01}\\\\\\\displaystyle k \approx \frac{7^{-0.01}-1}{-0.0304867}\\\\\\\displaystyle k \approx 0.63211155281122\\\\\\\displaystyle k \approx 0.632112\\\\\\[/tex]
We can now compute the doomsday time value
[tex]T = \frac{1}{c*(y_0)^c*k}\\\\\\T \approx \frac{1}{0.01*(5)^{0.01}*0.632112}\\\\\\T \approx \frac{1}{0.00642367758836}\\\\\\T \approx 155.674064621806\\\\\\T \approx 155.67\\\\\\[/tex]
The answer is approximately 155.67 months
Four movie tickets cost $36. At this rate, what is the cost of 5 and 11 movie tickets Please answer!
I need help please.
Answer:
e
Step-by-step explanation:
Garrett reflects points A and B across the y-axis to make the images of the points A' and B'. If the distance between points A and B is 10 units, what is the distance between points A' and B'? Explain your answer.
Answer:
A'B' = AB = 10Step-by-step explanation:
Reflection of points across y-axis doesn't change the distance between the points so AB = A'B' = 10 units
Let the coordinates be:
A = (x1, y1) and B(x2, y2)Reflection:
A'= (-x1, y1) and B(-x2, y2) as per ruleLets compare distances:
AB = √(x2-x1)² + (y2 - y1)²and
A'B' = √(-x2 - (-x1))² + (y2 - y1)² = √(-(x2 - x1))² + (y2-y1)² = √(x2-x1)² + (y2 - y1)²As we see the results are same
Answer:
Reflection of points across y-axis doesn't change the distance between the points so AB = A'B' = 10 units
Step-by-step explanation:
Find the area of this
Answer:
616
Step-by-step explanation:
Can anyone show me how to figure this out.
Answer:
Option A (5, 0)
Step-by-step explanation:
Step 1: Determine what is a solution
To find a solution of two lines, it has to be in the area where both of the colors intersect. As you can see the red line goes up and the blue line goes down, but there is a shaded region where there is just white, just blue, just red, and the red and blue. The shaded region where both red and blue is, that is where the solutions are.
(5, 0) -> This means that the x-value is 5 and the y-value is 0 meaning that it is in the area where there is both red and blue.
(1, -3) -> This means that the x-value is 1 and the y-value is -3 meaning that it is in the area where there is only red.
(3, 3) -> This means that the x-value is 3 and the y-value is 3 meaning that it is in the area where there is only blue.
(2, 1) -> This means that the x-value is 2 and the y-value is 1 meaning that it is in the area where there is only blue.
Answer: Option A (5, 0)
Brittany buys 2.55 pounds of turkey for $5.96 per pound and 3.7 pounds of
cheese for $3.35 per pound. She gave the clerk twenty dollars. How much
more money does Brittany need? Include your units.
Answer:
Brittany needs another $3.7405.
Step-by-step explanation:
Per pound Cost of turkey = $5.96 per pound
The amount Brittany buys the turkey = 2.55 pounds
Brittany's cost for turkey = 2.55 × $5.96 = $15.198
Per pound cost for cheese = $3.35 per pound
The amount Brittany buys the cheese = 3.7 pounds
Brittany's cost for cheese = 2.55 × $3.35 = $8.5425
So,
Brittany's total cost = Turkey cost + Cheese cost
= $15.198 + $8.5425
= $23.7405
As brittany gave the clerk 20 dollars.
So, the amount she further needs will be:
$23.7405 - $20 = $3.7405
Therefore, Brittany needs another $3.7405.
Diane ran 28.6 miles in a marathon She averaged 6 minutes per mile. How many total minutes did Diane run?
Answer:
171.6 minutes
Step-by-step explanation:
28.6*6
If line lis parallel to line m, find the value of x and y. (please help taking a test)
(7x + 12)
(12x - 28)
(9y - 77)"
O x = 10.3 and y = 17.9
O x = 8 and y = 21
O x = 7 and y = 12
x = 12 and y = 7
Answer:
x=8 and y=21
Step-by-step explanation:
12x-28=7x+12 (the 2 angles are equivalent)
12x-7x=12+28
5x=40
x=8
9y-77 + 12x-28 =180 (the sum of those 2 angles is a flat angle (180°))
9y-77+12*8-28=180
9y=180+28+77-96
9y=189
y=21
Complete the point-slope equation of the line through (−5,4) and (1,6).
Answer:
y-6=
Been trying to get this one answered for months, will make the first one to answer a brainliest :D Please explain how you did it so I can do the next one? Thanks in advance
Answer:
[tex]\frac{2}{7}[/tex]
Step-by-step explanation:
In order to find the slope of a line you must find where the points intersect, use the formula for slope, substitute values, and simplify if needed.
In this case we were already given the points for slope:
[tex]P1=(-4,-4) = (x1,y1)[/tex]
[tex]P2=(-2,3)=(x2,y2)[/tex]
Slope formula:
[tex]slope = \frac{y2-y1}{x2-x1}[/tex]
Now substitute:
[tex]\frac{-2--4}{3--4}[/tex]
Solve using KCC: (Keep, Change, Change)
[tex]-2+4=2[/tex]
[tex]3+4=7[/tex]
=[tex]\frac{2}{7}[/tex]
Because the slope isn't a negative you do not need to simplify the answer.
Hope this helps.
Find the area of a right isosceles triangle with hypotenuse 10\sqrt{2}10
2 units
Answer:
A = 50 square units
Step-by-step explanation:
Right Triangles
A right triangle is identified because it has one internal angle of 90°.
The longest side is called hypotenuse and the other two sides are called legs. Being c the hypotenuse and a and b the legs, the Pythagora's theorem relates the with the equation:
[tex]c^2=a^2+b^2[/tex]
If the triangle is also isosceles, then both legs have the same measure or a=b:
[tex]c^2=a^2+a^2=2a^2[/tex]
Since we know the hypotenuse has a measure of 10\sqrt{2}:
[tex](10\sqrt{2})^2=2a^2[/tex]
Operating:
[tex]100*2=2a^2[/tex]
Dividing by 2:
[tex]a^2=100~~\Rightarrow a=\sqrt{100}[/tex]
a = 10 units
The area of the triangle is:
[tex]\displaystyle A=\frac{a.b}{2}[/tex]
[tex]\displaystyle A=\frac{10*10}{2}[/tex]
A = 50 square units
2. Mr Alison fill ups his car at the gas station. He also gets a car wash at the station and visits with the manager, Then he drives to the next town on buisness
Which graph did you not choose for exercise 1 and 2?
Answer:
Hmm graph 3, i think.
Step-by-step explanation:
ADD NOTE
QUESTION GUIDE
EXIT TEST
6.
Raul spent 2
hours shopping for new clothes on Saturday,
1
O
Raul spent
hours shopping for shoes.
10
3
• He spent hour shopping for pants
2
• He spent
hour shopping for shirts
3
• He spent the rest of the time shopping for shoes
о
Raul spent
5
7
hours shopping for pants and shirts.
Raul spent the same amount of time shopping for shoes
as he spent shopping for pants.
O
Based on this information, which statement is true?
о
1
Raul spent
hours more time shopping for shoes than
6
he spent shopping for shirts.
e
CLEAR ALL
Answer:
D. Raul spent the same amount of time shopping for shoes as he spent shopping for pants
Step-by-step explanation:
just trust me :)
1,682 inches rounded to the narest tenth is 1.6 inches?
Answer:
yes
Step-by-step explanation:
(-3,6] to inequality
Answer:
-3 < x ≤ 6
Step-by-step explanation:
Left side is exclusive, right side is inclusive, hence the < and ≤, respectively.
If the temperature changes - 5/8 degrees per hour for 8 hours, what is the total change in temperature?
Answer:
I think it is 5.
Step-by-step explanation:
5/8 in decimal form is 0.625. 0.625 x 8 = 5. I hope this helps/ sorry if it didn't.
Johnny made 8 benches in 2 hours. At this rate, how
many benches will he make in 9 hours.
plzzzzzzzzzz!!!!!!!! help on thissss
Answer:
36
Step-by-step explanation:
4 benches in 1 hour
? benches in 9 hours
36 benches
HOPE THIS HELPS
PLZZ MARK BRAINLIEST
Answer:
36 is the answer :)
Step-by-step explanation:
(PLZ ASAP ANSWER !!!!!!)The number line shows the graph of an inequality: A number line is shown from negative 5 to positive 5 with increments of 0.5. All the whole numbers are labeled on the number line. An empty circle is shown on the first mark to the left of 0. The region to the left of the empty circle is shaded. Which statement explains whether −2.5 can be a value in the shaded region? (5 points) Yes it can, because −2.5 lies to the left of −0.5. Yes it can, because −2.5 lies to the right of −0.5. No it cannot, because −2.5 lies to the left of −0.5. No it cannot, because −2.5 lies to the right of −0.5.
it is a. Yes it can, because −2.5 lies to the left of −0.5. plz mark me as brainiest and tell me if I am wrong
Carmen is an engineer making plans to run a rail line, represented by the transversal t, through a city. Parallel lines v and w are crossed by transversal t. Clockwise from top left, the angles formed with line v are 155 degrees, blank, blank, blank; with line w are 1, 2, 3, 4. Examine Carmen’s rail plans to identify the measure of ∠1. The streets represented by lines V and W are parallel. What is the mAngle1? 25° 35° 145° 155°
Answer:
155
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
I took the quiz
Which of the following is an equation of a proportional relationship?
Group of answer choices
y = 25x
y = 5x + 25
Describe what the equation you chose above could represent. In other words, what real-world situation could this equation be used?
Answer:
Both are proportional, because as the value of x change (increases or decreases), the value of y changes (increases or decreases).
The first equation (y = 25x) could represent that amount of teachers per students. If x = teachers (let's say there is 1 teacher), then y = students (1 teacher would teach a class of 25 students).
The second equation (y = 5x + 25) could represent the amount of money you could earn babysitting. The starting/base amount would be $25, and you would earn $5 more for every hour you babysat.
Step-by-step explanation:
8y-2x=-72 in slope form
Answer:
y=1/4x-9
Step-by-step explanation:
Slope-intercept form is y=mx+b.
8y-2x=-72
Add 2x to both sides
8y=2x-72
Divide both sides by 8.
y=1/4x-9
HTH :)
A fashion designer wants to know how many new dresses women buy each year. Assume a previous study found the variance to be 2.89. She thinks the mean is 5.6 dresses per year. What is the minimum sample size required to ensure that the estimate has an error of at most 0.11 at the 98% level of confidence?
Answer:
The minimum sample required = 1296.65
Step-by-step explanation:
Given that:
Variance [tex]\sigma^2 = 2.89[/tex]
Standard deviation [tex]\sigma = \sqrt{2.89}[/tex]
Standard deviation [tex]\sigma = 1.7[/tex]
Margin of error = 0.11
Confidence Interval = 98%
Level of significance = 1 - 0.98 = 0.02
The critical value = [tex]Z _{\alpha//2} = Z_{0.02/2} = Z_{0.01}[/tex]
= 2.33
Thus, the minimum sample size is given by the formula:
[tex]n = \bigg ( \dfrac{Z_{\alpha/2} \times \sigma }{E} \bigg)^2[/tex]
[tex]n = \bigg (\dfrac{2.33 \times 1.7 }{0.11} \bigg)^2[/tex]
n = 1296.65
4598÷101 =? write your answer as a whole number and remainder
Answer:
45 R53
Step-by-step explanation:
Hope This Helps
Souvenir hats, t-shirts, and jackets are sold at a rock concert. Two hats, two t-shirts, and one jacket cost $141. Three hats, three t-shirts, and two jackets cost $239. One hat, three t-shirts, and three jackets cost $262. Find the prices of the individual items.
Answer:
Step-by-step explanation:
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Are the two hearts congruent? How do you know?
Answer:
yes they are congruent
Step-by-step explanation:
they both the same shape and size