The tangent line to f(x) at some point x has slope equal to f'(x), so first compute the derivative of f :
f(x) = -10x ² + 8x
f'(x) = -20x + 8
When x = 9, we have
f (9) = -10•9² + 8•9 = -738
f' (9) = -20•9 + 8 = -172
so the slope is -172.
If you also have to find the equation of the tangent line, use the point-slope formula:
y - (-738) = -172 (x - 9)
y = -172x + 810
backpacks originally cost $24 but if 40% back to school sale is going on determine the sale price of the backpack.
I need help right now
Really Important!!!!!!!
Answer: The price is now 14.40
Step-by-step explanation: The difference is 9.60
A man travels 320 miles in 8 hours. If he continues at the same rate, how many miles will he
travel in the next 2 hours?
Answer: 80 miles
Step-by-step explanation:
320miles/8hours= 40mph
40mph=xmiles/2hrs
40*2= 80 miles
Find the mean, median, and mode of the data set 8 2 7 2 6 5
Answer:
Mean is 6, median 5.5, mode 2
Step-by-step
Answer:
mean=8+2+7+2+6+5
=30
30÷6=5
note: divide the total with it's sum.
median=7+2
=9
9÷2= 4.5
note: median is the middle no. since there is no middle no. so just add those two no. and divide it by 2.
mode= 2
since it occurs twice
If the interest of sum of money is 6 yrs in 3/8 of the principal . what is the rate of interest?
Answer :
R = 6.25%
Solution,
Let P is the principal. It means interest will be :
I=3/8 P
The formula for the interest is given by :
[tex]I=\dfrac{PRT}{100}\\\\\dfrac{3}{8}P=\dfrac{PR\times 6}{100}\\\\\dfrac{3}{8}=\dfrac{6R}{100}\\\\R=\dfrac{300}{8\times 6}\\\\=6.25\%[/tex]
Hence, the rate of interest is 6.25%.
The sum of 2 numbers is 84 if one number is 4.less than the other find the numbers
Answer:
one number= x = 44
the other number= (x-4)= 40
Step-by-step explanation:
one number= x
the other number= (x-4)
x + (x-4) = 84
2x= 84+4
2x= 88
x= 88/2= 44
one number= x = 44
the other number= (x-4)= 40
What type of correlation does the scatter plot show?
A. Positive
B. Negative
C. Cannot tell
D. None
Can you please tell me if this is a function or not
Simplify fractions
3\10
1/8
Answer:
Already simplified
Step-by-step explanation:
Answer:
Step-by-step explanation:
its preety simple you just have to divide 3/10 and 1/8 and you will get your two answers
Levante changes 24 650 Hungarian forints to dollars.
The exchange rate is $1 = 290 forints.
Calculate how many dollars Levante receives.
Someone helpppppp
The relation between the dollars and forints will be directly proportional. Then the number of dollars will be $ 85.
What are ratio and proportion?A ratio is an ordered set of integers a and b expressed as a/b, with b never equaling 0. A proportional is a mathematical expression in which two things are equal.
Levante changes 24 650 Hungarian forints to dollars.
Then the relation between the dollars and forints will be directly proportional. Then we have
Let x be the number of the dollars. Then we have
x / 1 = 24650 / 290
x = $ 85
More about the ratio and the proportion link is given below.
https://brainly.com/question/14335762
#SPJ2
Let V(t) represent the value of a bank account, in thousands of dollars, t years after the account is opened in the bank
Answer:
Step-by-step explanation:
False,true,true
How many 1/2 yard lengths are in 1 yard
Answer:
1/2 yard is equal to 18 inches
Step-by-step explanation:
what percent of 30 is 16.5..................................
If it takes 3 gallons of gas to go 60 miles, how many gallons of gas does it take to go 440 miles at the same rate?
Answer:
it would take 22 gallons of gas
Step-by-step explanation:
3 divided by 60
that’s the amount of gas per single mile
then that number times 440 (number of miles you wish to go).
the letters of the word independent are written on individual card and the cards are put into a box a card is selected and then replaced and then a second card is selected find the probality of obtaining the letter p twice
Answer:
The probability of obtaining the letter p twice is 1/121
Step-by-step explanation:
Probability of Recurring Events
There are 11 letters in the word 'independent', one of which is the letter 'p'.
When those letters are written on individual cards and they are put into a box, there are 11 different choices to pick at random.
This means the individual probability of getting a 'p' is:
[tex]\displaystyle P_1=\frac{1}{11}[/tex]
The card is reinserted into the box, leaving the sample space unaltered, thus the second card has the same probability:
[tex]\displaystyle P_2=\frac{1}{11}[/tex]
We'll use the multiplication rule. Just multiply the probability of the first event by the second.
[tex]\displaystyle P=P_1*P_2=\frac{1}{11}*\frac{1}{11}[/tex]
[tex]\displaystyle P=\frac{1}{121}[/tex]
The probability of obtaining the letter p twice is 1/121
What is the graph of y=3/4x-3?
Answer:
Graph A
Step-by-step explanation:
you can write the equation into desmos (search it up on google) and it will produce a graph for you and just match it to the ones you have shown
Which relation below is not a function
Answer:
its c i believe <3
Sale! 25% OFF of the original price! Laura wants to buy a sleeping bag. The original price is $56. How much will Laura pay if she buys it during the sale.
Answer:
$14
Step-by-step explanation:
56 × 0.25 = 14
to check this, you can divide 14 ÷ 56 = 0.25
to turn a percentage into a decimal, just divide it by 100
Find the measure of X
Answer:
For the first one =5.29150262
Step-by-step explanation:
8 squared - 6 squared =64-36=28
square root of 28=5.29150262
Suppose a country's population at any time t grows in accordance with the rule dP dt = kP + I where P denotes the population at any time t, k is a positive constant reflecting the natural growth rate of the population, and I is a constant giving the (constant) rate of immigration into the country. If the total population of the country at time t = 0 is P0, find an expression for the population at any time t.
Answer:
[tex]\mathbf{P =\bigg (P_o +\dfrac{ I}{k} \bigg)e^{kt}- \dfrac{I}{k}}[/tex]
Step-by-step explanation:
Given that:
A country population at any given time (t) is:
[tex]\dfrac{dP}{dt}= kP+I[/tex]
where;
P = population at any time t
k = positive constant
I = constant rate of immigration into the country.
Using the method of separation of the variable;
[tex]\dfrac{dP}{kP+1}= dt[/tex]
Taking integration on both sides:
[tex]\int \dfrac{dP}{kP+I}= \int \ dt[/tex]
[tex]\dfrac{1}{k} log (kP + I) = t+c_1 \ \ \ here: c_1 = constant \ of \ integration[/tex]
[tex]log (kP + I) =k t+kc_1[/tex]
By applying the exponential on both sides;
[tex]e^{log (kP + I) }=e^{k t+kc_1 }[/tex]
[tex]KP+I = e^{kt} *e^{kc_1}[/tex]
Assume [tex]e^{kc_1 }= C[/tex]
Then:
[tex]kP + I = Ce^{kt}[/tex]
[tex]kP = Ce^{kt}-I[/tex]
[tex]P =\dfrac{ Ce^{kt}-I}{k} \ \ \---- Let \ that \ be \ equation \ (1)[/tex]
When time t = 0, The Total population of the country is also [tex]P_o[/tex]
[tex]P_o = \dfrac{Ce^{0(t)} -I}{k}[/tex]
[tex]P_o = \dfrac{Ce^{0} -I}{k}[/tex]
[tex]P_o = \dfrac{C-I}{k}[/tex]
C - I = kP₀
C = kP₀ + I
Substituting the value of C back into equation(1), we have:
[tex]P =\dfrac{ (kP_o+1)e^{kt}-I}{k}[/tex]
[tex]P =\dfrac{ (kP_o+1)e^{kt}}{k} - \dfrac{I}{k}[/tex]
[tex]\mathbf{P =\bigg (P_o +\dfrac{ I}{k} \bigg)e^{kt}- \dfrac{I}{k}}[/tex]
how many men have a waist measurement of more than 85cm
Answer:
29
Step-by-step explanation:
The amount of change that goes up
Answer:
rates of change, positive or negative
Step-by-step explanation:
what is the largest prime number?
Answer:
28258933-1
Step-by-step explanation:
hope it helps you
Find all the real square roots of -49
Answer:
-7
Step-by-step explanation:
Answer:
7i
Step-by-step explanation:
the square root of 49 is 7
i equals -1
7 squared times -1 equals -49
xoxo,your highness...Help with this problem!!!!
X/2-3=9
Answer:
pretty sure it's
2
−
3
=
9
\frac{X}{2}-3=9
2X−3=9
2
−
3
+
3
=
9
+
3
will give bralist HELP ME PLEASE
Answer:
It would be a I think
Step-by-step explanation:
Answer:
The answer is A
Step-by-step explanation:
The freshman basketball coach’s office has a doorway that is 77 inches high. The coach will only recruit those student athletes who have to duck to enter the office. Of all the freshmen who wish to play basketball, the mean height is 75 inches with a standard deviation of 2.82 inches. Meanwhile, the football coach will only recruit student athletes to play linebacker (a defensive position) who weigh 210 pounds or more. Of all the freshmen who wish to play linebacker, the mean weight is 190 inches with a standard deviation of 12.32 pounds. Who do you think will have a harder time recruiting players?
How much simple interest would Kaitlin earn on $300 at 6% for 3 months?
A. 27
B. 9
C. 54
D. 18
Answer:
C) $54.00
Step-by-step explanation:
300*6%*3
300*0.06*3
which is $54.
Hope this helps plz hit the crown :D
True or false
2+(-2) is equal to zero.
Answer:
It is TRUE.
Other:
Brainliest? Thanks!
Jack is 2 times as old as Lacy. 5 years ago the sum of their ages was 20. How old are they now?
Answer:
2x-6=8
2x-6=8+6
2x=24
x=12
Let f(x) = 9x and g(x) = x + 7. What's
the smallest number that is in the domain of
fºg?
Enter the correct answer.
OOOO
DONE
Clear all
Answer:
Let `f` be a function defined on [0,2]. Then find the domain of function `g(x)=f(9x^2-1)
Step-by-step explanation:
I'm not sure if that's right