The value of t for which the tangent line to the graph of f(t) has slope 1 is -1/5.
The given function is f(t)=10t²+5t+1.
We need to find the value of t for which the tangent line to the graph of f(t) has slope 1.
What is the tangent line to the graph?In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point. Leibniz defined it as the line through a pair of infinitely close points on the curve.
Now, f'(t) = slope of the tangent line to the curve at the point (t, f(t)).
Given, f'(t) = 1
f(t)=10t²+5t+1
⇒f'(t)=20t+5
⇒1=20t+5
⇒20t=-4
⇒t=-4/20
⇒t=-1/5
Therefore, the value of t for which the tangent line to the graph of f(t) has slope 1 is -1/5.
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i need help with 1 and 2
Is dividing 4/5 the same as multiplying by 5 then dividing by 4?
Each second for 20 seconds, an elevator descends 6 feet. Find the total change in elevation.
To decrease an amount by 7%, what single multiplier should you use?
Write an equation that defines the exponential function with base a > 0.
how do you evaluate the expression |4/13|
You own a house cleaning business. It takes you 2hours and 45 minutes to clean a house. You have 3 houses to clean tomorrow, how long would it take you to clean all three houses?
What is the simplified expression for –3cd – d(2c – 4) – 4d?
A:–5cd
B:cd – 8d
C:5cd – 8d
D:–5cd – 8d
A multivitamin tablet contains 14.5mg of calcium. How much calcium does a bottle of 50 tablets contain? Write your answer in grams.
Answer:
The correct answer is 725mg of calcium.
Step-by-step explanation:
To solve this problem, you can to use the rule of three.
1 tablet → 14.5 mg.50 tablets → x mg.Now, you have to multiply 50 tablets by 14.5 mg, then divide by 1 tablet:
[tex]x = \frac{50 tb * 14.5mg}{1 tb} = 725 mg[/tex] // tb divided by tb is 1
[tex]x = 725 mg[/tex]
Simplify the expression
- 3/6 - 5/7
can you show me how?
y = 5x – 1
–15x – 3y = 3
How many solutions does this linear system have?
one solution: (0, –1)
one solution: (1, 4)
no solution
infinite number of solutions
y = 5x - 1...so we sub 5x - 1 in for y in the other equation
-15x - 3y = 3
-15x - 3(5x - 1) = 3
-15x - 15x + 3 = 3
-30x = 3 - 3
-30x = 0
x = 0
y = 5x - 1
y = 5(0) - 1
y = -1
it has one solution (0,-1) <=
f(x) = 3x + 10x and g(x) = 4x – 2, find (f – g)(x)
Draw one card at random from a standard deck of cards. the sample space s is the collection of the 52 cards. assume that the probability set function assigns 1/52 to each of the 52 outcomes. let a = {x: x is a jack, queen, or king}, b = {x: x is a 9, 10, or jack and x is red}, c = {x: x is a club}, d = {x: x is a diamond, a heart, or a spade}.
We have P(A) = 3/13, P(A ∩ B) = 3/52, P(A ∪ B) = 17/52, P(C ∪ D) = 1, and P(C ∩ D) = 0.
(a) To find P(A), we first determine the number of outcomes in A, which consists of 12 cards (4 jacks, 4 queens, and 4 kings).
Since there are 52 cards in total, P(A) = 12/52 = 3/13.
(b) For P(A ∩ B), we look for the cards that are both in A and B.
There are 3 such cards (jack of hearts, jack of diamonds, and jack of hearts).
So, P(A ∩ B) = 3/52.
(c) To find P(A ∪ B), we combine the outcomes in sets A and B, but we avoid double-counting the jacks.
So, A ∪ B consists of 12 cards from A and 5 cards from B, totaling 17 cards.
Hence, P(A ∪ B) = 17/52.
(d) P(C ∪ D) includes all cards that are clubs, diamonds, hearts, or spades.
Since all cards fall into these categories, P(C ∪ D) = 1.
(e) P(C ∩ D) represents the probability of drawing a card that is both a club and either a diamond, heart, or spade.
Since clubs do not intersect with these suits, P(C ∩ D) = 0.
Complete Question:
Draw one card at random from a standard deck of cards. The sample space S is the collection of the 52 cards. Assume that the probability set function assigns 1/52 to each of the 52 outcomes.
Let
A = {x: x is a jack, queen, or king},
B = {x: x is a 9, 10, or jack and x is red},
C = {x: x is a club},
D = {x: x is a diamond, a heart, or a spade}.
Find (a) P(A), (b) P(A ∩ B), (c) P(A ∪ B), (d) P(C ∪ D), and (e) P(C ∩ D).
find the solution of
2x - 2y = -20 and -2x + 4y = 14
I have 7 hundreds blocks, 5 tens blocks, and 8 ones blocks. I use my blocks to model two 3-digit numbers. What could my two numbers be?
The GCF of two different numbers is greater than the LCM of the numbers
a grading machine can grade 48 tests in 1 minute. How
long will it take the machine to grade 300 tests?
The governor of state a earns $50,935 more than the governor of state b. If the total salaries is $287,225. Find the salaries for both
Which set of ordered pairs could be generated by an exponential function?
(0, 0), (1, 1), (2, 8), (3, 27)
(0, 1), (1, 2), (2, 5), (3, 10)
(0, 0), (1, 3), (2, 6), (3, 9)
(0, 1), (1, 3), (2, 9), (3, 27)
Answer:
THE ANSWER IS D
Step-by-step explanation:
THE ANSWER IS D because if you square 3 you get 9, if you cube 3, you get 27
Answer: (0, 1), (1, 3), (2, 9), (3, 27)
Step-by-step explanation:
A recursive arithmetic sequence is defined ad f(1)=6, f(n+1)=f(n)+5 for n>1. The first four terms of the sequence are shown in the table. Write an explicit formula that represents the sequence using function notation. Find the slope of the line that passes through the points given in the table. The slope is
Answer:
Find the slope of the line that passes through the points given in the table. The slope is
✔ 5
.
Use one of the given points to find the y-intercept. Substitute values for x, y, and m into the equation y = mx + b and solve for b. The y-intercept is
✔ 1
.
Write the formula as a function of n in slope-intercept form. The function is
✔ f(n) = 5n+ 1
for n in the set of natural numbers.
the some of two consecutive even integers is 170. find the two integers.
The required value of integers are 84 and 86 respectively.
How to write a linear equation?A linear equation for the given case can be written by assuming any variable as the unknown quantity. Then, as per the given data the required operations are done and it is equated to some value.
Suppose the first even integer be x.
Then, the second even integer is x + 2.
Since the sum is given as 170, the following equation can be formed as,
x + x + 2 = 170
⇒ 2x + 2 = 170
⇒ 2x = 168
⇒ x = 84
Then, the other integer is 84 + 2 = 86.
Hence, the two integers for the given case are 84 and 86 respectively.
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An automotive repair center charges $45 for any part of the first hour of labor, and $25 for any part of each additional hour. Which of the following is a correct cost?
A. C(t) = 95 for 1 < x ≤ 2
B. C(t) = 95 for 2 < x ≤ 3
C. C(t) = 120 for 2 < x ≤ 3
D. C(t) = 120 for 4 < x ≤ 5
If P = Q squared ⋅ O, express O in terms of P and Q.
walt is mixing fruit punch for the party. he combines 1 gallon 2 quarts 3 pints of orange juice , 1 gallon 3 quarts 7 pints of pineapple juice, and 1 gallon 3 quarts 3 pints of ginger ale. what is the total liquid measure of the punch ?
Ryan runs 9 miles in 73 minutes. How many minutes does he take per mile?
Solumedrol 1.5 mg/kg is ordered for a child weighing 50 lb. Solumedrol is available as 75 mg / 1 mL is available. How many mL must the nurse administer?
Which statement best describes the function h(t) 210- 15t
B. if lucinda has only $18 to spend and the price of kewpie dolls and the price of beanie babies are both $6, how many of each would lucinda buy if she were rational? 0 kewpie dolls and 3 beanie babies 3 kewpie dolls and 0 beanie babies 2 kewpie dolls and 1 beanie baby 1 kewpie doll and 2 beanie babies
Lucinda can rationally choose to buy 0 Kewpie dolls and 3 Beanie Babies, 3 Kewpie dolls and 0 Beanie Babies, 2 Kewpie dolls and 1 Beanie Baby, or 1 Kewpie doll and 2 Beanie Babies, as all combinations fit within her $18 budget. The prices for each are $6.
In order to determine how many Kewpie dolls and Beanie Babies Lucinda can buy, we need to explore her budget constraint. Lucinda has $18 to spend, and the prices of both Kewpie dolls and Beanie Babies are $6 each. We can calculate the maximum possible combinations of each that fit within her budget.
If Lucinda buys 0 Kewpie dolls and 3 Beanie Babies, she spends $0 + $18 = $18.If Lucinda buys 3 Kewpie dolls and 0 Beanie Babies, she spends $18 + $0 = $18.If Lucinda buys 2 Kewpie dolls and 1 Beanie Baby, she spends $12 + $6 = $18.If Lucinda buys 1 Kewpie doll and 2 Beanie Babies, she spends $6 + $12 = $18.All these combinations maximize her budget, so any of these options could be rational depending on her preference. Therefore, Lucinda could rationally choose to buy any of the following combinations: 0 Kewpie dolls and 3 Beanie Babies, 3 Kewpie dolls and 0 Beanie Babies, 2 Kewpie dolls and 1 Beanie Baby, or 1 Kewpie doll and 2 Beanie Babies.
An item is regularly priced at $91 . It is now priced at a discount of 15% off the regular price. What is the price now?
What is 3/8 written as a decimal