Assuming you mean f(t) = g(t) × h(t), notice that
f(t) = g(t) × h(t) = cos(t) sin(t) = 1/2 sin(2t)
Then the difference quotient of f is
[tex]\dfrac{\frac12 \sin(2(t+h)) - \frac12 \sin(2t)}h = \dfrac{\sin(2t+2h) - \sin(2t)}{2h}[/tex]
Recall the angle sum identity for sine:
sin(x + y) = sin(x) cos(y) + cos(x) sin(y)
Then we can write the difference quotient as
[tex]\dfrac{\sin(2t)\cos(2h) + \cos(2t)\sin(2h) - \sin(2t)}{2h}[/tex]
or
[tex]\boxed{\sin(2t)\dfrac{\cos(2h)-1}{2h} + \cos(2t)\dfrac{\sin(2h)}{2h}}[/tex]
(As a bonus, notice that as h approaches 0, we have (cos(2h) - 1)/(2h) → 0 and sin(2h)/(2h) → 1, so we recover the derivative of f(t) as cos(2t).)
A dump truck is filled with 82.16 pounds of gravel. It drops off 77.29 pounds of gravel at a construction site. How much gravel is left on the truck?
Answer:
4.87lbs
Step-by-step explanation:
82.16-77.29=4.87
Someone help?
Find the problem:
-5x - 16 = 8x - 1
Fix the problem:
?
[tex]-5x -16 = 8x -1\\\\\implies 8x +5x = -16 +1 \\\\\implies 13x = -15\\\\\implies x = -\dfrac{15}{13}[/tex]
Find an equation for the perpendicular bisector of the line segment whose endpoints
are (5, 4) and (-7,-8).
Answer:
y= -x -3
Step-by-step explanation:
A perpendicular bisector of a line cuts through the line at its midpoint perpendicularly (90°).
Let's find the slope of the line segment.
[tex]\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }[/tex]
Slope of line segment
[tex] = \frac{4 - ( - 8)}{5 - ( - 7)} [/tex]
[tex] = \frac{4 + 8}{5 + 7} [/tex]
[tex] = \frac{12}{12} [/tex]
= 1
The product of the slopes of 2 perpendicular lines is -1.
Let the slope of the perpendicular bisector be m.
m(1)= -1
m= -1
y= -x +c
To find the value of c, substitute a pair of coordinates in which the line passes through into the above equation.
Since the perpendicular bisector cuts through the midpoint of the line segment, let's find the coordinates of this midpoint.
[tex]\boxed{midpoint = ( \frac{x _{1} + x _2}{2} , \frac{y_1 + y_2}{2} )}[/tex]
Midpoint of line segment
[tex] = ( \frac{5 - 7}{2} , \frac{4 - 8}{2} )[/tex]
[tex] = ( \frac{ - 2}{2} , \frac{ - 4}{2} )[/tex]
= (-1, -2)
y= -x +c
When x= -1, y= -2,
-2= -(-1) +c
-2= 1 +c
c= -2 -1
c= -3
Thus, the equation of the perpendicular bisector is y= -x -3.
Karen stacks a set of cans as shown. The top can has a diameter of 2 inches, the middle can has a diameter of 5 inches, and the bottom can has a diameter of 6 inches.
Answer:
Unknown
Step-by-step explanation:
What is the question? You have the information listed but you forgot to ask the question.
The directions for Clean-All to mix 1 3/8 cups of cleaner with 2 2/5 cups water. Write a COMMON RATIO as
CLEANER to WATER
Answer:
Step-by-step explanation:
The Mega Clean mixture with 3 1/2 per gallon has more cleaner in it. The first mixture has .75 oz per quart. The second mixture has .875 oz per qt.
HOPE THAT HELP YOU
The local movie theater, Scene It Cinema, had a special showing of the latest dinosaur movie. There were 6 youth tickets sold for every 5 adult tickets sold.
If there were 70 adult tickets sold, how many movie tickets were sold altogether?
Answer:
Let the youth and adult tickets be y and x respectively.
6y + 5x ---> (1)
From statement (1):
(1) × 14
84y + 70x
For every 70 adult tickets sold, 84 youth tickets were sold.
Total number of tickets sold= 70 + 84
= 154
Yoni has a ribbon that measures 5/3 yards. She wants to cut it into 3 equal pieces. What is the length of each piece of ribbon? 5\8 yards 5/6 yards 5/9 yards 5/3 yards
Answer:
5/9 yards
Step-by-step explanation:
[tex] \frac{5}{3} \div \frac{3}{1} \\ = \frac{5}{3} \times \frac{1}{3} \\ = \frac{5}{9} [/tex]
How would the expression x3 -3 sqrt 3 be rewritten using difference of cubes?
O A. (x- 13 )(x2-3x - 3)
O B. (x+ 3)(x + 13 x + 3)
C. (x - 13 )(x2 + 3x + 3)
O D. (x- vb)(x2 + v3 x+3)
Answer:
x^3 - (√3)^3
I'm not so sure since it's not even an option
Step-by-step explanation:
x^3 - 3√3 = x^3 - 3^1 × 3^(1/2)from the laws of indices: 3^1 × 3^(1/2) = 3^(1 + 1/2)= 3^(3/2) which is the same as (√3)^3so it could be written as x^3 - (√3)^3Which table of ordered pairs represents a proportional relationship?
Answer:
C)
Step-by-step explanation:
Because Its equivalent
Monica says,"if 4 bottles cost $10, then 2 bottles cost $5 + $20." Is Monica correct? Explain
6 grade shiiii, help me out doe, thanks luvs <33.
Answer:
Monica is not correct.
Step-by-step explanation:
First of all, if 4 bottles only cost $4, then how would only 2 cost more? (She said the two bottles would be $25, which doesn’t make sense.)
Holly and Jimmy went shopping. For every $2
that Holly spent, Jimmy spent $5. If together
they spent $35, how much did Jimmy spend?
if you want it a a whole number, it would be for every 34$ 85 bucks for jimmy .
how to write into fractional expanded form 65.43
Answer:
6543/100
Step-by-step explanation:
Multiply both numerator and denominator by 10 for every number after the decimal point
65.43 × 100
1 × 100
=
6543
100
what is 1/4 of 5/6???
you search the LCD then you subtracted the top and left the bottom the same
Step-by-step explanation:
im not sure
select the correct product for the problem below. (−85)(23)(−4) =? -64/15 64/15 16/60 -16-60 64-60
Answer: 7,820
Sorry I have no help :(
The perimeter of a rectangle is 20/33 feet. The length of three sides together is 16/33 feet.
What is the length of the fourth side?
40 feet
4/33feet
16/33feet
20/33feet
Answer:
40 feet
Step-by-step explanation:
on edge
after a party 3/4 cake is leftover. Dennis eats 1/2 of the leftover cake. Which fraction model represents the amount of cake Dennis eats?
Question : Explore criteria of congruency of triangles using a set of triangle cut outs
Answer:
Explore Various Criteria for Congruence TrianglesSASASAAASSSSRHSWhat is 196.7 16 in simplest form?
Factor
3x2- 2x - 5
*(3xpower of 2 -2x-5)**
Answer:
16
Step-by-step explanation:
3×2-2×-5=
6-(-10)=
6+10=
16
please help will brain list if correct no links please
Answer:
C
Step-by-step explanation:
the angle opposite of it is 30
On Monday there are 25 pencils in a basket, If 3 pencils are taken out of the basket each day, how many pencils are left in the basket on Friday?
13 cuz add 4 days then friday so 4×3 which is 12 and 12-25 so ye its 13
You use a garden hose to fill a wading pool. If the water level rises 16 centimeters every 7 minutes
and you record the data point of (21,y), what is the value of y? Use slope to justify your answer.
The rate of change at which the water level rises is ____ centimeters per minute. So solving the equation ____ for y gives a y-value equal to ____
A researcher at the Centers for Disease Control and Prevention is studying the growth of a certain bacteria. He starts his experiment with 500 bacteria that grow at a rate of 16% per hour. He will check on the bacteria every 8 hours. How many bacteria will he find in 8 hours? Round your answer to the nearest whole number.
The population of the bacteria after 8 hours is 1639 bacteria.
An exponential function is given by:
y = abˣ
where y, x are variables, a is the initial value of y and b is the multiplier.
Let y represent the population of bacteria after x hours.
Given that he starts his experiment with 500 bacteria, hence
a = 500
The bacteria grow at a rate of 16% per hour, hence:
b = 100% + 16% = 1.16
The exponential equation becomes:
y = 500(1.16)ˣ
After 8 hours:
y = 500(1.16)⁸ = 1639
The population of the bacteria after 8 hours is 1639 bacteria.
Find out more at: https://brainly.com/question/12490064
Find the length of the hypotenuse.Round to the nearest 10th if necessary.(40pts)
Answer:
5 is our hypotenuse
Step-by-step explanation:
[tex]a^{2} + b^{2} = c^{2}[/tex]
c is our hypotenuse
[tex]3^{2} + 4^{2} = c^2[/tex]
[tex]9 + 16 = 25[/tex]
[tex]25 = c^{2}[/tex]
c = 5
5 is our hypotenuse
Answer:
x = 5
Step-by-step explanation:
[tex]c=\sqrt{a^2+b^2} \\a= \sqrt{3^2+4^2} \\c=\sqrt{9+16} \\c= \sqrt{25} \\c= 5[/tex]
put the following unit fractions in order from smallest to largest. 1/16 1/24 1/8 1/10 1/4 1/12 1/3 1/6 1/2
Answer:
1/24, 1/16, 1/12, 1/10, 1/8, 1/6, 1/4, 1/3, 1/2
Step-by-step explanation:
If you have this many fractions and they all have the same numerator, then the smallest number will have the biggest denominator and the biggest number will have the smallest.
So when you have all numbers with the same numerator and you're trying to put them in order from smallest to greatest, it's like putting the denominators in order from largest to smallest. (So, the 1/24 is the SMALLEST and the 1/2 is the BIGGEST.
Among 2165 passenger cars in a particular region, 235 had only rear license plates. Among 330 commercial trucks, 50 had only rear license plates. A reasonable hypothesis is that commercial trucks owners violate laws requiring front license plates at a higher rate than owners of passenger cars. Use a 0.10 significance level. Identify the P-value. Let population 1 correspond to the passenger cars and population 2 correspond to the commercial trucks. Let a success be a vehicle that only has a rear license plate Group of answer choices
Using the z-distribution, it is found that the p-value is of 0.0192.
At the null hypothesis, it is tested if commercial trucks owners do not violate laws requiring front license plates at a higher rate than owners of passenger cars, that is, the subtraction is of at most 0, hence:
[tex]H_0: p_2 - p_1 \leq 0[/tex]
At the alternative hypothesis, it is tested if commercial truck owners violate the laws more, that is, the subtraction is positive, hence:
[tex]H_1: p_2 - p_1 > 0[/tex]
For each sample, the size, the proportion and the standard error are given by:
[tex]n_1 = 2165, p_1 = \frac{235}{2165} = 0.1085, s_1 = \sqrt{\frac{0.1085(0.8915)}{2165}} = 0.0067[/tex]
[tex]n_2 = 330, p_1 = \frac{50}{330} = 0.1515, s_1 = \sqrt{\frac{0.1515(0.8485)}{330}} = 0.0197[/tex]
For the distribution of differences, the mean and the standard error are given by:
[tex]\overline{p} = p_2 - p_1 = 0.1515 - 0.1085 = 0.043[/tex]
[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{0.0067^2 + 0.0197^2} = 0.0208[/tex]
The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{s}[/tex]
In which [tex]p = 0[/tex] is the value tested at the null hypothesis.
Hence:
[tex]z = \frac{\overline{p} - p}{s}[/tex]
[tex]z = \frac{0.043 - 0}{0.0208}[/tex]
[tex]z = 2.07[/tex]
The p-value is found using a z-distribution calculator, for a right-tailed test, as we are testing if the proportion is more than a value, with z = 2.07.
Using the calculator, the p-value is of 0.0192.A similar problem is given at https://brainly.com/question/15545277
6x + 3 > 26
How do I solve the math problem above
Answer:
x > 23/6
Step-by-step explanation:
Solve this one the same way you would a 2-step linear equation.
6x +3 > 26 . . . . . given
6x > 23 . . . . . . . . subtract the unwanted constant from both sides (step 1)
x > 23/6 . . . . . . . .divide both sides by the coefficient of x (step 2)
__
Additional comment
If the coefficient of the variable in a 2-step linear inequality is negative, then the inequality symbol must be reversed when dividing by that negative number.
After a discount of 25%, the sale price of a game system is $149.25. what is the original price?
Answer:111.94
Step-by-step explanation:
'Percent (%)' means 'out of one hundred':
p% = p 'out of one hundred',
p% is read p 'percent',
p% = p/100 = p ÷ 100.
25% = 25/100 = 25 ÷ 100 = 0.25.
100% = 100/100 = 100 ÷ 100 = 1.
New value =
149.25 - Percentage decrease =
149.25 - (25% × 149.25) =
149.25 - 25% × 149.25 =
(1 - 25%) × 149.25 =
(100% - 25%) × 149.25 =
75% × 149.25 =
75 ÷ 100 × 149.25 =
75 × 149.25 ÷ 100 =
11,193.75 ÷ 100 =
111.9375 ≈
111.94
Pleasee help with this question
Answer:
(2 x^2 z^13)/(z^8 y^5)
Hope This Helps!!!
Answer:
2xz⁵/y⁴
Step-by-step explanation:
16/8 = 2
x²/x = x
y/y⁵ = y⁻⁴
z¹³/z⁸ = z⁵
SOMEONE PLEASE HELP ME!!
Answer:
should be 3
Step-by-step explanation:
hope you get a good grade