Recall the double angle identity,
sin(2x) = 2 sin(x) cos(x)
Then we can write
sin(9x) cos(9x) = 1/2 sin(2 • 9x) = 1/2 sin(18x)
Then
∫ sin(9x) cos(9x) dx
= 1/2 ∫ sin(18x) dx
= -1/2 • 1/18 cos(18x) + C
= -1/36 cos(18x) + C
though you could continue with another double angle identity,
cos(2x) = cos²(x) - sin²(x)
to rewrite the antiderivative as
= -1/36 (cos²(9x) - sin²(9x)) + C
= 1/36 (sin²(9x) - cos²(9x)) + C
Evaluate the expression. Write your answer in scientific notation.
(1.9 x 10^9) - 6,300,000 × (5.6 x 10^2)
Please solve this expression as a scientific notation when you answer and remember.
Answer:
- 1.628 x 10^9
Step-by-step explanation:
(1.9 x 10^9) - 6,300,000 × (5.6 x 10^2) = - 1628000000
- 1628000000 = - 1.628 x 10^9
write an equation of the line below
Answer:
y=3x
Step-by-step explanation:
A researcher is 95% confident that the interval from 5.2 hours to 7.8 hours captures u = the true mean amount of time
it takes to fully charge a battery pack.
Is it plausible that the true mean number of hours to charge all battery packs of this type may be 5?
O No, this is not a plausible value for the population mean, because 5 is within the 95% confidence interval.
No, this is not a plausible value for the population mean, because 5 is not within the 95% confidence interval.
O Yes, this is a plausible value for the population mean, because 5 is within the 95% confidence interval.
Yes, this is a plausible value for the population mean, because the lower bound of the confidence interval, 5.2, is
greater than 5.
No, this is not a plausible value for the population mean, because 5 is not within the 95% confidence interval.
====================================================
Explanation:
The greek letter mu is the population mean. It has the symbol [tex]\mu[/tex] which looks like the letter 'u' but with a tail at the front or left side.
The question is asking if mu = 5 is plausible if the researcher found the 95% confidence interval to be 5.2 < mu < 7.8
We see that 5 is not in that interval. It's a bit to the left of 5.2
Since mu = 5 is not in the interval, it's not a plausible value for the population mean.
Have we ruled it out with 100% confidence? No. Such a thing is not possible. There's always room for (slight) error. The researcher would need to do a census to be fully confident; however, such practices are very time consuming and expensive. This is the main reason why statistics is important to try to estimate the population with a sample.
What compass heading represents 20° north of east?
Answer:
45°
Step-by-step explanation:
Northeast (NE), 45°, halfway between north and east, is the opposite of southwest. Southeast (SE), 135°, halfway between south and east, is the opposite of northwest. Southwest (SW), 225°, halfway between south and west, is the opposite of northeast.
Brandon is half of Ella's age. Ella is three times Tristans age. In fifteen years, their combined age will be 89. How old is Brandon?
Answer:
Step-by-step explanation:
Let Brandon's age be [tex]x[/tex]
Therefore Ella=[tex]2x[/tex]
Tristan= [tex]\frac{2x}{3}[/tex]
Fifteen years time add 15 to each age
Brandon: [tex]x+15[/tex]
Ella: [tex]2x+15[/tex]
Tristan:[tex]\frac{2x}{3} +15[/tex]
All their ages together=89
So: [tex]x+15[/tex] + [tex]2x+15[/tex] + [tex]\frac{2x}{3} +15[/tex][tex]=89[/tex]
[tex]3\frac{2}{3} x=44[/tex]
[tex]x= \frac{44}{3\frac{2}{3} } =12[/tex]
What’s greater 7.8 mL or 0.78 L
Answer:
7.8 mL
Step-by-step explanation:
Answer:
.78 L
Step-by-step explanation:
Well, simple conversions
a milliliter is .0001 of a liter and 1 liter is 1000 mL, so we can safely say that .78 L is 780 mL, dwarfing the given 7.8 mL
which of the following is a graph of a line with the equation 3y-4x=-3
Plss help mee
you need to show your work
At the school's fall bake sale, all of the pies were cut into 6 pieces, so each person who bought a piece bought 1/6 of a pie. Each slice of pie sold for $1.00. How much money did the school make if all eleven pies were sold? (In other words, find 11 divided by 1/6 .)
Answer:
2 ⅓
Step-by-step explanation:
division is the same as a fraction
the dividend is the numerator and the divisor is the denominator
7÷3 is the same as 7/3
change 7/3 into a mixed number which is 2 ⅓
is a pentagon similar to a quadrilateral
Answer:
no
Step-by-step explanation:
quad- 4
pent- 5
they have a different number of sides
Which option is equivalent to the expression above
the total of 3/4 and a number is no more than 2
3/4=a fraction
Answer:
Step-by-step explanation:
Let the number be x
[tex]\dfrac{3}{4}+x \leq 2\dfrac{3}{4}\\\\\\\dfrac{3}{4}+ x \leq \dfrac{11}{4}[/tex]
Subtract 3/4 from both sides
[tex]\dfrac{3}{4}-\dfrac{3}{4}+x\leq \dfrac{11}{4}-\dfrac{3}{4}\\\\\\x \leq \dfrac{11-3}{4}\\\\\\x \leq \dfrac{8}{4}\\\\\\x \leq 2[/tex]
Answer: Any number less than or equal to 2
Which equation best represents the line graphed above? x = –1 x = 1 y = –1 y = x – 1
I think you forgot the graph. Please add it.
Answer:
I believe the answer is A: x = - 1
Solve the equation P=KTV for the letter K.
Answer:
K = [tex]\frac{P}{TV}[/tex]
Step-by-step explanation:
P = KTV
Divide both sides by TV
(P/TV) = K
7W FEW DOWO
Puzzle Three
Solve the following problems about functions. Match the correct
solution in the code at the bottom to find the code word to
unlock puzzle two.
E. Determine if the
P. Write the equation for
following graph is linear or non the following function:
F. Determine if the
R. Write the equation for
following graph is linear or non- the following function:
linear
L. Write an equation that
shows the slope is 3 and the y
intercept is -2.
U. Find the rate of change
between the two ordered pairs
(3,6) and (5,7)
What is the slope of
0. Find the rate of change W.
between the two ordered pairs the line
(1,4) and (-3,-2)
Code:
4y = 8x + 1
linear
2
y = 3x - 2
y=-3x + 1
y = 5x +4 non
31
1
2
linear
Answer:
The crossword style worksheet has problems that provide a simplified answer for the puzzle. See more ideas about high school math, middle school math, ...a box of 40 chocolates contains 56g of saturated fat. How much saturated fat is there in 1 chocolate
Divide total fat by number of chocolates
56/40 = 1.4 grams
answer: 1.4 grams
6 6 small bricks have the same mass as 5 large bricks. The mass of one small brick is 2.5 kg. What is the mass of one large brick?
Since 6 small bricks have the same mass as 5 large bricks and the mass of one small brick is 2.5 kg, the mass of one of the large bricks is 3 kg
What is mass?Mass is the quantity of matter in a physical body.
6 small bricks have the same mass as 5 large bricks.
let
the total mass of the small or large bricks = x
Therefore,
6 × 2.5 = x
x = 15 kg
Therefore, the mass of each large bricks can be calculated as follows:
let the mass of each large bricks = y
15 = 5y
divide both sides by 6
y = 15 / 5
y = 3 kg
Therefore, the mass of one of the large bricks is 3 kg
.learn more on mass here: https://brainly.com/question/895643
Identify the independent variable in the following hypothesis:
A person's opinion on immigration reform is influenced by their age.
The length of a rectangular parking lot is 32 meters and the width is 20 meters. The parking lot is surrounded by a sidewalk that is x meters wide. Find the expression that represents the area of the parking lot, including the sidewalk.
For the function g(x)=5x2+4x−5, find g(−5)
Answer:
100
Step-by-step explanation:
g(x)=5x^2+4x−5
Let x = -5
g(x)=5 ( -5)^2+4(-5)−5
= 5*25 - 20 -5
=125 - 25
= 100
If 1, x, 5 and 15 are in proportion, then the value of x is
a. 5
b. 4
c. 3
Answer:
3
Step-by-step explanation:
Here, 1:x =5:15
Solving which the value of x is 3.
help what are angles 3, 6, 8, 9, 11, 13, 14, 15, 16, 17, and 18
3. 128°
6. 136°
8. 96°
9. 96°
11. 136°
13. 52°
14. 128°
15. 44°
16. 136°
17. 128°
18. 52°
LMNP is a rectangle. Find the value of x and the length of each diagonal.
LN= 4x + 3 and MP = 8x -9
X=
Solution:
We know that:
Given diagonals: LN and MPLN and MP must be equal because they are diagonals of LMNP.LN = 4x + 3MP = 8x - 9Since LN and MP must be equation, equation formed: 4x + 3 = 8x - 9
Let's simplify the equation to find x.
Subtracting 4x both sides.
[tex]4x + 3 = 8x - 9[/tex]=> [tex]4x - 4x + 3 = 8x - 9 - 4x[/tex]=> [tex]3 = 4x - 9[/tex]Add 9 both sides.
=> [tex]3 = 4x - 9[/tex]=> [tex]3 + 9 = 4x - 9 + 9[/tex]=> [tex]12 = 4x[/tex]Divide 4 both sides.
=> [tex]12 = 4x[/tex]=> [tex]\frac{12}{4} = \frac{4x}{4}[/tex]=> [tex]x = 3[/tex]Now, let's find the length of each diagonal.
[tex]LN = 4x + 3 = 4(3) + 3 = 12 + 3 = 15 \space\ units[/tex][tex]MP = 8x - 9 = 8(3) - 9 = 24 - 9 = 15 \space\ units[/tex]Diagonals are equal
[tex]\\ \rm\Rrightarrow 4x+3=8x-9[/tex]
[tex]\\ \rm\Rrightarrow -4x=-12[/tex]
[tex]\\ \rm\Rrightarrow x=-12/-4[/tex]
[tex]\\ \rm\Rrightarrow x=3[/tex]
∠A and ∠B are complementary. The measure of ∠A is 21°.
What is the measure of ∠B?
Enter your answer in the box.
point theif = ban
Answer:
69°Step-by-step explanation:
Complementary angles sum to 90°.
We have the measure of one angle, find the missing one as below.
m∠A + m∠B = 90°21° + m∠B = 90°m∠B = 90° - 21°m∠B = 69°Complementary angles have sum 90°
[tex]\\ \sf\longmapsto x+21=90[/tex]
[tex]\\ \sf\longmapsto x=90-21[/tex]
[tex]\\ \sf\longmapsto x=69[/tex]
F(x)=2x^2-5x g(x)=-3x^2 find f(2)
Write an exponential function in the form y=ab^x that goes through points (0,10) and (9, 5120).
The form [tex]y=ab^x[/tex] has two unknowns, namely [tex]a[/tex] and [tex]b[/tex], so you would need to have two points to find the equation (which you do). Once you have your two points, you can create a system of equations by plugging in the x and y coordinates like below:
[tex]\left \{ {{10=ab^0} \atop {5120=ab^9}} \right.[/tex]
One thing you may remember is that ANY number to the power of 0 equals 1. Knowing that, we can replace [tex]b^0[/tex] in the first equation with 1. Since 1 multiplied by any number is just that same number, that leaves [tex]a[/tex] alone in the first equation.
[tex]\left \{ {{10=a} \atop {5120=ab^9}} \right.[/tex]
The first equation now tells us that [tex]a[/tex] is 10, so we can plug 10 in for [tex]a[/tex] in the other equation.
[tex]5120=10b^9[/tex]
Now we can divide both sides by 10 to isolate [tex]b^9[/tex].
[tex]512=b^9[/tex]
To get [tex]b[/tex] alone, we have to take the 9th root of both sides.
[tex]\sqrt[9]{512} =\sqrt[9]{b^9}[/tex]
That gives us:
[tex]2=b[/tex]
We can now plug [tex]a[/tex] and [tex]b[/tex] into the form they gave us to get:
[tex]y=10*2^x[/tex]
A triangle has two sides of lengths 4 and 15. What value could the length of
the third side be? Check all that apply.
What is cos 10° cos 8° − sin 10° sin 8° equal to?
Answer:
Step-by-step explanation:
cos 10° cos 8° − sin 10° sin 8° = cos(10° + 8°) = cos(18°)
Square A is a dilation of Square B. What is the scale factor?
the talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $4 each. If the total receipts were $1740, how many of each type of ticket were sold?
Answer:
Students = 380
Adults = 150
Step-by-step explanation:
3x + 4y = 1740
and a total tickets equation of: x + y = 530
3 x
Abigail keeps track of the number of pages she reads. Last year, she read 5,473 pages. The year before,
she read 2,379 pages. Select all of the choices that are good estimates by rounding to place values for the
total pages Abigail read over the two years.
A. 7,000
B. 7,500
C. 7.850
D. 7.900
E. 8,000
Answer:
A, C, and E I think
Step-by-step explanation: