Answer:
[tex]y=2-2\cos(x)[/tex]
Step-by-step explanation:
We have the differential:
[tex]y^\prime=2\sin(x)[/tex]
With the general solution:
[tex]y=C-2\cos(x)[/tex]
And we want to find the particular solution such that it satisfies the initial condition:
[tex]\displaystyle y\Big(\frac{\pi}{3}\Big)=1[/tex]
So, we have:
[tex]y=C-2\cos(x)[/tex]
Substituting π/3 for x and 1 for y yields:
[tex]\displaystyle 1=C-2\cos\Big( \frac{\pi}{3} \Big)[/tex]
Solve for C. Evaluate:
[tex]\displaystyle 1=C-2(\frac{1}{2})[/tex]
Simplify:
[tex]1=C-1[/tex]
Hence:
[tex]C=2[/tex]
Therefore, our particular solution will be:
[tex]y=2-2\cos(x)[/tex]
Hence, our answer is C
10 points
3. What is the slope of the line that passes through the points (2,6) and
(-2,5) ?
O A. undefined
O B. Zero
Oc. 114
OD. -1/4
Answer:
I think u kept option incorrect but the correct answer is 1/4
A coffee shop s ends $408 for an order of 17 cases of paper cups.
If the coffee shop adds 5 more cases of paper cups to the order, how
much will the total cost be?
A. $120
B. $493
O
C. $528
D. $2,040
What is the value of expression below?
Answer:
B)1.1
Step-by-step explanation:
I'm 100% sure
Answer:
ans b.1.1
Step-by-step explanation:
hey just follow an thank me thats it
Use the table to answer the question. X y -21-1 -1 -1 1 0 3 1 5 2 7 Which equation represents the relationship between x and y shown in the table? 1 O A. y = fx- -1 O B. y = x+3 Oc. C. y=2x-1 D. y = 2x + 3
Answer:
D. y = 2x + 3
Step-by-step explanation:
Use the table to answer the question.
x:-2 -1 0 1 2
y: -1 1 3 5 7
Which equation represents the relationship between x and y shown in the table.
Solution:
The table shows a linear relationship between x and y.
A linear equation is in the form y = mx + b, where y is a dependent variable, x is an independent variable, m is the rate of change (slope) and b is the value of y when x = 0.
The table (x, y) has the points (-2, -1) and (0, 3). The equation is given by:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-(-1)= \frac{3-(-1)}{0-(-2)} (x-(-2))\\\\y+1=2(x+2)\\\\y+1=2x+4\\\\y=2x+3[/tex]
The cost of 2.5 pounds of cheese is $5.60. Mrs. Peterson bought 9 pounds of cheese for her deli. How much money did Mrs. Peterson spend?
x/3a*x/4a
_______
x/8a
In a school with 300 students 18% of the students take violin lessons and 6% of the students take clarinet lessons.
A: find the number of students who take each type lesson.
B: How many more students take violin than take clarinet lessons?
In the figure below, find the angle measures
Six less than the product of 8 and a number is 7?
Step-by-step explanation:
Let x represent the number.
We have 8x - 6 = 7.
Therefore 8x = 13 and x = 1.625.
5
2
start fraction, 2, divided by, 5, end fraction of a number is what percentage of that number?
Answer:
Step-by-step explanation:
2/5=40/100 40 out of 100 is 40%
Necesito que me ayuden en todas si cada uno de ustedes me puede decir una por favorrrrrr
Step-by-step explanation:
the perimeter of rectangle is 24 cm and the sides are in the ratio find the length of the sides
Can someone pleaseeee help if you’re correct I’ll give u brainlist
Answer:
C
Step-by-step explanation:
Plz help its urgent
Answer:
what I think this question has mistake
Dion ordered a pizza from Domino’s. Domino’s charges 50 cents per topping.
What’s is the rate of change?
What’s the equation of the line?
Answer:
the answer is 50
Step-by-step explanation:
the answer is 50 because lets say the the amount for a plain pizza is $12 that will be your inital value. 50 is your rate of change cause they price is add onto by 50 cents per topping.
What are the answers here?
Answer:
The slope is 3
The y-intercept is -2
The linear equation is y = 3x - 2
Step-by-step explanation:
The form of the linear equation is y = m x + b, where
m is the slope of the lineb is the y-interceptThe rule of the slope of a line that passes through points (x1, y1) and (x2, y2) is m = [tex]\frac{y2-y1}{x2-x1}[/tex]∵ A line passes through points (2, 4) and (6, 16)
∴ x1 = 2 and y1 = 4
∴ x2 = 6 and y2 = 16
→ Substitute them in the rule of the slope above to find it
∵ m = [tex]\frac{16-4}{6-2}[/tex] = [tex]\frac{12}{4}[/tex] = 3
∴ m = 3
→ Substitute it in the form of the equation above
∴ y = 3x + b
→ To find b substitute x and y in the equation by the coordinates of
a point on the line
∵ Point (2, 4) is on the line
∴ x = 2 and y = 4
∵ 4 = 3(2) + b
∴ 4 = 6 + b
→ Subtract 6 from both sides to find b
∵ 4 - 6 = 6 - 6 + b
∴ -2 = b
→ Substitute its value on the equation above
∵ y = 3x + (-2)
∴ y = 3x - 2
→ Let us answer the questions
The slope is 3
The y-intercept is -2
The linear equation is y = 3x - 2
can someone help with me this pls
Answer:
a) The class interval containing the median is the interval 2 ≤ h < 3
b) The mean number of hours the children spent on their tablets is 2.2 hours.
Step-by-step explanation:
a) The given parameters are;
The number of students that spent 0 ≤ h < 1 hour = 4
The number of students that spent 1 ≤ h < 2 hours = 8
The number of students that spent 2 ≤ h < 3 hours = 11
The number of students that spent 3 ≤ h < 4 hours = 7
The median is given by the location of the 15th child which is located in the interval given as follows;
We note that the total number of children is obtained by adding the frequencies of the intervals together, as follows;
The number of children = 4 + 8 + 11 + 7 = 30
The frequency of the first interval = 4
The sum of the first + Second intervals = 4 + 8 = 12
The sum of the first + Second + Third intervals = 4 + 8 + 11 = 23
Therefore, the class interval containing the median is the interval 2 ≤ h < 3
b) We use the midpoint of each class interval to find the mean as follows;
The mean = ∑fh/∑h
∴ The mean = (4 × 0.5 + 8 × 1.5 + 11 × 2.5 + 7 × 3.5)/(4 + 8 + 11 + 7) = 2.2
The mean number of hours the children spent on their tablets = 2.2 hours.
Mia spends 45 minutes reading each day. She does 2/5 of her reading at school. How many minutes does Mia spend reading at school?
Answer:
18 minutes
Step-by-step explanation:
1. 45 minutes is the TOTAL amount she reads so it can be expressed as x/45
*x=a part
2. set up a proportion
x/45 = 2/5
3. now solve by either cross multiplication or finding a scale factor. I am finding a scale factor because that is easiest.
45/5=9
so 5 * 9 = 45
so 2 * 9 = 18
the asnwer is 18. I hope this helps
Reason Abstractly The inequalities 3x < 1 and 6x < 2 are equivalent inequalities. Writ e another inequality that
is equivalent to 3x < 1 and
6r<2.
Answer:
12x < 4
Step-by-step explanation:
6x < 2 is twice 3x < 1
so 12x < 4 is twice 6x < 2
which line graph of the liner equation x-2y=6
Answer:
x-coordinate
Step-by-step explanation:
Answer:
the answer is x coordinate
I will mark Brainliest please help
Answer:
f(x) = 2
Step-by-step explanation:
f(x) represents a linear function since it had the same first differences while the "x" values are evenly space out (which we know could happen only if the function is linear). Now that we determined that the function is linear we have to write the function as an expression.
We know that any linear function has a form of f(x) = mx + b, where "m" is the slope and "b" is the y intercept (y value when x is equal to 0).
As I already mentioned the b will be equal tp the "y" intersect which is equal to the "y" value when x is equal to zero. Luckily in our table they did tell us what will be the "y" value when x is equal to zero, and it is 2. So now we know b = 2.
Then we have have to find the slope which can be found by using the following formula.....
[tex]m = \frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
Now we have to choose two different points from table and let the one that has bigger x value be represented as [tex](x_{2} , y_{2} )[/tex] and the other one will be represented as [tex](x_{1}, y_{1} )[/tex]. In our case I choose the points (2,2) and (1,2). Now if we represent them as what I mentioned earlier we can substitute their values into the equation that we ca use to find the slope. You should obtain the following.....
[tex]m = \frac{y_{2} - y_{1} }{x_{2} - x_{1} } = \frac{2 -2}{2-1} = \frac{0}{1} = 0[/tex]
Now that we know both the "m" and "b" values we can substitute them into the equation, and we will get he following....
f(x) = mx + b
f(x) = 0x + 2
f(x) = 2
Find the exact value of sec 330° in simplest form with a rational denominator.
Answer:
2√3/3
Step-by-step explanation:
Sec(330°)
=1/cos(330°)
=1/√3/2 (since Cos (330°)=√3/2
=1×2/√3
=2/√3×√3/√3
=2√3/3
Answer:
[tex]\implies \sec 330^o = \dfrac{2}{\sqrt3}=\dfrac{2\sqrt{3}}{3}[/tex]
Step-by-step explanation:
Given :-
[tex]\sec 330^o [/tex]And we need to find out its value . Firstly we know that 330° lies in 4th quadrant . And In fourth quadrant , cosine and secant are positive . Therefore , the result will be positive. Now we know that ,
[tex]\implies \sec (360^o-\theta)= \sec\theta [/tex]
Using this ,
[tex]\implies \sec (330^o) \\\\\rm\implies sec(360^o-30^o) \\\\\rm\implies \sec 30^o [/tex]
And the value of sec 30° is ,
[tex]\implies \sec 30^o = \dfrac{2}{\sqrt3}[/tex]
And by question we need to write it with a rational denominator .So on rationalising the denominator , we have ,
[tex]\implies \sec 30^o = \dfrac{2}{\sqrt3}=\boxed{\red{\dfrac{2\sqrt3}{3}}}[/tex]
Hence the required answer is 2√3/3.
i need questions 1-8 pla
Answer:.
Step-by-step explanation:.
PLS HELP LOL, t is the value of the expression −100÷25? Enter your answer as an integer in the box.
Answer:
4
Step-by-step explanation:
100 divided by 25=4
Answer:
-4 as the answer but as an integer maybe 0-4?
Step-by-step explanation:
When will The Ghost of Christmas present cease to exist?
Answer:
never ever not in a million years
Step-by-step explanation:
Find the greatest number which
divides 304 to leave a remainder
of 4 and which also divides 298
to leave a remainder of 4.
Answer:
304-4=300
300/30=10
298-4=294
294/3=98
Can someone help me out with this problem How tall is a stack of cube shaped blocks whose volumes are 375 cube inches, 648 cube inches, and 1029 cube inches?
Answer:
The stack of blocks is 25.96 inches tall
Step-by-step explanation:
The Volume of a Cube
Given a cube-shaped figure of side length L, the volume is calculated by:
[tex]V=L^3[/tex]
If the volume is known, then the side length can be found by solving for L:
[tex]L=\sqrt[3]{L}[/tex]
We are given three cube-shaped blocks with known volumes. We'll find the individual side lengths and add them up to find the height that results when they stack up vertically.
Block 1, volume 375 cube inches:
[tex]L_1=\sqrt[3]{375}=7.21\ inch[/tex]
Block 2, volume 648 cube inches:
[tex]L_2=\sqrt[3]{648}=8.65\ inch[/tex]
Block 3, volume 1029 cube inches:
[tex]L_3=\sqrt[3]{1029}=10.10\ inch[/tex]
Total height=7.21 inch+8.65 inch+10.10 inch=25.96 inch
The stack of blocks is 25.96 inches tall
a car that was originally worth 29500$ it depreciates at a rate of 2500$ per year find the value of the car after six years
Answer:
14,500
Step-by-step explanation: Just took the test.
One side of a right triangle is 8 cm shorter than the hypotenuse and 7 cm shorter than the third side. Find the lengths of the sides of the triangle.
Answer:
5 cm
Step-by-step explanation:
Let the shorter side be a, longer side be b, hypotenuse be c
By Pythagorean theorem:
a² + b² = c²
a² + (a + 7)² = (a + 8)²
a² + a² + 14a + 49 = a² + 16a + 64
a² - 2a - 15 = 0
a² + 3a - 5a - 15 = 0
a(a + 3) - 5(a + 3) = 0
(a + 3)(a - 5) = 0
a = -3 or a = 5
Because a is a side length and is a positive number
a = 5
trina wrote forty- five and sixty five thousandths as 45.65. is her answer correct or error if so what is the error explain
Answer: 45.65 is incorrect.
Step-by-step explanation: it’s a place value problem; right of the decimal is ones, tens, hundredths, thousandths which is 4 place values so 45.065 shows the correct placement
9n+1
2n+25.5
add the result of both equations together