Answer:
[tex]a=4[/tex]
Step-by-step explanation:
So we have the equation:
[tex]a+2a-1=11[/tex]
First, combine like terms:"
[tex]3a-1=11[/tex]
Now, add 1 to both sides:
[tex]3a=12[/tex]
Divide both sides by 3:
[tex]a=4[/tex]
And we're done!
How do you do this question?
Answer:
y' = -4eˣ sin⁵(eˣ)
Step-by-step explanation:
Part 1 of the Fundamental Theorem of Calculus simply says that the definite integral of a function is equal to the antiderivative evaluated between the limits.
∫ₐᵇ f(x) dx = F(b) − F(a), where F(x) = ∫ f(x) dx.
y = ∫ₑₓ⁰ 4 sin⁵(t) dt
To integrate, use Pythagorean identity.
y = 4 ∫ₑₓ⁰ (1 − cos²(t))² sin(t) dt
Ignoring the limits for the moment, let's say u = cos(t) and du = -sin(t) dt.
y = 4 ∫ (1 − u²)² (-du)
y = -4 ∫ (1 − 2u² + u⁴) du
y = -4 (u − ⅔u³ + ⅕u⁵) + C
y = -4 (cos(t) − ⅔ cos³(t) + ⅕ cos⁵(t)) + C
Evaluate between t = eˣ and t = 0.
y = -4 (cos(0) − ⅔ cos³(0) + ⅕ cos⁵(0)) + C − [-4 (cos(eˣ) − ⅔ cos³(eˣ) + ⅕ cos⁵(eˣ)) + C]
y = -4 (1 − ⅔ + ⅕) + 4 (cos(eˣ) − ⅔ cos³(eˣ) + ⅕ cos⁵(eˣ))
Now take derivative with respect to x.
y' = 0 + 4 (-sin(eˣ) eˣ − 2 cos²(eˣ) (-sin(eˣ) eˣ) + cos⁴(eˣ) (-sin(eˣ) eˣ))
y' = -4eˣ sin(eˣ) (1 − 2 cos²(eˣ) + cos⁴(eˣ))
y' = -4eˣ sin(eˣ) (1 − cos²(eˣ))²
y' = -4eˣ sin⁵(eˣ)
This can be more easily calculated using the Second Fundamental Theorem of Calculus.
Solve each calculation. Be sure to report your answer with the correct number of decimal places. 7.365 ms 0.250 ms + 10.3 ms ms 125.010 cL 4.1023 cL – 0.30 cL cL
Answer:
1.17.9
2. 120.61
Step-by-step explanation:
Answer:
17.9
120.61
Step-by-step explanation:
13w-8w =20 ??????????
Answer:
w = 4
Step-by-step explanation:
13w-8w =20
Combine like terms
5w = 20
Divide each side by 5
5w/5 = 20/5
w = 4
Answer:
w=4
Step-by-step explanation:
13w-8w=20
5w=20
w=4
Given the set A=(2,5) and B=(5,7,9) find the following: AnB
a
5
b
2.9
n
2,5,7,9
7,9
d
Greetings from Brasil....
The intersection of two sets is given by the elements that are common - present in both - to the sets.
A = {2; 5}
B = {5; 7; 9}
Element in both sets = 5.... So
A ∩ B = {5}Solve the equation 12x+6y= 24 for x.
Answer: x = -1/2y + 2
Step-by-step explanation:
12x + 6y = 24 To solve for x first start by subtracting 6y from both sides
- 6y -6y
12x = 24 - 6y Now divide each side by 12
x= 2 - 1/2y
Given the formula below, solve for x. y - y1 = m(x-x1)
Answer:
y-3 = 2/9 (x-8)
Step-by-step explanation:
Twice the sum of six "x" and seventy eight.
Answer:
2(6x+78)
Unless it's the exact number. You hadn't specified what x is.
The College of Business at Tech is planning to begin an online MBA program. The initial start-up cost for computing equipment, facilities, course development, and staff recruitment and development is $350,000.The college plans to charge tuition of $18,000 per student per year. However, the university administration will charge the college $12,000 per student for the first 100 students enrolled each year for administrative costs and its share of the tuition payments.
a. How many students does the college need to enroll in the first year to break even?
b. If the college can enroll 75 students the first year, how much profit will it make?
c. The college believes it can increase tuition to $24,000, but doing so would reduce enrollment to 35. Should the college consider doing this?
Answer:
a).To break even
They need to enroll 87 student
B) Profit=$100000
C) yeah they can think of that.
Profit= $70000
Step-by-step explanation:
Initial start up cost = $350000
Cost from adminstrative bodies
= 12000 for first 100 student
= $1200000
Total cost =$1200000+$350
Totral cost =$ 1550000
Tuition cost
= $18000 per student
To break even
The college needs to enroll
1550000/18000= 86.1
They need to enroll 87 student
B) if they enroll 75 students
Adminstrative cost = 12000*75
Adminstrative cost= 900000
Total cost= 350000+900000
Total cost =$ 1250000
Tuition fee= $18000*75
Tuition fee=$ 1350000
Their profit= 1350000-1250000
Profit=$100000
C).if tuition is $24000 and enrollment number= 35
Adminstrative cost = 35*12000
Adminstrative cost = $420000
Total cost= $770000
Tuition fee= $24000*35
Tuition fee= $840000
Profit= $840000-$770000
Profit= $70000
What is the molar mass of UF6??
Answer:
I think it's 352. 02 g/mol
Step-by-step explanation:
googled it :)
Answer:
352.02 g/mol
In chemistry, the molar mass of a chemical compound is defined as the mass of a sample of that compound divided by the amount of substance in that sample, measured in moles.
Answer please quick
Answer:
1 metric ton is = to 1000 kilograms
Joe will rent a car for the weekend. He can choose one of two plans. The first plan has no initial fee but costs $0.80 per mile driven. The second plan has an initial fee of $75 and costs an additional $0.60 per mile driven. How many miles would Joe need to drive for the two plans to cost the same?
Answer:
375 miles
Step-by-step explanation:
m=miles
I set it up as an equation. $75+.60m=.80m
And solved from there
Answer:
375 miles :D
Step-by-step explanation:
Dimensional analysis: How many atoms are in a kilogram of silver, if there are 6.02 x 10^23 atoms per mole and silver weighs 107.9 grams/mole?
Answer:
5.58×10²⁴ atoms.
Step-by-step explanation:
From the question given above, the following data were obtained:
1 mole of silver = 107.9 g
Number of atoms in 1 mole of silver = 6.02×10²³ atoms.
Number of atoms in a kilogram of silver =.?
Next, we shall convert 1 kg of silver to grams (g). This can be obtained as follow:
1 kg = 1000g
Therefore, 1 kg of silver is equivalent to 1000g.
Finally, we shall determine the number of atoms in 1 kg (i.e 1000 g) of silver as follow:
107.9 g of silver contains 6.02×10²³ atoms.
Therefore, 1000 g of silver will contain = (1000 × 6.02×10²³) / 107.9 = 5.58×10²⁴ atoms.
Thus, a kilogram of silver contains 5.58×10²⁴ atoms.
Is the expression (5 • 2) x equal to the expression 10 x
Answer:
Yes
Step-by-step explanation:
(5*2)x = 10x
5*2 = 10 so
10x = 10x
They are equal.
Answer:
Yes
Step-by-step explanation:
5 x 2 is 10, and so 5(2)x is 10x
Find a formula for the inverse of the function. f(x) = e^6x − 9
Answer:
[tex]f^{-1}(x)=\frac{1}{6}\ln(x+9)[/tex]
Step-by-step explanation:
So we have the function:
[tex]f(x)=e^{6x}-9[/tex]
To solve for the inverse of a function, change f(x) and x, change the f(x) to f⁻¹(x), and solve for it. Therefore:
[tex]x=e^{6f^{-1}(x)}-9[/tex]
Add 9 to both sides:
[tex]x+9=e^{6f^{-1}(x)}[/tex]
Take the natural log of both sides:
[tex]\ln(x+9)=\ln(e^{6f^{-1}(x)})[/tex]
The right side cancels:
[tex]\ln(x+9)=6f^{-1}(x)[/tex]
Divide both sides by 6:
[tex]f^{-1}(x)=\frac{1}{6}\ln(x+9)[/tex]
And we're done!
The area of a rectangle is at least 10 more than 3 times the width of the rectangle. If the area of the rectangle is at least 250 square units, what are the possible values for the width (w) of the rectangle?
What is wrong with this problem. 2(n +3) = 2n +3
Steps to solve:
2(n + 3) = 2n + 3
~Distribute left side
2n + 6 = 2n + 3
~Subtract 6 to both sides
2n = 2n - 3
~Subtract 2n to both sides
n = -3
Best of Luck!
Estimate 8.25% sales tax on a $39.89 purchase
Turn the percentage into a decimal.
8.25% / 100 = 0.0825
Multiply.
39.89 * 0.0825 ≈ $3.29
Subtract.
39.89 + 3.29 = $43.18
Best of Luck!
WILL GIVE BRAINLY FOR ANSWER!! Please help with this question!!! Given the piecewise function: f(x) = 1/2x + 5, x > 2 6, x = 2 x + 4, x < 2 a. Write f' (f prime) as a piecewise function b. Determine if f is differentiable at x = 2. Give a reason for your answer. Photo is attatched.
Answer:
A)
[tex]f'(x) = \left\{ \begin{array}{lIl} \frac{1}{2} & \quad x >2 \\ 0& \quad x =2\\1&\quad x<2 \end{array} \right.[/tex]
B) Continuous but not differentiable.
Step-by-step explanation:
So we have the piecewise function:
[tex]f(x) = \left\{ \begin{array}{lIl} \frac{1}{2}x+5 & \quad x >2 \\ 6& \quad x =2\\x +4&\quad x<2 \end{array} \right.[/tex]
A)
To write the differentiated piecewise function, let's differentiate each equation separately. Thus:
1)
[tex]\frac{d}{dx}[\frac{1}{2}x+5}][/tex]
Expand:
[tex]\frac{d}{dx}[\frac{1}{2}x]+\frac{d}{dx}[5][/tex]
The derivative of a linear equation is just the slope. The derivative of a constant is 0. Thus:
[tex]\frac{d}{dx}[\frac{1}{2}x+5}]=\frac{1}{2}[/tex]
2)
[tex]\frac{d}{dx}[6][/tex]
Again, the derivative of a constant is 0. Thus:
[tex]\frac{d}{dx}[6]=0[/tex]
3)
We have:
[tex]\frac{d}{dx}[x+4][/tex]
Expand:
[tex]\frac{d}{dx}[x]+\frac{d}{dx}[4][/tex]
Simplify:
[tex]=1[/tex]
Now, let's substitute our original equations for the differentiated equations. The inequalities will stay the same. Therefore:
[tex]f'(x) = \left\{ \begin{array}{lIl} \frac{1}{2} & \quad x >2 \\ 0& \quad x =2\\1&\quad x<2 \end{array} \right.[/tex]
B)
For a function to be differentiable at a point, the function must be a) continuous at that point, and b) the left and right hand derivatives must be equivalent.
Let's first determine if the function is continuous at the point. Remember that a function is continuous at a point if and only if:
[tex]\lim_{x \to n^-} f(n)= \lim_{x \to n^+}f(n)=f(n)[/tex]
Let's find the left hand limit of f(x) at it approaches 2.
[tex]\lim_{x \to 2^-}f(x)[/tex]
Since it's coming from the left, let's use the third equation:
[tex]\lim_{x \to 2^-}f(x)\\=\lim_{x \to 2^-}(x+4)[/tex]
Direct substitution:
[tex]=(2+4)=6[/tex]
So:
[tex]\lim_{x \to 2^-}f(x)=6[/tex]
Now, let's find the right-hand limit:
[tex]\lim_{x \to 2^+}f(x)[/tex]
Since we're coming from the right, let's use the first equation:
[tex]\lim_{x \to 2^+}(\frac{1}{2}x+5)[/tex]
Direct substitution:
[tex](\frac{1}{2}(2)+5)[/tex]
Multiply and add:
[tex]=6[/tex]
So, both the left and right hand limits are equivalent. Now, find the limit at x=2.
From the piecewise function, we can see that the value of f(2) is 6.
Therefore, the function is continuous at x=2.
Now, let's determine differentiability at x=2.
For a function to be differentiable at a point, both the right hand and left hand derivatives must be equivalent.
So, let's find the derivative of the function as x approahces 2 from the left and from the right.
From the differentiated piecewise function, we can see that as x approaches 2 from the left, the derivative is 1.
As x approaches 2 from the right, the derivative is 1/2.
Therefore, the right and left hand derivatives are not the same.
Thus, the function is continuous but not differentiable.
Solve for u.
9u+16=7(u+2)
Simplify your answer as much as possible.
U=
Answer:
u=-1
Step-by-step explanation:
Answer:
Isolate the variable by dividing each side by factors that don't contain the variable.
u= -1
Acellus
x = [?]°
1040
1170
X
124°
1000
Hint: Sum = (n-2)180
Answer:
x = 95°
Step-by-step explanation:
The sum of the interior angles of any polygon is
sum = 180° (n - 2)
Here n = 5, thus
sum = 180° × 3 = 540°
Sum the given angles in the polygon and equate to 540
104° + 117° + 100° + 124° + x = 540°, that is
445° + x = 540° ( subtract 445° from both sides )
x = 95°
3n-5=-8(6+5n) in distributive property
Answer:
n=-1
Step-by-step explanation:
3n-5=-8(6+5n)
3n-5=-48-40n
add 40n to both sides
43n-5=-48
n=-1
Step-by-step explanation:
Solve the linear equation. 3x = 24 x = ?
Answer:
3x =24
x = 24 -3
x = 21 (ans)
Answer:
X=8
Step-by-step explanation:
3x=24
divide each side by 3 to isolate x
x=8
What is the quotient of 29,596÷28?
Answer:
√ 96
log
( 7 )
6 ! /3 !
Step-by-step explanation:
What is the value of x?
3
6
10
12
Answer:
value of x is 6.
please follow me.
Your answer would be B- 6. Hope this helps you!!
How I do this?
3x+4y=11
X-2y=-3
Answer:
[tex]\huge\boxed{x=1,\ y=2\to(1,\ 2)}[/tex]
Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}3x+4y=11\\x-2y=-3&\text{multiply both sides by (-3)}\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}3x+4y=11\\-3x+6y=9\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\ \ \ \ 10y=20\qquad\text{divide both sides by 10}\\.\qquad\qquad\boxed{y=2}\\\\\text{subtitute it to the second equation:}\\x-2(2)=-3\\x-4=-3\qquad\text{add 4 to both sides}\\\boxed{x=1}[/tex]
Use the equation solver to find the value of x that makes the mathematical statement true. -0.5 0.5 0.87 1.5
Answer:-0.5
Step-by-step explanation:
ben has bundled cable television and internet service. he pays $89.92 each month for the service. how much will he pay per year for cable and internet
Answer:
$1,079.04
Step-by-step explanation:
multiply: 89.92x12=1078.04
Is 815 divisible by 10?
No.
Here is why:
If you mean equally divided then no because of the little 5 in the ones's place. If that 5 was a 0, it would definitely be divided equally.
Hope this makes sense!
Answer:
no
Step-by-step explanation:
1 mile to yards, as a fraction..
Answer:
[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
Since 3 feet is a yard, one foot is 1/3.
So that is the answer.
Answer:
1/3
1 mile to yards as a fraction would probably be 1/3. I'm not so sure...
Find the slope (-4,8) and (-3,-6)
Answer:
-14
Step-by-step explanation:
[tex] \boxed{gradient = \frac{y1 - y2}{x1 - x2} } [/tex]
Using the above formula, slope
[tex] = \frac{8 - ( - 6)}{ - 4 - ( -3 )} \\ = \frac{8 + 6}{ - 4 + 3} \\ = \frac{14}{ - 1} \\ = - 14[/tex]