Answer:
The answer is "[tex]{c=-6+3\sqrt{14}[/tex]"
Step-by-step explanation:
Given:
[tex]\to F(x) = \frac{x}{x+6} , \ [1, 12][/tex]
[tex]\to f'(c)=\frac{f(b)-f(a)}{b-a}[/tex]
As per the given intervals:
[tex][1,12]\\\\ a=1 \\ b=12.[/tex]
Calculating the values of f(a) and f(b).
[tex]\to f(1)=\frac{1}{1+6}= \frac{1}{7} \\\\ \to f(2)=\frac{12}{12+6}= \frac{12}{18}=\frac{2}{3} \\\\ \to f(x)=\frac{x}{x+6}\\\\[/tex]
[tex]\to f\:'\left(x\right)=\frac{d}{dx}\left(\frac{x}{x+6}\right)\: \\\\[/tex]
[tex]=\frac{\frac{d}{dx}\left(x\right)\left(x+6\right)-\frac{d}{dx}\left(x+6\right)x}{\left(x+6\right)^2} \\\\=\frac{1\cdot \left(x+6\right)-1\cdot \:x}{\left(x+6\right)^2}\\\\[/tex]
[tex]\to f'(x)=\frac{6}{\left(x+6\right)^2}[/tex]
Calculating the value of [tex]\ f'(c):[/tex]
[tex]\to \mathbf{f\:'\left(c\right)=\frac{6}{\left(c+6\right)^2}}[/tex]
Replacement of the values in the mean theorem of value now.
[tex]\to \frac{6}{\left(c+6\right)^2}=\frac{\frac{2}{3}-\frac{1}{7}}{12-1}\\\\\to \frac{6}{\left(c+6\right)^2}=\frac{\frac{11}{21}}{11}\\\\\to \frac{6}{\left(c+6\right)^2}=\frac{1}{21}\\\\[/tex]
Apply the cross multiplication:
[tex]\to (c+6)^2=126 \\\\\to c^2+12c +36= 126\\\\\to c^2+12c +36-126= 126-126 \\\\\to c^2+12c -90= 0\\\\\to c=\frac{-12\pm \sqrt{12^2-4\cdot \:1\left(-90\right)}}{2\cdot \:1}\\\\ \to \mathbf{c=-6+3\sqrt{14}} \\\\[/tex]
Plzzz help 5 min leftttt
Answer:
Time for learning?
Answer is A i think
Solve the equation 3x2 + 11z – 4= 0.
Help I need to plug these in and find the two answers for x
Step-by-step explanation:
Explanation:
Given:
−3x2+12x+1=0
This is in the form:
ax2+bx+c=0
with a=−3, b=12 and c=1
In order to decide which method to use, we can first examine the discriminant:
Δ=b2−4ac=122−4(−3)(1)=144+12=156
Since Δ>0 we can tell that the quadratic has 2 distinct real solutions, but because it is not a perfect square we can also tell that those solutions are irrational.
So there is no rational factorisation and we can discount the use of an AC method or similar.
We can use the quadratic formula or we can complete the square.
If we choose to use the quadratic formula, then we find:
x=−b±√b2−4ac2a
x=−b±√Δ2a
x=−(12)±√1562(−3)
x=−12±2√39−6
x=2±√393
When completing the square, note that b=12 is already divisible by a=−3 and by
4
10
-6
-544
32"
2 3 4 5 6
8
9 10
O y = -0.2(x + 3)2 – 4
Oy= -0.2(x – 3)2 - 4
Submit Answer
O y = 0.2(x + 3)2 - 4
O y = 0.2(x - 3)2 – 4
Answer:
10 -6 -544 32" 2 3 4 5 6 8 9 10 O y = -0.2(x + 3)2 – 4 Oy= -0.2(x – 3)2 - 4
Which value is a solution of the inequality 9 >_ 1/2x
The > has the line under it
Please solve I put it 50 points
Answer:
x [tex]\leq[/tex] 18.
Step-by-step explanation:
Since we have the following inequality, 9 [tex]\geq[/tex] 0.5x, we can multiply both sides of the inequality by 2. Doing this, gets up x [tex]\leq[/tex] 18.
Hope this helped!
Help me please and please explain why this is incorrect or correct
Answer:
Im sorry but there is no question..!
Step-by-step explanation:
Step-by-step explanation:
where is question. ..........
what we have to explain correct or incorrect
Find the area of the compound shape below.pls help
Answer:
22cm²
Step-by-step explanation:
For the area of triangle,
base = 2 + 2 + 2 = 6cm
height = 4cm
Area = 1/2 x base x height
= 1/2 x 6 x 4
= 12cm²
For area of the rectangle,
length = 5cm
breadth = 2cm
Area = length x breadth
= 5 x 2
= 10cm²
Area of compound shape = 12 + 10 = 22 cm²
For rectangle ABCD, find m∠ADB.
Answer:
we know all angles are 90° in the rectangle
therefore, angle d = bdc+bda = 90
=> 31+bda = 90
=>angle bda= 59
The measurement of the angle ADB should be considered as the 59 degrees.
Calculation of the measurement of the angle ADB:Since we know that all angles in the rectangle should be of 90 degrees
So,
Here angle d = bdc + bda
= 90
Now
31 + bda = 90
So, bda = 90 - 31
= 59
hence, The measurement of the angle ADB should be considered as the 59 degrees.
Learn more about rectangle here: https://brainly.com/question/1916433
In a two-digit number, the tens' digit is 1 less than the units' digit. If the digits are
interchanged, the sum of the number obtained and the original number is 143. Find
the number.
Answer:
67
Step-by-step explanation:
Number: AB
A = B-1
BA + AB = 143
10*B + A + 10*A + B = 143
11A + 11B = 143
A + B = 13
(B-1) + B = 13
2B = 14
B = 7
A = 6
The number is 67
check: 6 = 7-1 and 67 + 76 = 143
A. [-2,3]
B. [-4,5]
C. [1,3]
D. [-5,0]
PLEASE ANSWER ASAP !!!
Given a line with slope of 5 and y-intercept of -1, which of the ordered pairs given below would NOT be on the line?
(4, 18)
(0, -1)
(2, 9)
(3, 14)
Answer:
(4,18)
Step-by-step explanation:
Evaluate 1/2(4^3-6*3^2)
What is the solution to the inequality -3x - 42 > 3?
O A. X > -13
O B. X<-13
o c. X > -15
O D. x < -15
Answer:
the solution is D, x<-15.
Answer:
D.x<-15
Step-by-step explanation:
-3x-42>3
-3x>3+42
-3x>45
x<-45/3
x<-15
Which of the fractions are in ascending order below (from smallest to largest) *
(a) 3/4, 1/4, 1/2
(b) 1/2, 1/4, 3/4
(c) 1/2, 3/4, 1/4,
(d) 1/4, 1/2, 3/4
Answer:
B
Step-by-step explanation:
because i know and you have to trust me
Patrick can make 185 tacos in 2 hours. How many tacos can he make in one hour?
Answer:
92.5
Step-by-step explanation:
HELP!! Please scale a rectangular prism that is 300 inches, by 50 inches, by 30 inches to have a volume in the 60-70 cubic inch range.
Answer:
Scale factor 1/19, volume 65.6 in³Step-by-step explanation:
Volume of the prism:
V = abh V = 300*50*30 = 450000 in³Scaled volume is 60 - 70 in³
Find the scale factor k;
450000/60 = 7500450000/70 = 64281/6428 < 1/k³ < 1/75001/∛6428 < 1/∛k³ < 1/∛75001/18.59 < 1/k < 1/19.571/k = 19 is bestSo the scale factor is
k = 1/19and the volume of the smaller prism is:
450000 / 19³ = 65.6 in³
Answer:
Scale factor 1/19, volume 65.6 in³
Step-by-step explanation:
Volume of the prism:
V = abh
V = 300*50*30 = 450000 in³
Scaled volume is 60 - 70 in³
Find the scale factor k;
450000/60 = 7500
450000/70 = 6428
1/6428 < 1/k³ < 1/7500
1/∛6428 < 1/∛k³ < 1/∛7500
1/18.59 < 1/k < 1/19.57
1/k = 19 is best
So the scale factor is
k = 1/19
and the volume of the smaller prism is:
450000 / 19³ = 65.6 in³
What is the distance between points (-3, -1) and (2, 3)?
Answer:
26
Step-by-step explanation:
decimal form 5.09901951
20) The sales tax on a $25 shirt purchased at the Laker Store in Russell Springs is $1.99. What is the sales tax rate in Russell Springs?
Answer:
the cost is $26
i think ths answer would be help full
What situation could this diagram represent?
rolling two number
cubes
tossing one coin once
spinning a tri-color
spinner
tossing two coins once
Answer:tossing two coins once
Step-by-step explanation:
Given g(x) = -2x + 3, solve for x when g(x) = -3.
Sin θ = ____ csc θ = ____ cos θ = ____ sec θ = ____ tan θ = ____ cot θ = ____ Equation of the Circle: _ the unit circle (r = 1), find the value of the six trig ratios:
Answer:
a. Sin θ = y/r
b. csc θ = r/y
c. cos θ = x/r
d. sec θ = r/x
e. tan θ = y/x
f. cot θ = x/y
g. x² + y² = 1
Step-by-step explanation:
Where (x, y) are the x and y coordinates of the position with radius r and angle θ measured from the positive x axis. y is the opposite side to the angle θ and x is the adjacent side to the angle θ and r is the hypotenuse side of the right-angled triangle formed by x, y and r. Also, x² + y² = r²
a. Sin θ = opposite/hypotenuse = y/r
b. csc θ = hyotenuse/opposite = 1/Sin θ = r/y
c. cos θ = adjacent/hypotenuse = x/r
d. sec θ = hypotenuse/adjacent = 1/cos θ = r/x
e. tan θ = opposite/adjacent = y/x
f. cot θ = adjacent/opposite = 1/tan θ = x/y
g. Equation of the Circle: _ the unit circle (r = 1),
Since x² + y² = r² ,for a unit circle, r = 1. So,
x² + y² = 1²
x² + y² = 1
which property is
used below?
A. Distributive Property
B. Multiplication Property of Inequality
C. Subtraction Property of Inequality
D. Associative Property of Multiplication
Answer:
B
Step-by-step explanation:
.
Multiplication Property of Inequality because you are multiplying each side by 3. I hope this helps! :)
Please solve! 20 points!
A blueberry muffin recipe calls for 3/4 cup of
sugar. How many cups of sugar would be
needed to make the muffin recipe 3 times?
Answer:
9/4 or 2 1/4 cups of sugar.
Step-by-step explanation:
To find the answer we multiply 3/4 by 3. Because the bottom stays the same, we wont multiply it. Since 3 x 3 = 9, it will be 9/4. Therefore, 9/4 or 2 1/4 is your answer.
Simplify the given expression below:
(3 + 4i) + (5 - 2i)
1) -2 + 6i
2) 2 - 2i
3) 7 +3i
4) 8 + 2i
Answer:
4) 8+2i
Step-by-step explanation:
When you expand you get 3+4i+5-2i
when you add the like terms you get 8+2i
Answer:
3
Step-by-step explanation:
The answer is 3 3+4 is 7 and 5-2 is 3
Write the decimal 0.532 as a percent.
a. 53.2%
b. 532%
C. 5.32%
d. 0.532%
A line passes through the points (0, -2) and (3, 4). Find the slope of the line.
is P= {a, b} then the number of subsets of P is what?
Answer:
4
Step-by-step explanation:
The number of subsets of P simply refers to the power of the sets.
P(P) = 2^n(P)
where P(P) is the power of the set P
n(P) is the cardinality of set P
P(P) = 2^2 = 4
Write the equation of each line in slope-intercept form
Answer:
1) y=4/5x-8
3) y=7/5x -2
Step-by-step explanation:
Slope- intercept form is y=mx+b (y = (slope)x+ (y-intercept))
I hope this helps :)
Mike is catering a party. He plans on having 4 trays of 5 appetizers each on the buffet at the beginning of the party and will rotate in new trays as those become empty. To ensure that he does not run out of appetizers during the party, he is going to make 2 appetizers per person in addition to the initial number put out on the buffet. Which of the following represents A, the amount of appetizers Mike needs to make, in terms of p, the amount of people attending the party?
Answer:
A = 20 + 2p
Step-by-step explanation:
Write a recursive function for each of the following sequences
9, 15, 27, 51, 99
Answer:
N=6
Step-by-step explanation: