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slope:change in x\change in y
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anyone who solves this problem for me .... I really need help
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a) The value of [tex]k'(0)[/tex] is [tex]\frac{3\sqrt{3}}{2}[/tex].
b) The value of [tex]m'(5)[/tex] is approximately -0.034.
c) The value of [tex]x[/tex] is approximately 0.622.
a) [tex]f(x)[/tex] is a piecewise function formed by two linear functions, whose form is defined by the following definition:
[tex]f(x) = \frac{y_{2}-y_{1}}{x_{2}-x_{1}} \cdot x + b[/tex] (1)
Where:
[tex](x_{1}, y_{1})[/tex], [tex](x_{2}, y_{2})[/tex] - Two distinct points of the line.[tex]x[/tex] - Independent variable.[tex]f(x)[/tex] - Dependent variable.[tex]b[/tex] - x-InterceptNow we proceed to determine the linear functions:
Line 1: [tex]x \in [-1, 2)[/tex]
[tex](x_{1}, y_{1}) = (0, 3)[/tex], [tex](x_{2}, y_{2}) = (1, 5)[/tex], [tex]b = 3[/tex]
[tex]f(x) = \frac{5-3}{1-0}\cdot x + 3[/tex]
[tex]f(x) = 2\cdot x + 3[/tex]
Line 2: [tex]x \in [2, 8][/tex]
[tex](x_{1}, y_{1}) = (2, 7)[/tex], [tex](x_{2}, y_{2}) = (8, 3)[/tex]
First, we determine the slope of function:
[tex]m = \frac{3-7}{8-2}[/tex]
[tex]m = -\frac{2}{3}[/tex]
Now we proceed to determine the intercept of the linear function:
[tex]7 = -\frac{2}{3}\cdot 2 + b[/tex]
[tex]b = \frac{25}{3}[/tex]
[tex]f(x) = -\frac{2}{3}\cdot x +\frac{25}{3}[/tex]
The first derivative of a linear function is its slope, and the first derivative of a product of functions is defined by:
[tex]k'(x) = f'(x)\cdot g(x) + f(x)\cdot g'(x)[/tex]
If we know that [tex]f(x) = 2\cdot x + 3[/tex], [tex]f'(x) = 2[/tex], [tex]g(x) = \sqrt{x^{2}-x+3}[/tex], [tex]g'(x) = \frac{2\cdot x - 1}{2\cdot \sqrt{x^{2}-x+3}}[/tex] and [tex]x = 0[/tex], then:
[tex]k'(x) = 2\cdot \sqrt{x^{2}-x+3}+\frac{(2\cdot x +3)\cdot (2\cdot x - 1)}{2\cdot \sqrt{x^{2}-x+3}}[/tex]
[tex]k'(0) = 2\sqrt{3}-\frac{3}{2\sqrt{3}}[/tex]
[tex]k'(0) = \frac{12-3}{2\sqrt{3}}[/tex]
[tex]k'(0) = \frac{9}{2\sqrt{3}}[/tex]
[tex]k'(0) = \frac{3\sqrt{3}}{2}[/tex]
The value of [tex]k'(0)[/tex] is [tex]\frac{3\sqrt{3}}{2}[/tex].
b) The derivative is found by means of the formulas for the derivative of the product of a function and a constant and the derivative of a division between two functions:
[tex]m'(x) = \frac{f'(x)\cdot g(x)-f(x)\cdot g'(x)}{2\cdot [g(x)]^{2}}[/tex] (2)
If we know that [tex]f(x) = -\frac{2}{3}\cdot x +\frac{25}{3}[/tex], [tex]f'(x) = -\frac{2}{3}[/tex], [tex]g(x) = \sqrt{x^{2}-x+3}[/tex], [tex]g'(x) = \frac{2\cdot x - 1}{2\cdot \sqrt{x^{2}-x+3}}[/tex] and [tex]x = 5[/tex], then:
[tex]f(5) = 5[/tex]
[tex]f'(5) = -\frac{2}{3}[/tex]
[tex]g(5) = \sqrt{23}[/tex]
[tex]g'(5) = \frac{9\sqrt{23}}{46}[/tex]
[tex]m'(5) = \frac{\left(-\frac{2}{3} \right)\cdot \sqrt{23}-\left(-\frac{2}{3} \right)\left(\frac{9\sqrt{23}}{46} \right)}{3\cdot 25}[/tex]
[tex]m'(5) \approx -0.034[/tex]
The value of [tex]m'(5)[/tex] is approximately -0.034.
c) In this case we must find a value of [tex]x[/tex], so that [tex]h'(x) = 2[/tex]. Hence, we have the following formula below:
[tex]5\cdot e^{x}-9\cdot \cos x = 2[/tex]
A quick approach is using a graphing tool a locate a point so that [tex]5\cdot e^{x}-9\cdot \cos x = 2[/tex]. According to this, the value of [tex]x[/tex] is approximately 0.622.
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Which function results in f(x)=13?
Answers
Answer:
The answer is B
Step-by-step explanation:
plug 2 into x to see
A.
x^2 + 8
2^2 + 8
4 + 8 = 12
B.
3x^2 + 1
3(2)^2 + 1
3(4) + 1
12 + 1 = 13
C.
2x^3 + 5
2(2)^3 + 5
2(8) + 5
16 + 5 = 21
D.
x^2 + x
2^2 + 2
4 + 2 = 6
Which statement is generally true about retirement?
A. Your income will increase, while your expense will stay the same.
B. Your income will decrease, while your expenses will increase.
C. Your income will increase, while your expenses will decrease.
D. Your income will decrease, while your expenses will stay the same.
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The general statement that is true about retirement is B. your income will decrease, while your expenses will increase.
Retirement is the leaving of one's of occupation. This means you cease to be involved in active service in a job or occupation especially when one is considered old and of retirement age.
During retirement, retirement benefits and pension are usually made available to retirees. However, one's income will come to a decline which makes most people scared of retirement. Keeping up with the standard of living they are used to becomes difficult as income to sustain such may not be available.
Therefore, the general statement that is true about retirement is B. your income will decrease, while your expenses will increase.
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Answer:
It's B
Step-by-step explanation:
Just took it
Use the GCF and the Distributive property to find the sum of 66+78
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Here is ur answer of your question
can someone plzzz help me with this (multiple choice ) i have more if anyone is good at this
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Simplify fully
x2 - 9
3x2 + 8x - 3
+
X-3
x+2
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(-3x³+2x²+4x+24) (x-2)
---------------------------------
8x
A bakery asks 75 customers to vote for a new bagel flavor. Onion flavor receives 33 votes. Cheddar flavor receives 42 votes. Use this information to answer the questions below. What fraction shows the proportion of customers who voted for cheddar flavor? What percent of customers voted for cheddar flavor?
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Using proportions, it is found that:
The fraction that shows the proportion of customers who voted for cheddar flavor is [tex]\frac{42}{75}[/tex]56% of customers voted for cheddar flavor.A proportion is the number of desired outcomes divided by the number of total outcomes.A percentage is the proportion multiplied by 100%.In this question, 42 out of 75 customers voted for the cheddar flavor, hence:
[tex]p = \frac{42}{75}[/tex]
That is, the fraction that shows the proportion of customers who voted for cheddar flavor is [tex]\frac{42}{75}[/tex]
The percentage is:
[tex]\frac{42}{75} \times 100\% = 56\%[/tex]
56% of customers voted for cheddar flavor.
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Let F(x)=∫
t−3
t
2+7
for − ∞ < x < ∞
x
0
(a) Find the value of x where F attains its minimum value.
(b) Find intervals over which F is only increasing or only decreasing.
(c) Find open intervals over which F is only concave up or only concave down.
Answers
(a) It looks like you're saying
[tex]\displaystyle F(x) = \int_0^x (t - 3t^2 + 7) \, dt[/tex]
Find the critical points of F(x). By the fundamental theorem of calculus,
F'(x) = x - 3x² + 7
The critical points are where the derivative vanishes. Using the quadratic formula,
x - 3x² + 7 = 0 ⇒ x = (1 ± √85)/6
Compute the second derivative of F :
F''(x) = 1 - 6x
Check the sign of the second derivative at each critical point.
• x = (1 + √85)/6 ≈ 1.703 ⇒ F''(x) < 0
• x = (1 - √85)/6 ≈ -1.370 ⇒ F''(x) > 0
This tells us F attains a minimum of
[tex]F\left(\dfrac{1-\sqrt{85}}6\right) \approx \boxed{-6.080}[/tex]
(b) Split up the domain of F at the critical points, and check the sign of F'(x) over each subinterval.
• over (-∞, -1.370), consider x = -2; then F'(x) = -7 < 0
• over (-1.370, 1.703), consider x = 0; then F'(x) = 7 > 0
• over (1.703, ∞), consider x = 2; then F'(x) = -3 < 0
This tells us that
• F(x) is increasing over ((1 - √85)/6, (1 + √85)/6)
• F(x) is decreasing over (-∞, (1 - √85)/6) and ((1 + √85)/6, ∞)
(c) Solve F''(x) = 0 to find the possible inflection points of F(x) :
F''(x) = 1 - 6x = 0 ⇒ 6x = 1 ⇒ x = 1/6
Split up the domain at the inflection point and check the sign of F''(x) over each subinterval.
• over (-∞, 1/6), consider x = 0; then F''(x) = 1 > 0
• over (1/6, ∞), consider x = 2; then F''(x) = -11 < 0
This tells us that
• F(x) is concave up over (-∞, 1/6)
• F(x) is concave down over (1/6, ∞)
LAST ATTEMPT MARKING AS BRAINLIEST!! ( write a rule to describe each transformation)
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Answer:
See explanation
Step-by-step explanation:
Dilation of 4
G (0, 1) G' (0, 4)
F (1, 1) F' (4, 4)
Gx'/Gx = 0 / 0 = 0
Gy' / Gy = 4 / 1 = 4
Fx' / Fx = 4 / 1 = 4
Fy' / Fy = 4 / 1 = 4
One angle in a complementary pair of angles measures 3 times the other angle.
What is the measure, in degrees, of the
smaller angle?
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Answer:
22.5 degrees
Step-by-step explanation:
Complementary angles add up to be 90 degrees. You can model the simple equation [tex]x+3x=90[/tex] where is x is the small angle and 3x is the large angle.
[tex]4x=90\\x=22.5[/tex]
the smaller angle is 22.5 degrees
What is the formula for calculating momentum?
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Answer:
(c) p = vm
Step-by-step explanation:
Momentum, represented by 'p', is the product of mass and velocity. It is a vector quantity, just as velocity is a vector quantity.
p = vm
need help with solving this please
Answers
cos60 = opposite / hypothenuse = x / sqrt3
cos60 = 1/2
x = sqrt3/2
Answer:
3/2
Step-by-step explanation:
Since the shape is an equilateral triangle, all the angles are equal measure, 60° and all the sides are also of equal measure that was given, root3. So half of the triangle has length (root3)/2. The perpendicular drawn in the interior is also an angle bisector. The triangles created are 30°-60°-90° triangles. The sides of this special right triangle are in the ratio
s : 2s : sroot3
The longest side of the 30-60-90 triangle is given. The shortest side is half the length of the longest side. The length of the long leg is the short leg × root3
In this diagram the short leg is (root3)/2 .
(root3)/2 × root3 = 3/2
See image.
Luigi's Fine Dining charges $32.09 for its prix fixe meal plus $39.26 for every drink, d, you purchase. The equation that models the total cost (T) is T(d )= 39.26d + 32.09 Which value in the equation represents the rate of change?
A .. The number of drinks purchased
B .. $32.09
C .. $39.26
D .. $71.35
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Answer:
C. $32.09, since it's not the fixed cost, it changes based on how much drinks are purchased.
It depends on the amount of drinks purchased to change the bill
A local rectangular shaped pool used by lap swimmers has dimensions 25 yd by 26 yd and is 5.1 feet deep. Find the cost for filling the pool if the city charges $1.50 per 1000 gallons. Use the conversion 1 gallon = 0.134 cubic ft.
Round your answer to two decimal places.
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The cost for filling the pool if the city charges $1.50 per 1000 gallons is $333.97
Given:
Length = 25 yd
width = 26 yd
Height = 5.1 ft
convert yard to feet
25 yd = 75 ft
26 ft = 78 ft
Volume of the pool = length × width× height
= 75 × 78 × 5.1
= 29,835 cubic ft
1 gallon = 0.134 cubic ft.
222,649.3 gallon = 29,835 ft
charges per 1000 gallon = $1.50
Total charges = 222,649.3 gallon / 1000 gallon × $1.50
= 222.6493 × 1.50
= 333.97395
Approximately,
$333.97
Therefore, the cost for filling the pool if the city charges $1.50 per 1000 gallons is $333.97
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another fraction problem. Have tried this one a couple of times and cant find fault in what i did
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Answer:
Perimeter = 12 1/2 in
Area = 9.375 in
Step-by-step explanation:
Perimeter:
(3 3/4) + (3 3/4) + (2 1/2) + (2 1/2) = 12 1/2
Area:
(3 3/4) * (2 1/2) = 9.375
Answer:
P = 12 1/2 in
A = 9 3/8 in²
Step-by-step explanation:
L = 3 3/4 in
W = 2 1/2 in
Area:
A = L × W
A = (3 3/4 in)(2 1/2 in)
A = 15/4 in × 5/2 in
A = 75/8 in²
A = 9 3/8 in²
Perimeter:
P = 2(L + W)
P = 2(3 3/4 in + 2 1/2 in)
P = 2(15/4 in + 5/2 in)
P = 2(15/4 in + 10/4 in)
P = 2(25/4 in)
P = 25/2 in
P = 12 1/2 in
Helppp it’s due today
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Answer:
128
Step-by-step explanation:
SOMEBODY PLZ CHECK IF MY ANSWER ARE CORRECT NO LINKS PLZ AND THANK YOU
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Answer:
the first one's right i think
Image attached giving 25 points please help
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Answer:
i think x = -5, y = -7 is a other solution set
expand and simplify 3(5x+1)+5(5x-4)
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Answer:
40x-17
Step-by-step explanation:
1plss help, its time
Answers
Answer:
60 degrees
Step-by-step explanation:
Similar shapes have the same angles but different side lengths.
Answer:
The answer is 60°
Step-by-step explanation:
Because pentagon JKLMN is basically the same as pentagon VWXYZ and if you see in the smaller pentagon the angle for L is 90° and same goes for the bigger pentagon
What is 0.459 roused to the nearest hundredth
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Answer:
0.459
the 9 rounds the 5 up to a 6 so its 0.46
Answer:
The answer is 0.46
Step-by-step explanation:
The 9 is over 5, so you round up which bumps the 5 up to a 6. It could also be written as 0.460 but the extra 0 is unnecessary.
Help, please
Erica solved the equation −5x − 25 = 78; her work is shown below. Identify the error and where it was made.
−5x − 25 = 78
Step 1: −5x − 25 − 25 = 78 − 25
Step 2: −5x = 53
Step 3:negative five times x over negative five = fifty-three over negative five
Step 4: x = negative fifty-three over five
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Answer:
The first step.
Step-by-step explanation:
Help Meh I need it SOON
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Step-by-step explanation:
the option you chose (<C~=<Y) is absolutely correct.
The store is 7⁄8 of a mile away from your house. You walked 1⁄5 of a mile towards the store before getting on the bus. If the bus went directly to the store, how many miles long was the bus ride?
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1/5 = 8/40
35 8 27
—- ➖ —- = —-
40 40 40
27/40 miles
6 lb = how many oz .
Answers
Answer:
96 oz
Step-by-step explanation:
1 lb= 16 oz
so, 16×6=96
Solve the inequality below for z.
8z+3>3z-17
A.z>-4
B.z<-14/5
C.z<-4
D.z>-14/5
Answers
8z+3 > 3z-17
subtract 3 from both sides
8z > 3z -20
subtract 3z from both sides
5z > -20
divide both sides by 5
z > -4
Therefore, the solved inequality is z > -4.
Hoped this helped.
[tex]BrainiacUser1357[/tex]
Solve |2x - 5| = 4.
a. {x | x = 0.5 or x = 4.5}
b. {x | 0.5 < x < 4.5}
c. {x | x = -4.5 or x = 4.5}
Answers
Step-by-step explanation:
|2x - 5| = 4
The absolute value has two solutions one positive and one negative
2x-5 = 4 2x-5 = -4
Add 5 on each side
2x-5+5 = 4+5 2x-5+5 = -4+5
2x = 9 2x =1
Divide by 2
2x/2 =9/2 2x/2 = 1/2
x = 4.5 x = .5
A cafeteria sells 30 drinks every 15 minutes. How many drinks can be sold in one hour?
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Answer:30 drinks
Step-by-step explanation:
Melissa has 120 kilograms of rice. Her mother sold 105 kilograms. What percent of the rice was sold? with solution :D please
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Answer:
225
Step-by-step explanation:
po ang answer ko
please comment if I'm wrong
SHOW YOUR WORK!!! PLEASE HELP!!! ASAP!!!!
Answers
Answer:
84
Step-by-step explanation:
TPS + SPR = RPT and TPS = RPT - SPR
The measure of RPT and SPR are given so we just need to place them and do the calculation
TPS = 137 - 53
TPS = 84