Answers
(a) mtan refers to the slope of the tangent line. Given f(x) = 9 + 7x ², compute the difference quotient:
[tex]\dfrac{f(x+h)-f(x)}h = \dfrac{(9+7(x+h)^2)-(9+7x^2)}h = \dfrac{(9+7x^2+14xh+7h^2)-9-7x^2}h = \dfrac{14xh+7h^2}h[/tex]
Then as h approaches 0 - bearing in mind that we're specifically considering h near 0, and not h = 0 - we can eliminate the factor of h in the numerator and denominator, so that
[tex]m_{\rm tan} = \displaystyle \lim_{h\to0}\frac{f(x+h)-f(x)}h = \lim_{h\to0}\frac{14xh+7h^2}h = \lim_{h\to0}(14x+7h) = 14x[/tex]
and so the slope of the line at P (0, 9), for which we take x = 0, is 0.
(b) The equation of the tangent line is then y = 9.
Related Questions
A chair can be purchased in one of four colors: red, white, green, or blue. The number of chairs
purchased in each color is listed below.
• red: 150
• white: 450
• green: 225
• blue: 375
Based on the information shown in the list, what is the probability that the next chair purchased
will be red
Answers
Answer: I believe it’s 1/8
Step-by-step explanation:
You add up all chairs purchased which is 1200 to get the total. Then you do 150/1200 which is 1/8
:)
Total chairs
150+450+225+375600+6001200P(Red)
150/120015/1201/89) If two lines intersect and form equal, adjacent
angles, then the lines are
1) perpendicular 2) collinear
3) parallel
4) complementary
Answers
Answer:
1 perpendicular
Step-by-step explanation:
it's the only way for them to be equal
what is −4 1/3 ÷( −2 3/5)
Answers
Answer:
5/3
1.6
Step-by-step explanation:
mixed number from: 1 2/4
Pt=3x+8and TQ =5x-6 PT=?
Answers
Because yeah I just don’t know that question to the answer so hopefully somebody finds it and you have a good day
The perimeter of a
triangle is 42cm.
The sidelengths
are x,x+2 and
x+4, what is the
length of the longest
side ?
Answers
Answer:
The longest side is 16 cm
Step-by-step explanation:
[tex]x + (x + 2) + (x + 4) = 42cm \\ x + x + 2 + x + 4 = 42cm \\ 3x + 6 = 42cm \\ 3x = 36cm \\ x = 12[/tex]
check and finish
[tex]12 + (12 + 2) + (12 + 4) = 42cm \\ 12 + 12 + 12 + 6 = 42 cm\\ 36 + 6 = 42cm \\ 42cm = 42cm[/tex]
lengths of sides
[tex]12 + 4 = 16cm \\ 12 + 2 = 14cm \\ 12cm[/tex]
write the Quotient for the following 5 1/3 ÷2
Answers
Answer:
34
Step-by-step explanation:
51/3/2=51x2/3=102/3=34
5 1/3 divided by 2 is actually 2.6 or 8/3
The number of CRT and LCD monitors in a company are in the ratio 2:5. If the total number of monitors in the company is 49, how many of them are LCD monitors?
Answers
Answer:
35 LCD monitors.
Step-by-step explanation:
The ratio is 2:5, which means the total amount of parts is 7 (2 + 5 = 7).
There are 49 monitors in all. Divide 49 with 7:
49/7 = 7
Each part has 7 monitors within. Remember, there are 5 parts of LCD monitors compared to 2 CRT monitors. Multiply 7 with 5:
7 x 5 = 35.
There are 35 LCD monitors, and 14 CRT monitors.
~
you have 100 million dollars your friend wants 6k your mom wnats 8k your dad wants 9k you havnt pay your takes so you have to give up 9 to the power of 4 how much money do you have left
Answers
Answer:
ninety-nine million nine hundred seventy thousand four hundred thirty-nine
11. What is the mass of 30,000 molecules? Express your answer in scientific notation 0
Answers
Answer:
the mass of 30,00 molecules of oxygen is gram
Step-by-step explanation:
plz brainliest
how many irrational numbers are there between 6 and 7 ?
Answers
Jessica makes her favorite shade of purple paint by mixing blue paint and red paint in a ratio of 3 : 2
Answers
Answer:
In fraction form, it would be 3/2
Help!!! Please Please Please!! :(
Suppose y varies directly with x, and y= 24 when x= 8. What is the value of y when x=10?
A. 10
B. 30
C. 80
D. 240
Answers
Answer:
[tex]\huge\boxed{\sf y = 30}[/tex]
Step-by-step explanation:
Given that:
y ∝ x
Turning proportionality into equality by putting the constant 'k'
y = kx ---------------------(1)
We know that y = 24, when x = 8
24 = k(8)
Divide both sides by 8
24 / 8 = k
3 = k
OR
k = 3
Now, Finding y when x = 10
Put x = 10 and k = 3 in Eq. (1)
y = (3)(10)
y = 30
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807The shorter leg of a right triangle is 14 feet less than the other leg. Find the length of the two legs if the hypotenuse is 34 feet.
Answers
Answer:
side a = 30 feet long.and side b = 30-14 = 16 feet long.
Step-by-step explanation:
Right triangle, with sides a, b=a-14 and h=34
By Pythagorean rule, h2 = 342 = a2 + b2 = a2 + (a-14)2 ==> a2 + a2 - 28a + 196
Simplify to get 1156 = 2a2 - 28a + 196
Subtract 1156 from both sides to get 2a2 - 28a - 960 = 0
Divide all terms by 2: a2 -14a - 480 = 0
Use quadratic equation to find that a = 30 or a = -16.
a = -16 will not work.
Therefore side a = 30 feet long.and side b = 30-14 = 16 feet long.
Check: 302 + 162 = 900+256=1156. SQRT(1156) = 34 feet, the given hypotenuse.Right triangle, with sides a, b=a-14 and h=34
By Pythagorean rule, h2 = 342 = a2 + b2 = a2 + (a-14)2 ==> a2 + a2 - 28a + 196
Simplify to get 1156 = 2a2 - 28a + 196
Subtract 1156 from both sides to get 2a2 - 28a - 960 = 0
Divide all terms by 2: a2 -14a - 480 = 0
Use quadratic equation to find that a = 30 or a = -16.
a = -16 will not work.
Therefore side a = 30 feet long.and side b = 30-14 = 16 feet long.
Check: 302 + 162 = 900+256=1156. SQRT(1156) = 34 feet, the given hypotenuse.
The side length of the other sides is 30 feet and 16 feet if the shorter leg of a right triangle is 14 feet less than the other leg.
What is a right-angle triangle?It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
It is given that:
The shorter leg of a right triangle is 14 feet less than the other leg.
From the Pythagoras theorem:
hypotenuse² = perpendicula² + base²
perpendicular = base - 14
34² = (base - 14)² + base²
34² = base² - 28base + 196 + base²
2base² - 28base - 960 = 0
base = 30, -16
side length cannot be negative
base = 30 feet
The length of another leg:
perpendicular = 30 - 14 = 16 feet
Thus, the side length of the other sides is 30 feet and 16 feet if the shorter leg of a right triangle is 14 feet less than the other leg.
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-4.13(u - 19) = 12.38
u =
PLEASE HELP ME
thank u :)
Answers
Answer:
[tex]u=16.0024213[/tex]
Step-by-step explanation:
[tex]-4.13(u-19)=12.38\\-(4.13u-4.13*19)=12.38\\-(4.13u-78.47)=12.38\\(-4.13u+78.47)+(-78.47)=12.38+(-78.47)\\-4.13u+78.47-78.47=12.38-78.47\\-4.13u=-66.09\\\frac{4.13u}{4.13} =\frac{66.09}{4.13} \\u=\frac{66.09}{4.13} \\u=16.0024213[/tex]
Select the locations on the number line to plot the points −212 and 612.
may give brainleist and thanks
Answers
Answer:
See below
Step-by-step explanation:
The points are located:
-2 1/2 = -2.5 is in between -2 and -36 1/2 = 6.5 is in between 6 and 7See the attached
Look at picture CORRECT ANSWER GETS BRAINEST
Answers
Answer:
-2 1/10
Step-by-step explanation:
This simplifies to 21/4 divided by 5/2. Keep, change, flip. 21/4 x -2/5. -42/20 which equals -2 2/20 which simplifies to -2 1/10.
solve the following problem below
Answers
PLS HELP ME UNDERSTAND THIS
Answers
Answer:
the answer as a decimal is -0.7
{put the given value of j and k in the given equation.. and solve ....}
Answer:
0.45
Step-by-step explanation:
This question is asking you to find the value of the equation when j = -4 and when k = -0.7. To do this, we must substitute j with -4 and k with -0.7:
(-4 * -0.7 - 1) / -4
= (2.8 - 1) / 4
= (1.8) / 4
= 0.45
In a basket ,there are 25apples, of which 2/5 are rotten .How many apples are good?
Answers
Step-by-step explanation:
remaining apples =1-⅖ = ⅗
no. of apples good = ⅗×25 = 15.
hope this helps you.
Does anyone know how to do GCF
Answers
Answer:
Hope this helps!
Step-by-step explanation:
List the prime factors of each number.
Circle every common prime factor — that is, every prime factor that's a factor of every number in the set.
Multiply all the circled numbers. The result is the GCF.
-3x+12<18 please help
Answers
Answer:
[tex] - 3x + 12 < 18 \\ - 3x < 18 - 12 \\ - 3x < 6 \\ - x < \frac{6}{3} \\ - x < 2 \\ x > - 2 \\ thank \: you[/tex]
Answer:
x > -2
Step-by-step explanation:
Q. Solve the inequality.
-3x + 12 < 18
Solve for x.
-3x + 12 < 18Step 1:- Move constant to the right hand side and change their sign.
-3x < 18 - 12Step 2:- Subtract.
-3x < -6Step 3:- Divide both side of the inequality by -3 and flip the inequality sign.
x > -2Write an equivalent expression by distributing the "-−" sign outside the parentheses:
-(9v+6.3w-3.3)
Answers
Answer:
parethses is expressed of the sign air water land etc
Step-by-step explanation:
Whats the 11th number in this fibonacci sequence 0,1,1,2,3,5
Answers
Answer:
0,1,1,2,3,5,8,13,21,34,55
Your answer is 55!
Step-by-step explanation:
In order to get this, you need to add the 2 numbers before.
Ex. 1+1 is 2. 1+2 is 3. 2+3 is 5. 5+ 3 is 8. 8 + 5 is 13. 8 + 13 is 21. 21 + 13 is 34 and finally, 34 + 21 is 55!
[tex]\huge\boxed{\sf 55}[/tex]
A series of integers known as the Fibonacci sequence begins with a zero, is followed by a one, another one, and then a series of increasing numbers. Each number in the series equals the sum of the two numbers before it. Every succeeding pair of Fibonacci numbers has a quotient resembling the golden ratio.
[tex]\sf 0, 1, 1, 2, 3, 5, 8, 13, 21, 34,\boxed{55}, 89, 144, 233,...[/tex]
PLEASE HELP!!!! WILL GIVE BRAINLIEST!!!!
Answers
Answer:
85 degrees.
Those two quads are Similar polygons. Just match up the shape and basically do 360 - 110 - 75 - 90 = 85.
A point estimate of the percentage of defectives in all manufactured bulbs is_____.
Answers
Answer:
inih bagus menurut kamuh inih bagus tidak
A point estimate of the percentage of defectives in all manufactured bulbs is the Sample proportion.
How to find a point estimate of a proportion?
p'= x / n where x is the number of successes and n is the sample size. The variable p is the sample ratio and serves as a point estimate of the true ratio of the population.
Point estimation for population parameters is a single value for statistics. For example, the sample mean x is a point estimate of the population mean μ. Similarly, the sample ratio p is a point estimate of the population ratio P.
The average point estimate for the population is obtained by calculating the average of the samples taken from the population. The average calculation is the sum of all samples divided by the number of values.
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r(t) = < V4-t2, e-3t , In (t +1) >
Answers
Answer:
(1,-2)
Step-by-step explanation:
shriya measured four nails using a ruler. then she showed the lenghts on a line plot which line plot correctly shows the lenghts of the nails.
pls help its due tommorow!!
Answers
Drag the tiles to the correct boxes to complete the pairs.
Match the subtraction expressions to their correct answers.
Answers
Answer:
#1- 6 4/9 - 3 2/9 - 8 2/9 = - (6 + 3 + 8 + 4/9 + 2/9 + 2/9) = - (17 + 8/9) = - 17 8/9#2-12.48 - (-2.99) - 5.62 = - (12.48 + 5.62) + 2.99 = - 18.1 + 2.99 = - 15.11#3- 19 2/9 - 4 1/9 - (- 3 4/9) = -23 3/9 + 3 4/9 = - 19 8/9#4-353.92 - (-283.56) - 131.29 = - (353.92 + 131.29 - 283.56) = - 201.65$583 1/5 - 108 2/5 - (- 99 1/5) = 83 1/5 + 99 1/5 - 108 2/5 = 74Aiyana needs 3/8 pounds of sweet potato for each serving of sweet potato fries she can make with 1 1/2 pounds of sweet potato.
Answers
Answer:
four servings
Step-by-step explanation:
Luisa took a job in which her salary can be modeled by the exponential function y = 36,000(1.025)^x, where x is the number of years after she is hired. Damon took a job with a starting salary of $38,500 and yearly raises of $800. Pick EACH correct statement about the scenario.
[] The difference in the starting salaries is $1,600.
[] The difference in the starting salaries is $2,500.
[] The difference in the starting salaries is $2,000.
[] Luisa will make more money in the first 8 years.
[] Damon will make more money in the first 8 years.
[] They will make the same amount of money in the first 8 years.
Answers
Answer:
B and D are the correct answer
Step-by-step explanation:
I took the test
The difference in the starting salaries is $2,500 and Luisa will make more money in the first 8 years thus (B) and (D) are correct.
What is a function?A certain kind of relationship called a function binds inputs to essentially one output.
A function can be regarded as a computer, which is helpful.
Given salary of Luisa by function,
y = 36,000(1.025)^x
The starting salary of Luisa,
x = 0 → y = 36000(1.025)^0 = $36000
Starting salary Damon = $38500
Difference = 38500 - 36000 = $2500
Amount of money that Luisa make in first 8 years ⇒
36,000(1.025)¹ + 36,000(1.025)² + ...up to 8 times
Amount of money that Damon makes in first 8 years ⇒
38500 + (38500 + 800) + (38500 + 2 × 800) + ...up to 8 times.
The rate of increment of Luisa > Damon
Hence "The difference in the starting salaries is $2,500 and Luisa will make more money in the first 8 years".
For more about the function,
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