The answer is b. 15ft
Calculus please help me
(1) f(x) = (1 - x³) / (x - 1)
(a) The domain is the set of values that this function can take on. If x = 1, the denominator becomes 0 and the function is undefined. Any other value of x is okay, though, since for x ≠ 1, we have
f(x) = (1 - x³) / (x - 1) = - (1 - x³) / (1 - x) = -(x² + x + 1)
which is defined for all x. This also tells us that the plot of f(x) is a parabola with a hole at x = 1. So, the domain is the interval (-∞, 1) ∪ (1, ∞).
(b) The range is the set of values that the function actually does take on. Taking the simplified version of f(x), we can complete the square to write
-(x² + x + 1) = -(x² + x + 1/4 - 1/4) - 1 = -(x + 1/2)² - 3/4
which is represented by a parabola that opens downward, with a maximum value of -3/4. So the range is the interval (-∞, -3/4).
(c) Judging by the plot of f, the limits at both negative and positive infinity are -∞.
(d) Same answer as part (a).
(2) f(x) = x³ - x
(a) The derivative of f at x = 3, and hence the slope of the tangent line to this point, is
[tex]f'(3)=\displaystyle\lim_{h\to0}\frac{f(3+h)-f(3)}h[/tex]
[tex]f'(3)\displaystyle=\lim_{h\to0}\frac{((3+h)^3-(3+h))-24}h[/tex]
[tex]f'(3)=\displaystyle\lim_{h\to0}\frac{(27+27h+9h^2+h^3)-(3+h)-24}h[/tex]
[tex]f'(3)=\displaystyle\lim_{h\to0}\frac{26h+9h^2+h^3}h[/tex]
[tex]f'(3)=\displaystyle\lim_{h\to0}(26+9h+h^2)=\boxed{26}[/tex]
(b) The tangent line at x = 3 has equation
y - f (3) = f ' (3) (x - 3)
y - 24 = 26 (x - 3)
y = 26 x - 54
We also want to find any other tangent lines parallel to this one, which requires finding all x for which f '(x) = 26. We could use the same limit definition as in part (a), but to save time, we exploit the power rule to get
f '(x) = 3 x² - 1
Then solve for when this is equal to 26:
3 x² - 1 = 26 ==> x² = 9 ==> x = ±3
The other tangent line occurs at x = -3, for which we have f (-3) = -24, and so the equation for the tangent is
y - f (-3) = 26 (x - (-3))
y + 24 = 26 (x + 3)
y = 26 x + 54
Help I’m stuck and confused
Answer:
-8
Step-by-step explanation:
A triangle is always 180 degrees
(btw I'm not sure if this is addition or multiplication so sorry if i'm wrong!)
65 + 40 = 105
180 - 105 = 75
75 - 83 = -8
Answer:
the angle itself is 75 degrees so x=-8
Step-by-step explanation:
The sum of three different numbers is 223. The largest number is 13 more than the smallest number. The sum of the largest number and the smallest
number is 7 more than twice the middle number. What is the largest of these numbers?
Answer:
82.
Step-by-step explanation:
Let the largest number of be 'a'.
Let the middle number be 'b'.
Let the smallest number be 'c'.
From the question given above,
The sum of the three numbers is 223. This can be written as:
a + b + c = 223 .... (1)
The largest number is 13 more than the smallest number. This can be written as:
a = c + 13 ..... (2)
The sum of the largest number and the smallest number is 7 more than twice the middle number. This can be written as:
a + c = 2b + 7..... (3)
Summary:
a + b + c = 223 .... (1)
a = c + 13 ..... (2)
a + c = 2b + 7..... (3)
Substitute the value of a in equation 2 into equation 3. This is illustrated below:
a + c = 2b + 7
a = c + 13
c + 13 + c = 2b + 7
2c + 13 = 2b + 7
Make b the subject
2c + 13 – 7 = 2b
2c + 6 = 2b
2(c + 3) = 2b
Divide both side by 2
b = 2(c + 3) / 2
b = c + 3 ..... (4)
Substitute the value of a in equation 2 and the value of b in equation 4 into equation 1. This is illustrated below:
a + b + c = 223
a = c + 13
b = c + 3
(c + 13) + (c + 3) + c = 223
c + 13 + c + 3 + c = 223
3c + 16 = 223
Collect like terms
3c = 223 – 16
3c = 207
Divide both side by 3
c = 207/3
c = 69
The smallest number (c) is 69
Substitute the value of c into equation 2 to obtain the largest number (a). This is illustrated below:
a = c + 13
c = 69
a = 69 + 13
a = 82
Therefore, the largest number (a) is 82
The Washington monument is 555 feet 5 1/8 inches tall and weighs 90,854 tons. The monument is topped by an aluminum square pyramid. The sides of the pyramid’s base measure 5.6 inches, and the pyramid is 8.9 inches tall. Estimate the slope that a face of the pyramid makes with its base.
Answer:
3.2
Step-by-step explanation:
Imagine a straight line from the top of the pyramid to the base, the point where the line will meet the base will be half the side of the pyramid. This will form a right angles triangle.
Slope is given by
[tex]\text{Slope}=\dfrac{\Delta y}{\Delta x}\\\Rightarrow \text{Slope}=\dfrac{8.9}{\dfrac{5.6}{2}}=3.17857\\\Rightarrow \text{Slope}\approx3.2[/tex]
The slope of the face of the pyramid is 3.2
The lowest point in New Orleans is 8 feet below sea
level. You can represent that numerically using
The highest point in Chicago is 735 feet above sea
level. You can represent that numerically using
Answer:
[tex]-8,+735[/tex]
Step-by-step explanation:
The lowest point in New Orleans is 8 feet below sea level.
This can be represented numerically using [tex]-8[/tex]
(negative sign denotes below sea level)
The highest point in Chicago is 735 feet above sea level.
This can be represented numerically using [tex]+735[/tex]
(positive sign denotes above sea level)
Answer:
This is correct but if some people are confused it’s a negative integer and a positive integer
Step-by-step explanation:
(01.04 MC)
What is the slope of the line which passes through (2,5) and (3, 6)? (5 points)
Answer:1
Step-by-step explanation:6-5/3-2=1/1
Solve the system of equations: y=x^2, y=x+6
A.(3,9)
B.(-3,9),(2,4)
C. (-2,4),(3,9)
D.(-2,-4),(3,9)
A squirrel needs to look for some nuts in the forest every day. It can find 24 nuts on a sunny
day and 10 nuts on a rainy day. If the squirrel found 98 nuts last week, write and solve a
system of equations in order to find:
How many sunny days were there in last week? |
sunny days
How many rainy days were there in last week?
rainy days
Answer:
24x+10y=98
2sunny days
5rainy days
Step-by-step explanation:
x=number of sunny days
y=number of rainy days
(2*24)+(10*5)=98
vualah :)
70 + x + 55 + 30 = 180
Answer:
x=25
Step-by-step explanation:
First, we add all like terms. Then, we solve for x.
[tex]70+x + 55 + 30 = 180\\x+70 + 55 + 30 = 180\\x+155=180\\x=25[/tex]
We can rearrange some things because order does not matter with addition. Next, we just use basic equation solving techniques.
Answer:
25. Hope this helps :)
Step-by-step explanation:
180-70=110
110-55=55
55-30=25
Your missing answer would be 25
X=25
Can somebody please help me with this math problem
Answer:
According to the question 25% of the students wore jackets.
Thus 25% of 12 wore jackets
The number of students can be found easily by multipling 12 with 25//100
12*25/100
12*1/4
12/4
thus, 3 students
Therefore, option 3 is correct
For a certain type of sand, 1 cubic foot weighs 80 pounds. The sand goes in a container that weighs 40 pounds. Use the Ray tool to make a graph that shows the total weight of the container and sand, w, filled with n cubic feet of this sand. I need the coordinates for the graph please.
Answer:
First, let's write our equation in a general way.
We know that:
1 cubic foot weighs 80 pounds.
The container weighs 40 pounds.
Then, if i put n cubic feet of sand in the container, the total mass will be one time the mass of the container plus n times the mass of one cubic foot of sand.
We can write this as:
w(n) = 40lb + n*80lb
This is a linear equation, where the y-axis will represent the mass in pounds and the x-axis will be the number of cubic feet of sand in the container in units, a graph of this is shown below.
You can see that it is really steep, this is because for really small increments in n, the weight increases a lot.
Answer
ok, Just plot the points at (0,40) and (2,200) :))
1. tentukan hasil dari 243⅔?
2. tentukan hasil dari
√32 +3√18-2√50?
3.tentukan hasil dari 1000 ⅔×64⅙?
4. resionalkan bentuk akar dari 3/4+√2?
5. hasil dari 2√3×√18:√2 adalah?
6 bentuk sederhana dari :12/3+√3 adalah ?
7. hasil dari √1000—2√40 adalah
8. hasil dari 2- ¹+3-¹ adalah?
9. bentuk dari 5√5, jika dirsionalkan penyebutnya adalah?
10. hasil dari 2√3×√18:√6 adalah ?
[tex]tolong bantu nya[/tex]
Penjelasan langkah demi langkah:
1)
[tex]= 243^{\frac{2}{3} }\\= (\sqrt[3]{243})^2\\= 7^2\\= 49[/tex]
2) √32 +3√18-2√50
= √16*2 +3√9*2-2√25*2
= 4√2 + 3(3√2)-2(5√2)
= 4√2 + 9√2-10√2
= 13√2-10√2
= 3√2
3) 1000 ⅔×64⅙
[tex]= (\sqrt[3]{1000}) ^2 \times (2^6)^{1/6} \\= 10^2 \times 2\\= 100 \times 2\\= 200[/tex]
4) 3/4+√2
[tex]3/4+\sqrt{2} \\= \frac{3+4\sqrt{2} }{4 }[/tex]
5) 2√3×√18
= 2√3×√9*2
= 2√3×3√2
= (2*3)(√3*√2)
= 6√6
6) 12/3+√3
= 4+√3
7) √1000—2√40
= 10 -2 (√4*10)
= 10-2(2√10)
= 10 - 4√10
8) 2- ¹+3-¹
[tex]= \frac{1}{2} + \frac{1}{3}\\ = \frac{3+2}{6}\\ = \frac{5}{6}[/tex]
9)
[tex]\frac{5}{\sqrt{5} }\\ merasionalisasikan\\= \frac{5}{\sqrt{5} }\times \frac{\sqrt{5} }{\sqrt{5} }\\= \frac{5\sqrt{5} }{\sqrt{25} }\\= \frac{5\sqrt{5} }{5}\\ = \frac{\sqrt{5} }{1}[/tex]
Jika pernyataannya opsional, penyebutnya adalah 1
10) 2√3×√18
= 2√3×√9*2
= 2√3×3√2
= (2*3)(√3*√2)
= 6√6
Jasmine drives every morning to her office that is 12 miles from her home.
c
Suppose Jasmine drives from home to the office in 20 minutes. Use this information and part (b) to write an equation. QUICK RSM HELL EMERGENCY DUE TOMARO
Answer:
d = 36tStep-by-step explanation:
We need to calculate the speed of Jasmine first as shown:
Speed = Distance/Time
Given:
Distance = 12miles
Time = 20mins
Time = 20/60 hr
Time = 1/3 hr
Speed = 12/(1/3)
Speed = 12 * 3/1
Speed = 38mi/hr
From the formula:
S = d/t
To get the equation needed, substitute s = 36 into the formula:
36 = d/t
d = 36t
Hence the required equation is d = 36t where d is the distance in miles and time in hour
Answer:
36
Step-by-step explanation:
Complete the sentence. |-0.05| =
Answer:
|0.05|
Step-by-step explanation:
no absolute value can be negative
Answer:
0.05
Step-by-step explanation:
The lines outside the number mean absolute value. The absolute value of a number is how far it is from 0, so it's always positive. Basically, you just swap the sign of whatever number you are looking at. In this case, absolute value of -0.05 would simply be 0.05. Hope this helped!
New help math please I am stuck
Answer: Can u post a question?
Step-by-step explanation:
The length of a rectangle is 2 times the width. If the perimeter is to be less than 96 meters. What are the possible
values for the width? (Use w as the width)
Preview
TIP
Enter your answer using inequality notation. Example: 3 <=w<4
Use or to combine intervals. Example: w< 2 or w >= 3
Enter all real numbers for solutions of that type
Enter each value as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 243,
5+4)
Enter DNE for an empty set. Use oo to enter Infinity.
Answer:
W>16
Step-by-step explanation:
The formula for calculating the perimeter of a rectangle:
P = 2L+2W
L is the length of the rectangle
W is the width of the rectangle:
Given
P = 96m
If the length of a rectangle is 2 times the width, then L = 2W
Substitute into the formula:
Since the perimeter is less than 96m
96 < 2(2W)+2W
96 < 4W+2W
96 < 6W
Divide both sides by 6:
96/6 < 6W/6
16 < W
W>16
Hence the possible values of the width are all values greater than 16.
Casey is using a recipe that requires 2/3 Cups of flour for every 2 cups of milk. If Casey uses 5 cups of milk how many cups of flour are needed
Answer:
15 cups of flour
Step-by-step explanation:
HELP IM GIVING BRAINLIEST
Answer:
AB, BC, AC
Step-by-step explanation:
Hopefully I helped!! :)
Each morning, Jessica's mom drives 3.85 miles to take Jessica to school, then 4.9 miles to work. How many miles does
Jessica's mom drive each morning? Explain how you solved the problem.
Find FH. please and thank you :)
Answer:
[tex]22[/tex]
Step-by-step explanation:
If FG= 8
and GH=14
G is a midpoint
To find FH you would add 8 and 14.
[tex]8 + 14 = 22[/tex]
Answer:
add it FH +GH
=8+14
=22 ans.....
The sum of the angles of a triangle is 180 degrees. If one of the acute angles of a right triangle is 52 degrees, what is the measure of the other acute angle? A: Let x be the measure of the unknown acute angle. Write an equation relating this measure to the known quantities. Do not include units in your equation.
Answer:
An equation is [tex]x+52\°+90\°=180\°[/tex]
Step-by-step explanation:
Let [tex]x[/tex] be the measure of the unknown acute angle.
According to angle sum property of a triangle, sum of all the angles of a triangle is equal to 180°.
One of the acute angles of a right triangle is equal to 52°.
Also, the triangle is a right angled triangle, one of the angle must be equal to 90°.
[tex]x+52\°+90\°=180\°\\x+142\°=180\°\\x=38\°[/tex]
So, an equation is [tex]x+52\°+90\°=180\°[/tex]
Jason delivers newspapers on Saturdays and Sundays only. Each newspaper weighs about 1 pound 5 ounces. If he delivers 15 newspapers each day, how much do the two days' worth of newspapers weigh in pounds and ounces?
Answer:
39pounds 6oz
Step-by-step explanation:
15x2=30
1x30=30pounds
5x30=150oz
30p+150oz=39.37500
37500p=6oz
39pounds and 6 oz
HELP ASAP!!!!!!!!!!!!!!
Answer: is it a function-yes
why: none of the y values are the same
Step-by-step explanation:
Slope -2/3 through (-9,10)
Answer:
y = − 2 /3 x + 4
Step-by-step explanation:
Answer: y=-2/3x + 4
Step-by-step explanation:
If a recipe calls for 4 1/2 cups of flour for 48 cookies, how much flour would be needed for 24 coockies?
Answer:
2 1/4
Step-by-step explanation:
melody won 8 tokens. Trish won 2 more than 5 times as many tokens as melody. What computation will give the number of tokens Trisha won?
Answer:
8^5 + 2 = Trisha's Tokens
Step-by-step explanation:
Answer:
42
Step-by-step explanation:
8 x 5 +2
jessie worked four more hours than Ben. They worked a total of 25 hours. How many hours did each boy workz?
Answer:
jessie: 14.5
ben: 10.5
Maura runs 5 miles in 1.25 hours. Ava runs 3 miles in 50 minutes, or 0.83 hour. Who runs faster.
Answer:
ava ran the fastest
Step-by-step explanation:
8 groups of ___ hundredths is 0.32
Answer:
the answer is 0.4 The reason is because 0.4 x8=0.32
Step-by-step explanation:
y = -(x + 5)2-1
Find vertex
Answer:
The vertex is (-5, -1)
Step-by-step explanation:
Standard vertex form is a(x - b)^2 + c where (b, c) is the vertex.
