Answers
Answer:
A
Step-by-step explanation:
So we have the piecewise function:
[tex]f(x)= \begin{cases}\sqrt{2x} & \text{if }x<3 \\2x+10 & \text{if }3\leq x<8\\42&\text{if } x\geq 8\end{cases}[/tex]
And we want to find f(8).
Since our input value is 8, choose the equation that fits our input.
The first equation demand x to be less than 3. 8 is not less than 3, so we won't use that.
The second equation demand x to e greater than or equal to 3 and less than 8. 8 is not less than 8. So, we won't use that.
The third equation demands x to be greater than or equal to 8. 8 is greater than or equal to 8, so we'll use the third equation.
So:
[tex]f(x)=42\text{ if }x\geq 8[/tex]
[tex]f(8)=42[/tex]
There're nothing more to do, we're done :)
The answer is A.
Edit: Improved Format
Related Questions
Find sin(2A) if sin(A)=[tex]\frac{1}{4}[/tex] and [tex]0\leq A\leq \frac{\pi }{2}[/tex]
Answers
Step-by-step explanation:
sin(2A)
Use double angle formula:
= 2 sin(A) cos(A)
Use Pythagorean identity. 0 ≤ A ≤ π/2, so cos(A) > 0.
= 2 sin(A) √(1 − sin²(A))
Substitute and simplify.
= 2 (¼) √(1 − (¼)²)
= ½ √(¹⁵/₁₆)
= ⅛ √15
Which number has the greatest absolute value?
A) 0
B) −18
C) −31
D) −44
Answers
Answer:
D
Step-by-step explanation:
If the number is positive, the absolute value is the same as the number. If the number is negative, the absolute value is just a positive version of that number. So the absolute value of 0 is 0, -18 is 18, -31 is 31, and -44 is 44. Out if these, D has the greatest absolute value, so it would be D
Answer:
D. -44.
Step-by-step explanation:
Absolute value of -44:
= |-44| = 44
Jose just removed the children's playset from his back yard to make room for a rectangular garden. He wants to put a fence around the garden to keep out the dog. He has a 90 foot roll of fence in his garage that he plans to use. To fit in the backyard, the width of the garden must be 15 feet. How long can he make the other side, in feet, if he wants to use the entire roll of fence?
Answers
===================================================
Explanation:
He has 90 feet of fencing overall. This is the perimeter of the rectangle as its the distance around all four sides.
Two of the opposite sides are the width = 15 ft. So we have 15+15 = 30 feet taken up and 90-30 = 60 feet left for the other two opposite sides to add to. Call each of those sides x
x+x = 60
2x = 60
x = 60/2
x = 30
The other side must be 30 feet long.
This rectangle is 30 by 15
perimeter = 30+15+30+15 = 45 + 45 = 90
which helps confirm we have the right answer
---------------
Or you can solve this way
P = 2*(L+W) is the perimeter of a rectangle with length L and width W
Plug in the perimeter P = 90 and the width W = 15. Solve for L
P = 2*(L+W)
90 = 2*(L+15)
2(L+15) = 90
L+15 = 90/2
L+15 = 45
L = 45-15
L = 30
Which number is the solution of the inequality 8-1/4b> 27
Answers
Answer:
B < -76
Step-by-step explanation:
You start out with writing out the equation
8-1/4b> 27
Then, you subtract 8 from each side, so the -1/4b can be by itself
-1/4b>27-8
-1/4b>19
After that, you want to get rid of that -1/4, so you multiply both sides by -4
This makes the > sign flip to <
So, this makes:
b < -76
Point B is the midpoint of Line segment A C .
Answers
Answer:
Angle ABC is bisected by BD
BC =Half AC
2 mangle DBC =mangle ABC
Assuming that it takes 1.25 seconds for light to travel from the Moon to the Earth, how
many miles away is the Moon?
Answers
Answer:
238,900 miles away
Answer:
238,900
Step-by-step explanation:
Light travels at a speed of 186,282 miles per second, you multiply this number by 1.25 you get your answer.
Which of the values in the set {3, 4, 5, 6} is a solution to the equation 4x + 2 = 22?
03
04
05
06
Answers
HELP! WILL GIVE BRAINLIESY.
Answers
Answer:
$1 for one tube
Step-by-step explanation:
Ratio is 10:10
if you keep on reducing it
you will eventually get to 1:1
Therefore, the answer is $1 for one tube
Put in standard form 7xy+8x+5xyz+5x^5
Answers
Answer:
[tex]5x^5+5xyz+7xy+8x[/tex]
Step-by-step explanation:
When putting an equation in standard form, you always prioritize the term with the most variables - unless terms have a greater exponent.
The prioritization order is:
Exponents
Amount of variables
Value of coefficient
So, [tex]5x^5[/tex] is the only term with an exponent in this expression, so it will go first.
Next up, we have to choose between [tex]8x[/tex], [tex]5xyz[/tex], and [tex]7xy[/tex]. We know that [tex]5xyz[/tex] has more variables than the other ones, so it goes next.
Now we're left with [tex]7xy[/tex] and [tex]8x[/tex]. [tex]7xy[/tex] has more variables than [tex]8x[/tex], so it goes next.
This leaves [tex]8x[/tex] last.
So, the expression becomes [tex]5x^5+5xyz+7xy+8x[/tex].
Hope this helped!
I know that the answer isn't x=0. Please help.
Answers
(2x+8)/6=1/3(x+4)
3(2x+8)=6(x+4)
6x+24=6x+24.
0=0.
∴There are no real solutions.
Sixteen boxes that are each 1 5/8 feet high are stacked. Find the height of the stack
Answers
Explanation: 1 5/8 is equal to 13/8. 8/8 is equal to 1, and 8 plus 5 is 13. 13/8 is an improper fraction, but we will change that later. Since there are sixteen boxes, we must do 13/8 times 16, which is 208/8 if we do the math. 208 divided by 8 is 26.
There are 5 different pairs of gloves, where left and right are distinguishable. Select 4 of the 10 gloves. (a) How many are there to select 2 pairs of gloves? (b) How many ways are there to select 4 gloves out of the 10 such that 2 of the 4 make a pair. (a pair consists of any right glove and left glove.)
Answers
Answer:
(a) How many are there to select 2 pairs of gloves?
10 ways
(b) How many ways are there to select 4 gloves out of the 10 such that 2 of the 4 make a pair. (a pair consists of any right glove and left glove.)
130 ways
Step-by-step explanation:
For the above questions we apply that combination formula
(a) How many are there to select 2 pairs of gloves?
There are 5 pairs of gloves according to the question above, hence:
5C2 = 5!/2! × (5 - 2)!
= 5!/2! × 3!
= 5 × 4 × 3 × 2 × 1/2 × 1 × 3 × 2 × 1
= 10 ways.
Therefore, there are 10 ways to select 2 pairs of gloves
(b) How many ways are there to select 4 gloves out of the 10 such that 2 of the 4 make a pair. (a pair consists of any right glove and left glove.)
i) A way to select 4 gloves out of 10 gloves =
10C4 = 10!/4! ×(10 - 4)!
= 10!/ 4! × 6!
= 210 ways
ii) In order for 2 of the 4 gloves selected to be a pair, note that we have 5 pairs of gloves hence:
5 × 2⁴
= 80 ways.
Therefore, the number of ways which we can select 4 gloves out of the 10 such that 2 of the 4 make a pair. (a pair consists of any right glove and left glove.) = 210 ways - 80 ways
= 130 ways
-7b=-56 pls answer with the work and steps
Answers
Answer:
b=8
Step-by-step explanation:
Solution steps:
-7b=-56
b=-56 / -57
b=8
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{ b = 8}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{ - 7b = - 56}[/tex]
divide both sides of the equation by -7
[tex] \sf{ \dashrightarrow\frac{ - 7b}{ - 7} = \frac{ - 56}{ - 7} }[/tex]
Calculate
[tex] \dashrightarrow \sf{b = 8}[/tex]
Hope I helped!
Best regards! :D
Calculus 2 master needed; evaluate the integral PLEASE SHOW STEPS IF IM WRONG [tex]\int{sin^3x/\sqrt{cosx} } \, dx[/tex] I split off the sin^3 so i can use the pythag identity and allows for u substitution u=cosx du=-sinx dx -du=sin dx [tex]\int{1-u^2/\sqrt{u}*-du }[/tex] I move the negative towards the outside of the integral. then i divide the terms by sqroot 2||| [tex]-\int{(1/\sqrt{u} - u^2/\sqrt{u} )} \, du[/tex] I eventually get to a=1/2 b =5/2 [tex]-2{cos^a x +2/5cos^b} \, dx[/tex] did I miss anything? Or is this the final answer?
Answers
Answer:
Your process is indeed correct!
The full solution is:
[tex]\displaystyle \int\frac{\sin ^3 x}{\sqrt{\cos x}}\, dx= \frac{2}{5} \cos^{{}^{5}\!/\!{}_{2}} x - 2\cos ^{{}^{1}\!/\!{}_{2}}x + C[/tex]
Step-by-step explanation:
We want to evaluate the integral:
[tex]\displaystyle \int \frac{\sin^3(x)}{\sqrt{\cos(x)}}\, dx[/tex]
As you had done, we can rewrite our integral as:
[tex]\displaystyle =\int \frac{\sin(x)(\sin^2(x))}{\sqrt{\cos(x)}}\, dx[/tex]
Using the Pythagorean Identity, this is:
[tex]\displaystyle =\int \frac{\sin(x)(1-\cos^2(x))}{\sqrt{\cos(x)}}\, dx[/tex]
Now, we can make a substitution. Let u = cos(x). Then:
[tex]\displaystyle du = - \sin x \, dx[/tex]
Substitute:
[tex]\displaystyle = \int\frac{1-u^2}{\sqrt{u}} \, \left(- du\right)[/tex]
Simplify:
[tex]\displaystyle = -\int \frac{1}{\sqrt{u}} - \frac{u^2}{\sqrt{u}}\, du[/tex]
Rewrite:
[tex]\displaystyle = -\int u^{{}^{-1}\!/\!{}_{2}} - u^{{}^{3}\!/\!{}_{2}}\, du[/tex]
By the Reverse Power Rule:
[tex]\displaystyle = -\left(2u^{{}^{1}\!/\!{}_{2}} - \frac{2}{5} u^{{}^{5}\!/\!{}_{2}}\right) + C[/tex]
Simplify:
[tex]\displaystyle = \frac{2}{5} u^{{}^{5}\!/\!{}_{2}}-2u^{{}^{1}\!/\!{}_{2}} + C[/tex]
Back-substitute:
[tex]\displaystyle = \frac{2}{5} \cos^{{}^{5}\!/\!{}_{2}} x - 2\cos ^{{}^{1}\!/\!{}_{2}}x + C[/tex]
Answer:
= - 2 [tex]\sqrt{cos(x)}[/tex] + 2 cos⁵/₂ (x) + C
5
Step-by-step explanation:
∫ sin³ (x) dx
[tex]\sqrt{cos(x)}[/tex]
= ∫ sin² (x) sin (x) dx
[tex]\sqrt{cos(x)}[/tex]
= ∫ (1 - cos² (x) sin (x) dx
[tex]\sqrt{cos(x)}[/tex]
= ∫ - 1 - u² du
√u
= ∫ - 1 + u³/₂ du
√u
= - ∫ 1 du + ∫ u³/₂ du
√u
substitute it back
= - 2 √u + 2 cos⁵/₂ (x)
5
add constant, therefore
= - 2 [tex]\sqrt{cos(x)}[/tex] + 2 cos⁵/₂ (x) + C
5
Use polnt-slope form to write the following equation of the line passing through the point (7,-5) with the slope m=1
Answers
Answer:
Step-by-step explanation:
y + 5 = 1(x - 7)
y + 5 = x - 7
y = x - 12
Each of a sample of four home mortgages is classified as fixed rate (F) or variable rate (V). (Enter your answers as a comma-separated list. Enter ∅ for the empty set.)
(a) What are the 16 outcomes in ?
(b) Which outcomes are in the event that exactly three of the selected mortgages are fixed rate?
(c) Which outcomes are in the event that all four mortgages are of the same type?
(d) Which outcomes are in the event that at most one of the four is a variable-rate mortgage?
(e) What is the union of the events in parts (c) and (d)?
What is the intersection of these two events?
(f) What is the union of the two events in parts (b) and (c)?
What is the intersection of the two events in parts (b) and (c)?
Answers
Answer:
a)
{FVVV,FFVV,VFVV,VVVV,FVFV,FFFV,VFFV,VVFV,FVVF,FFVF,VFVF,VVVF,FVFF,FFFF,VFFF,VVFF}
b)
{FFFV,FFVF,FVFF,VFFF}
c)
{FFFF,VVVV}
d)
{FFFV,FFVF,FVFF,FFFF,VFFF}
e)
{FFFV,FFVF,FVFF,FFFF,VFFF,VVVV}
{FFFF}
f)
{FFFV,FFVF,FVFF,VFFF,FFFF,VVVV}
{ }
Step-by-step explanation:
a)
The 16 outcomes for a sample of four home mortgages classified as fixed and variable rate are
Sr.No Outcomes
1 FVVV
2 FFVV
3 VFVV
4 VVVV
5 FVFV
6 FFFV
7 VFFV
8 VVFV
9 FVVF
10 FFVF
11 VFVF
12 VVVF
13 FVFF
14 FFFF
15 VFFF
16 VVFF
b)
Let A be the event that exactly three are fixed rate. Thus, event A consists of following outcomes
A={FFFV,FFVF,FVFF,VFFF}
c)
Let B be the event that all four are of same type. The event B consists of either all fixed rate or all variable rate. Thus, event B consists of following outcomes
B={FFFF,VVVV}
d)
Let C be the event that at most one of four is variable rate. The event C consists of less than and equal to one variable rate. Thus, event C consists of following outcomes
C={FFFV,FFVF,FVFF,FFFF,VFFF}
e)
Let union of part(c) and part(d) can be represented as BUC. The union represents all the outcomes in event B and event C.
B∪C={FFFF,VVVV}∪{FFFV,FFVF,FVFF,FFFF,VFFF}
B∪C={FFFV,FFVF,FVFF,FFFF,VFFF,VVVV}
Let intersection of part(c) and part(d) can be represented as B∩C. The intersection represents the common outcomes in event B and event C.
B∩C={FFFF,VVVV}∩{FFFV,FFVF,FVFF,FFFF,VFFF}
B∩C={FFFF}
f)
Let union of part(b) and part(c) can be represented as AUB. The union represents all the outcomes in event A and event B.
A∪B={FFFV,FFVF,FVFF,VFFF}∪{FFFF,VVVV}
A∪B={FFFV,FFVF,FVFF,VFFF,FFFF,VVVV}
Let intersection of part(b) and part(c) can be represented as A∩B. The intersection represents the common outcomes in event A and event B.
A∩B={FFFV,FFVF,FVFF,VFFF}∩{FFFF,VVVV}
A∩B={ }
So intersection of part(b) and part(c) is an empty set as there is no common outcome in these two sets.
Sample of four homes.
The sample of 4 homes is on a mortgage and has been classified as a fixed rate of F and a variable rate of V. The mortgage is thus an agreement between the lender of the money and the borrower. The lender has the right to take away the property.
Thus answer is given below.
The set of 16 outcomes of the variable and the fixed rates is given as {FVVV,FFVV,VFVV,VVVV,FVFV,FFFV,VFFV, and VVFV,FVVF,FFVF,VFVF,VVVF,and the FVFF,FFFF,VFFF,VVFF}. The outcomes in the events that exactly is of 3 of the selected mortgages at a fixed rate is about {FFFV, FFVF,FVFF, VFFF}The outcomes of the events that all four mortgages are of the same type are about {FFFF, VVVV} The union of events in parts of c and d are as {FFFV, FFVF, FVFF, FFFF, VFFF}.Learn more about the sample of four homes.
brainly.com/question/14565659.
If justin has 90 tacos and loses 15 how many does he have
Answers
Answer:75
Step-by-step explanation:
90-15=75
Answer:
He has 75 tacos left.
90 - 15 = 75.
Write the equation of a line that is perpendicular to 6x - 3y - 15 = 0 and goes through the point (4, 6) in y-intercept form.
Answers
Answer:
y= -1/2(x) +8
gradient= -1/2
Intercept= 8
Step-by-step explanation:
Let's transform the equation to y -intercept form first
6x - 3y - 15= 0
-3y= -6x+15
Y= -6/-3(x) +(15/-3)
Y= 2x -5
Intercept c= -5
Gradient m =2
Rule of perpendicularity
mm'= -1
m'= -1/m
m' = -1/2
Equation of line of the point (4, 6)
(Y-Y1)/(x-x1)=m'
(Y-6)/(x-4)= -1/2
2(y-6)= -1(x-4)
2y -12 = -x +4
2y= -x +4+12
2y= -x+16
y= -1/2(x) +8
gradient= -1/2
Intercept= 8
A Holiday aircraft charters an aircraft to fly to Malta at a cost of $22000. It then sells 150 seats at $185 each and a further 35 seats at a 20% discount. calculate the profit made per seat if the plane has 200 seats.
Answers
Answer:
Hope it helped u if yes mark me BRAINLIEST pzllzllzl
A music service chargers a $2.99 monthly membership fee plus $0.05 for each song purchased. If Naomi charges for the month was $10.89 how much songs did she purchase
Answers
Answer:
158
Step-by-step explanation:
10.89-2.99 = 7.90
.5/7.90=158
Answer:
158 songs
Step-by-step explanation:
Monthly membership = 2.99
Each song cost = .05
Total Amount spent after 1 month = 10.89
S = Songs purchased
=> 2.99 + .05S = 10.89
=> 2.99 - 2.99 + .05S = 10.89 - 2.99
=> .05S = 7.9
=> .05S / .05 = 7.9 / .05
=> S = 158
So, she purchased 158 songs that month.
Find the indefinite integral and check the result by differentiation. (Use C for the constant of integration.)
∫ (x + 8x) dx
Answers
Answer:
[tex]y = \frac{9x^2}{2} + c[/tex]
Step-by-step explanation:
Given
[tex]\int\limits^ _[/tex][tex](x + 8x) dx[/tex]
Required
(a) Integrate
(b) Check using differentiation
To integrate, we make use of the following formula;
if
[tex]\frac{dy}{dx} = \int\limits^{} _{} ax^n[/tex]
then
[tex]y = \frac{ax^{n+1}}{n+1}[/tex]
So; [tex]\int\limits^ _[/tex][tex](x + 8x) dx[/tex] becomes
[tex]y = \frac{x^{1+1}}{1+1} + \frac{8x^{1+1}}{1+1} + c[/tex]
[tex]y = \frac{x^{2}}{2} + \frac{8x^{2}}{2} + c[/tex]
[tex]y = \frac{x^{2}}{2} + 4x^2 + c[/tex]
Take LCM
[tex]y = \frac{x^{2} + 8x^2}{2} + c[/tex]
[tex]y = \frac{9x^2}{2} + c[/tex]
To check using differentiation, we make use of
if [tex]y = ax^n[/tex], then
[tex]\frac{dy}{dx} = nax^{n-1}[/tex]
Using this formula
[tex]y = \frac{9x^2}{2} + c[/tex] becomes
[tex]\frac{dy}{dx} = 2 * \frac{9x^{2-1}}{2}[/tex]
[tex]\frac{dy}{dx} = 2 * \frac{9x}{2}[/tex]
[tex]\frac{dy}{dx} =9x[/tex]
[tex]9x = x + 8x[/tex]
So;
[tex]\frac{dy}{dx} = x + 8x[/tex]
ASAP!!! ASAP!!!
What is the volume of the rock???
Answers
Answer:
10 cm³
Step-by-step explanation:
According to Archimedes, if we place an object in water, the rise of the water in mL will be the volume of the object in cm³.
Without the rock, the water measures 20 mL.
With the rock, the water measures 30 mL.
The change here is [tex]30-20=10[/tex], so 10 cm³ is the volume of the rock.
Hope this helped!
The smallest 4-digit number with different digits is ---------. (Don’t use same digit)
Answers
Answer:
The smallest 4-digit number with different digits is 1023.How many integers satisfy the inequality 0<|x|<5
Answers
Answer:
4
Step-by-step explanation:
0</x/<5
0</1, 2, 3, 4/>5
(1,2,3,4) there are 4 numbers that are greater than 0 and less than 5.
Answer:
8
Step-by-step explanation:
All possible answers are 1,2,3,4,-1,-2,-3, and -4. Since we are using the absolute value here, the opposites of the positive values are also included.
I enter the bedroom. There are 34 people. You kill 30. How many people are in the bedroom?
Answers
Answer:
34
Step-by-step explanation:
The dead bodies are still in the room.
Find the HCF of the following numbers using continued division
method:
a. 255,238
b. 1155,462
c. 47,61
d. 115,138
e. 18,45 and 72
Answers
Answer:
a. 17
b. 231
c. 1
d. 23
e. 9
If the area of the base of a cube is 100m, whats the volume
Answers
Answer:
1000 m³
Step-by-step explanation:
The base of a cube is just a square.
The area of a square is [tex]l^2[/tex], where l is the length.
Since we know the area of the base (the square) we can find l easily.
[tex]l^2 = 100\\\\l = \sqrt{100}\\\\l=10[/tex]
Now that we know the length of the sides, we have to take note that a cube has side lengths that are all congruent.
This means the height of the cube is also 10m.
Since the volume of a cube is represented as [tex]l^3[/tex], where l is the length, we can substitute 10 in as [tex]l[/tex] to find it's total volume.
[tex]10^3 = 1000[/tex]
So the volume of this cube is 1000 m³.
Hope this helped!
Find the midpoint of the line segment joining the points R(3,3) and S(-5,5).
Answers
Answer:
(-1,4)
Step-by-step explanation:
Need help asap!! close to running out of time to turn this in!
Answers
One side of a triangle is 3 times the second side. The third side is 13 feet longer than the second side. The perimeter of a triangle is 68 feet. Find the length of each side.
Answers
Answer:
33, 11, 24 feet
Step-by-step explanation:
Let s represent the length of the second side. Then the length of the first side is 3s and the length of the third side is s+13. The perimeter is the sum of side lengths:
(3s) +(s) +(s +13) = 68
5s = 55 . . . . . subtract 13
s = 11 . . . . . . . divide by 5
The side lengths are ...
33, 11, 24 feet