Answer:
The x coordinate of P is [tex]\frac{4}{3}[/tex].
Step-by-step explanation:
Let is find the rate of change of the equation in time, which consists in a composite differentiation. That is:
[tex]\frac{dy}{dt} = 2\cdot x \cdot \frac{dx}{dt} -2\cdot \frac{dx}{dt}[/tex]
According to the statement of the problem, these variables are known:
[tex]\frac{dx}{dt} = 6[/tex] and [tex]\frac{dy}{dt} = 4[/tex]
Hence, the x coordinate of P is found by direct substitution:
[tex]4 = 2\cdot x \cdot (6)-2\cdot (6)[/tex]
[tex]4 = 12\cdot x -12[/tex]
[tex]x = \frac{4}{3}[/tex]
The x coordinate of P is [tex]\frac{4}{3}[/tex].
A cylindrical tank whose diameter is 1.4 metres and height 80 cm is initially empty. Water whose volume is 492.8 litres is poured into the tank. Determine the fraction of the tank filled with water. (4 mark
Answer:
The fraction filled with water is 7/40
Step-by-step explanation:
Okay.
Here we start by calculating the volume of the cylindrical tank.
Mathematically, that would be;
V = π * r^2 * h
From the question
r = 80 cm = 80/100 = 0.8 meters
h = 1.4 meters
π = 22/7
Plugging these values into the volume equation, we have;
V = 22/7 * 0.8 * 0.8 * 1.4 = 2.816 m^3
But mathematically;
1 m^3 = 1000 liters
So 2.816 m^3 = 2.816 * 1000 = 2816 liters
So the fraction filled with water will be;
492.8/2816 = 0.175 = 175/1000 = 7/40
PLEASE ANSWER QUICKLY ASAP
READ QUESTIONS CAREFULLY
Answer:
Increase in profit = 531.52
Step-by-step explanation:
I'll take your word for it.
What you'd need to do for each kind of pizza and price, multiply the number sold and profit/loss for each, and add them up.
Calculations have been tabulated and shown in the attached diagram.
Answer
Increase in profit
= 2221.88 - 1690.36
= 531.52
Write the other side of this equation so it's true for all values of x: 1/2(6x-10)-x=?
Answer:
2x 5
Step-by-step explanation:
1/2(6x - 10) - x =
= 3x - 5 - x
= 2x - 5
The other side of the given equation so it's true for all values of x is 2x-5.
Given that, 1/2(6x-10)-x.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Now, 6x/2 - 10/2 -x
= 3x-5-2
= 2x-5
Therefore, the other side of the given equation so it's true for all values of x is 2x-5.
To learn more about an equation visit:
https://brainly.com/question/14686792.
#SPJ2
Evaluate -3(8).
I know the answer is -24 but I don’t know who to work it out, can someone please help me
Answer:
-24
Step-by-step explanation:
-3 multiply 8 = -24
Because when ever you multiply a negative number with a positive number result will always be negative and 3 multiply 8 is 24.
Answer: -24
Step-by-step explanation: When you're asked to multiply
positives and negatives together, the rules are simple.
positive times a positive is a positive
positive times a negative is a negative
negative times a positive is a negative
negative times a negative is a positive
One way that I think will help you is to think
about the problem in terms of the signs.
If the signs are the same, the product will always be positive.
For example, (+3) · (+6) = +18 and (-6) · (-2) = +12.
If the signs are different, the product is negative.
So (+6) · (-4) is -24 and (-10) · (+5) is -50.
So don't get caught up on the signs.
Do the problem first, then determine if the
signs are the same or if they are different.
the maximum value of 3/5sinx-12cosx+19
Answer:
Step-by-step explanation:
The given trigonometric expression is :
11 cos^2 x +3 sin^2 x+6sinx cosx +5
or, we can write it as,
(9 cos^2 x + 2 cos^2 x) + (2 sin^2 x + sin^2 x) + 6sinx cosx +5
Again, after rearranging the terms, we can write the whole expression as,
(9 cos^2 x + sin^2 x + 6sinx cosx) + (2 cos^2 x + 2 sin^2 x) + 5
Then if you factor the following underlined section as you would with a polynomial:
(9 cos^2 x + sin^2 x + 6sinx cosx) + (2 cos^2 x + 2 sin^2 x) + 5
You get:
(3 cos x + sin x)^2 + 2 (cos^2 x + sin ^2 x) + 5
Now, the term inside the second bracket (cos^2 x + sin ^2 x) is a very popular trigonometric identity and it's value is equal to one.
So, now the whole expression becomes,
(3 cos x + sin x)^2 +7
Now, the maximum and the minimum value of the whole expression depends upon the maximum and the minimum value of the term (3 cos x + sin x), which is of the form (a cosx + b sinx),
The maximum and minimum value of (a cosx + b sinx) is relatively easy to find.
So, I've attached a screenshot from a relevant document below:
Here, a=3 and b=1,
So, R= √10
As the value of cosine of any angle lies between -1 to 1, so the value of the value of expression cos(x − α) will lie between -1 to 1.
Hence, the maximum and the minimum value of (a cosx + b sinx) will be -R and R and all the values of the expression will lie between them.
i.e., in our case between (-√10) to √10.
Again, coming back to our original expression,
(3 cos x + sin x)^2 +7
The value of the term in bracket will lie between (-√10) and √10.
But, there is a catch here, as the squares of negative terms come out be positive, hence we can't take the negative term to find the minimum value of our expression. the minimum value of the expression will be at the minimum non-negative value in the range, which is zero.
So, the minimum value will be,
(0)^2 + 7=7
and the maximum value will be,
(√10)^2 +7 = 17
a hotel manager wants miriam to tile their lobby using the dame design she created for Mr.Rivera.The lobby measures 45 feet by 45 feet. he wants the outer edge to be the same color as the center tile. will this occur ? justify your answer
Answer:
Yes it will occur
Step-by-step explanation:
The lobby measures 45 feet by 45 feet
Area of the lobby = 45 * 45
=2025 ft^2
So, the lobby has 2025 tiles
subtract 1 black tile in the center
2025 tiles - 1 black tile =2024 tiles
The number of blue tiles and black tiles is 2024 tiles
He wants the outer edge to be the same color as the center tile so, divide by 2
2024/2 = 1012 tiles
The number of tiles in the outer edge is 1012 tiles and the number of tiles in the center is 1012 tiles
CAN ANYBODY HELP ME OUT
Answer:
Correct option is
b. If two sides and one included angle are equal in triangles PQS and PRS, then their corresponding sides are also equal.
Step-by-step explanation:
Here, we are given the line RQ, which is divided in two equal parts by a line PS which is perpendicular to RQ.
The foot S of PS is on the line RQ.
First of all, let us do a construction here.
Join the point R with P and P with Q.
Please refer to the attached image.
Now, let us consider the triangles PQS and PRS:
Side QS = RS (as given)[tex]\angle PSR = \angle PSQ = 90^\circ[/tex]Side PS = PS (Common side in both the triangles)Now, Two sides and the angle included between the two triangles are equal.
So by SAS congruence we can say that [tex]\triangle PRS \cong \triangle PQS[/tex]
Therefore, the corresponding sides will also be equal.
RP = QP
RP is the distance between R and P.
QP is the distance between Q and P.
Hence, to prove that P is equidistant from R and Q, we have proved that:
b. If two sides and one included angle are equal in triangles PQS and PRS, then their corresponding sides are also equal.
A. X>0
B. xis all real numbers.
C. O sxs 5
D. -5 sxs 5
Answer:
B
Step-by-step explanation:
The domain of a function is all of the x values of a function. Since there seem to be no constraints on the values of x (we know this because the function is continuous and it goes on forever in both sides), the answer is B.
Answer:
B. All real numbers
Step-by-step explanation:
Hey there!
Well the domain is all the x-values in the graph and by looking at where the lines are going we can tell that the graph domain is all real numbers.
Hope this helps :)
Suppose the graph in part A can be represented by the function f(x)=1.5x+750/x . What is the domain of this function? Consider the context of the function in your answer.
Answer:
Domain:
( − ∞ , 0 ) ∪ ( 0 , ∞ ) , { x | x ≠ 0 }
Step-by-step explanation:
i used math. way for help
Factorise : x²-17x+ 60 Step by Step
Answer:
Step-by-step explanation:
x^2 - 17 x + 60
we should find two numbers such that their sum is equal to -17 and product is equal to 60
The two numbers are -12 and -5
now, x^2 - 12 x - 5 x + 60 { splitting the middle term }
x ( x- 12 ) - 5 ( x - 12 )
= ( x - 5 ) ( x - 12 )
hope this helps
plz mark as brainliest !!!!!!
Answer:
x² - 17x + 60 = (x - 12)(x - 5)Step-by-step explanation:
[tex]x^2-17x+60\quad \implies\quad a=1\,,\quad b=-17\,,\quad c=60\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x=\dfrac{-(-17)\pm\sqrt{(-17)^2-4\cdot1\cdot60}}{2\cdot1}=\dfrac{17\pm\sqrt{289-240}}{2}=\dfrac{17\pm\sqrt{49}}{2}\\\\x_1=\dfrac{17-7}{2}=5\quad,\qquad x_2=\dfrac{17+7}{2}=12\\\\\\x^2-17x+60=(x-5)(x-12)[/tex]
or:
x² - 17x + 60 =
= x² - 12x - 5x +60 =
= x(x - 12) - 5(x - 12) =
= (x - 12)(x - 5)
Let f(x) = 4x - 5 and g(x) = 3x + 7. Find f(x) + g(x) and state its domain.
Answer:
7x + 2
Step-by-step explanation:
Answer:
All real numbers
Step-by-step explanation:
Adding f(x) and g(x) together gets you, (4x-5) + (3x-7) = 7x - 12
If you graph this function you get a slanted line, which extends forever so the domain will be all real numbers.
Write this expression as a complex number in standard form
Answer:
[tex]81+144i[/tex]
Step-by-step explanation:
We want to simplify:
[tex]\displaystyle (-3\sqrt{-81})(-5+\sqrt{-9}) + 9i[/tex]
Recall that:
[tex]\displaystyle \sqrt{-a} = i\sqrt{a}[/tex]
Therefore:
[tex]\displaystyle \begin{aligned} (-3\sqrt{-81})(-5+\sqrt{-9}) + 9i & = (-3i\sqrt{81})(-5+i\sqrt{9})+9i \\ \\ &= -(3i(9))(-5+i(3))+9i \\ \\ & = -27i(-5+3i)+9i \\ \\ & = 135i -81i^2 + 9i \\ \\ & = 144i - 81i^2 \\ \\ & = 81+144i\end{aligned}[/tex]
Note that i² = -1.
In conclusion:
[tex]\displaystyle (-3\sqrt{-81})(-5+\sqrt{-9})+9i = 81 + 144i[/tex]
If f(x)= Square root of X +12 and g(x)= 2 Square root of X what is the value of (f-g)(144)
Answer:
0
Step-by-step explanation:
A scout troop consists of 10 boys and 10 girls. The total weight of their backpacks is 600 pounds. All the boys have to carry backpacks that weigh the same amount. All the girls, too, must carry bags of equal weight, but the girls' backpacks are 1.5 times lighter than the boys' backpacks. How heavy is one boy's backpack?
Answer:
36 lbs
Step-by-step explanation:
let the weight of each boy's backpack be B and the weight of each girl's backpack be G.
Given that the total weight of all (i.e 10 boys' and 10 girls') backpacks equals 600 lbs, i.e.
10B + 10G = 600 (simplifying by dividing both sides by 10)
B + G = 60 ------- eq 1
Also given that a girl's backpack is 1.5 times LESS than a boy's backpack.
written another way, we can say that a boy's backpack is 1.5 times MORE than a girl's backpack, or:
B = 1.5G (rearranging)
B - 1.5G = 0 ------ eq 2
We can solve eq 1 and eq 2 by elimination,
(eq 1) - (eq 2)
(B + G) - (B - 1.5G) = 60 - 0
B + G - B + 1.5G = 60
G + 1.5G = 60
2.5G = 60 (divide both sides by 2.5)
G = 60 / 2.5
G = 24 lbs (substitute this into equation 1)
B + G = 60
B + 24 = 60
B = 60 - 24
B = 36 lbs
Which of the following is true? Tangent is positive in Quadrant I. Sine is negative in Quadrant II. Cosine is positive in Quadrant III. Sine is positive in Quadrant IV.
Answer:
A
Step-by-step explanation:
I had this question and got it right the user above explains it in detail
(3)/(22)+(-(1)/(11) find the sum without use of a number line
Answer:
1/22
Step-by-step explanation:
Simplify it.
It becomes 3/22-1/11
Change the denominator to 22 becasue that is the LCM.
It becomes 3/22-2/22 which is 1/22. :)
I REALLY NEED HELP WITH THESE 5 QUESTIONS!!!!!!!!!
Answer:
is -5,-3
Step-by-step explanation:
set up the tablet and done
2x(7a+8a)-5 +56*2÷3
Answer:
Below
Step-by-step explanation:
● 2x(7a+8a) -5+56×2÷3
● 14ax + 8a -5 +56×2÷3
When you have multiplication and division go from left to right
● 14ax + 8a -5 +112÷3
● 14ax + 8a -5 +112/3
● 14ax + 8a - 15/3 + 112/3
● 14ax + 8a + 97/3
how many eighth rests are in a half rest?
Find an equation of the line with x-intercept 8 and y-intercept 4
Answer:
y = -1/2x + 4
Step-by-step explanation:
We have two points ( 8,0) and ( 0,4)
We can find the slope
m =(y2-y1)/(x2-x1)
= (4-0)/(0-8)
4/-8
-1/2
We can use the slope intercept form
y = mx+b where m is the slope and b is the y intercept
y = -1/2x + 4
Answer:
Step-by-step explanation:
eq. of line with intercepts a and b is
[tex]\frac{x}{a} +\frac{y}{b} =1\\here ~eq. ~of ~line~ is ~ \frac{x}{8} +\frac{y}{4} =1\\or x+2y=8\\[/tex]
Add the matrices to find the answer.
Answer:
[tex]\large \boxed{\mathrm{Option \ C}}[/tex]
Step-by-step explanation:
[tex]{\mathrm{view \ attachment}}[/tex]
I need help with 3 and 4
Answer:
Step-by-step explanation:
3) G
Step-by-step explanation:
Q(-1,-1) R(3,1) S(2,-4)
x+2 y+3 translation then rotation 180 (x,y) be (-x,-y)
Q -1+2 -1+3 (1,2) (-1,-2)
R 3+2 1+3 (5,4) (-5,-4)
S 2+2 -4+3 (4,-1)
Please I Need Help :(
Answer:
D, 9^4 * 8^4
Step-by-step explanation:
The rule is whenever you have multiplication inside arentheses and it is raised to a power, you distribute the power to both the number s and solve.
I confirmed D is right on a calculator also.
Answer:
D
Step-by-step explanation:
Observe how the land division was planned for the preparation of a vegetable garden.
In it, lettuce, tomatoes, carrots, beets and corn will be planted.
Determine the monomial that represents the measure:
1-lettuce
2-beets
3-tomato
4-corn
5-carrot
Answer:
1-lettuce 4ab x 12ab = 48a²b²
2-beets 3ab x 3ab = 9a²b²
3-tomato 4ab x 5ab = 20a²b²
4-corn 2ab x 3ab = 6a²b²
5-carrot 12ab x 3ab = 36a²b²
Step-by-step explanation:
What is the measure of
Answer:
40 degrees.
Step-by-step explanation:
Rotations are a rigid transformation and therefore preserve size and angles.
2x+3-x=7
what is the answer to this by using solving multistep equations using combining like terms
Hey there! I'm happy to help!
Like terms are numbers with the same variable and same power. 5 and 7 are like terms because they have no variable. 6x and 6y are not because they have different variables. 7x² and 6y² are also not like terms because they have different variables. 7x and 5x are like terms, and 5y³ and 9y³ are like terms.
We see that 2x and -x have the same variables. We can then combine them.
2x-x=x
Now we have x+3=7.
We subtract 3 from both sides, giving us x=4.
Have a wonderful day! :D
find the sum of partial fraction for x^4/(x-1)(x²-4)
Answer:
see attachment
Step-by-step explanation:
If the production rate is 975 brownies per hour at a bakery, how many brownies will be produced in an 8 hour shift?
Answer:
[tex]\large \boxed{\mathrm{7800 \ brownies}}[/tex]
Step-by-step explanation:
975 brownies are produced per 1 hour.
To find how many brownies are produced in 8 hours, multiply the brownies amount by the hours.
975 × 8 = 7800
7800 brownies will be produced in an 8 hour shift.
Answer:
the answer is 7800
Step-by-step explanation:
975 brownies are created per 60 minutes.
To discover what number of brownies are created in 8 hours, duplicate the brownies sum continuously.
975 × 8 = 7800
7800 brownies will be created in a 8 hour move.
The drama club is selling tickets to its play. An adult ticket costs $15 and a student ticket costs $11. The auditorium will seat 300 ticket-holders. The drama club wants to collect at least $3630 from ticket sales.
Answer:
83 adult tickets and 217 student tickets.
Step-by-step explanation:
Let number of adult tickets sold = [tex]x[/tex]
Given that total number of tickets = 300
So, number of student tickets = 300 - [tex]x[/tex]
Cost of adult ticket = $15
Cost of student ticket = $11
Total collection from adult tickets = $[tex]15x[/tex]
Total collection from student tickets = [tex](300-x)\times 11 = 3300-11x[/tex]
Given that overall collection = $3630
[tex]15x+(3300-11x) = 3630\\\Rightarrow 15x-11x=3630-3300\\\Rightarrow 4x = 330\\\Rightarrow x = 82.5[/tex]
So, for atleast $3630 collection, there should be 83 adult tickets and (300-83 = 217 student tickets.
Now , collection = $3632
A bookstore decides to divide its space into three sections: nonfiction books, novels, and stationery. The bookstore wants to devote 1/6 of its space to stationery. If the total area of the bookstore is 288 square feet, and the stationery section will be 12 feet long, how wide will the stationery section be?
Answer:
Stationery section will be 4 feet wide.
Step-by-step explanation:
Total area of bookstore = 288 sq ft
Area to be devoted to stationery = [tex]\frac{1}6[/tex] of total area = [tex]\frac{1}{6} \times 288 = 48\ sq\ ft[/tex]
Length of stationery section = 12 ft
To find:
Width of stationery section = ?
Solution:
First of all, let us have a look at the area of rectangle:
[tex]A = Length \times Width[/tex]
Here, we are given the length for stationery section and area of stationery section has been calculated above.
And we have to find the Width of stationery section.
So, let us put the two values to find the third value.
[tex]\Rightarrow 48 = 12 \times Width\\\Rightarrow Width = \dfrac{48}{12}\\\Rightarrow \bold{Width = 4\ ft}[/tex]
So, the answer is:
Stationery section will be 4 feet wide.
