Answer:
The answer is "0.45385".
Step-by-step explanation:
The time is taken to reach the coast [tex]= \frac{\sqrt{(2^2 + x^2)}}{4}[/tex]
The time is taken to reach Q after reaching the coast [tex]= \frac{\sqrt{(1 + (3-x)^2)}}{4}[/tex]
Total time, [tex]T= \frac{\sqrt{(1 + (3-x)^2)}}{4}+ \frac{\sqrt{(1 + (3-x)^2)}}{4}[/tex]
This has to be minimum,
[tex]\to \frac{dt}{dx} = 0[/tex]
[tex]\to \frac{\sqrt{(2^2 + x^2)}}{2} + \frac{\sqrt{1 + (3-x)^2}}{3}\\\\ \frac{x}{4}\sqrt{(4+x^2)} + \frac{(x-3)}{(4\sqrt{(x^2-6x+10)}} = 0\\\\\frac{x^2}{16} \times (4+x^2) = \frac{(x-3)^2}{16 \times (x^2-6x+10)}\\\\x^2(4+x^2) = \frac{(x-3)^2}{(x^2-6x+10)}\\\\4x^2+x^4 = \frac{ x^2+9-6x}{(x^2-6x+10)}\\\\ 4x^2+x^4(x^2-6x+10) = x^2+9-6x\\\\4x^4-24x^3+40x^2+x^6-6x^5+10x^4= x^2+9-6x\\\\x^6-6x^5+ 14x^4-24x^3+39x^2+6x-9=0\\\\[/tex]
x=0.45385
What is the area, height, and base of this triangle?
Grade:
Subject: Ma
Stream: Advanced
Number of P
End of Term 1 Exam
Academic Year 2018/2019
Part 1
Circle the letter corresponding to the correct answer.
1) Write an algebraic expression for "3 times X squared minus 4 times X"
a) 3x - 4x?
c) 3x² - 4
b) 3x - 4x
d) 3x2 - 4x
What is the value of x?
Enter your answer in the box
672
X=
D
60°
х
Basic
45°
А.
B
9514 1404 393
Answer:
x = 3
Step-by-step explanation:
It is convenient to remember the ratios of side lengths of these "special triangles."
The side ratios of ΔABC are 1 : 1 : √2, so BC = AC/√2 = 6.
The side ratios of ΔBCD are 1 : √3 : 2, so BD = BC/2 = 6/2 = 3.
The value of x is 3.
Item 2
Multiply. Write the answer in simplest form.
3/7×1/4=
Answer:
in multiplication we just multiply
Step-by-step explanation:
3/7×1/4
3/28
Chris has a collection of dimes and quarters worth $4.25. If she has 22 coins total, how many quarters does she have?
Given:
Chris has a collection of dimes and quarters worth $4.25.
To number of coins = 22
To find:
The number of quarters.
Solution:
Let x be the number of dimes and y be the number of quarters.
Total coins : [tex]x+y=22[/tex] ...(i)
we know that, 1 dime = $0.10 and 1 quarter = $0.25.
Total value : [tex]0.10x+0.25y=4.25[/tex] ...(ii)
Multiply equation (i) by 0.10 and subtract the result form (ii).
[tex]0.10x+0.25y-0.10(x+y)=4.25-0.10(22)[/tex]
[tex]0.10x+0.25y-0.10x-0.10y=4.25-2.20[/tex]
[tex]0.15y=2.05[/tex]
Divide both sides by 0.15.
[tex]y=\dfrac{2.05}{0.15}[/tex]
[tex]y=13.6667[/tex]
Number of quarter cannot be a decimal value.
[tex]y\approx 17[/tex]
Therefore, the number of quarter is about 17.
Find the unit rate. 12 laps in 30minutes.
Asking for fraction
Answer:
4/10 maybe cuz 12 divided by 30 is 0.4 and 0.4 would be 4/10
Graph a line with a slope of
−
2
5
−
5
2
minus, start fraction, 2, divided by, 5, end fraction that contains the point
(
−
3
,
5
)
(−3,5)
I need help
1/2 + 1/3
Answer:
5/6
Step-by-step explanation:
1/2x3= 3/6
1/3x2=2/6
3/6+2/6=5/6
Find the value of X.
Geraldo has 3 fewer marbles than Yan. Together, they have 21 marbles. Which equation
represents this situation?
x + (3 - x) = 21, where x is the number of marbles Geraldo has
x + (3 - x) = 21, where x is the number of marbles Yan has
x + (x - 3) = 21, where x is the number of marbles Yan has
x + (x - 3) = 21, where x is the number of marbles Geraldo has
Done
My Progress >
Answer:
x + (x-3) = 21
x + x - 3 = 21
2 x - 3 = 21
Explanation:
In this problem, let us first analyze the situation. It says here that Geraldo and Yan both had marbles of their own. The problem states that together, they have a total of 21 marbles. However, we know here from the problem that they have different number of marbles each. Geraldo seems to have lesser number of marbles than Yan. Yan have three marbles more than Geraldo.
We can write the equation starting from assigning the unknown.
We'll use x.
x is the number of marbles that Yan have.
if x is Yan's, then, we can say that x-3 is Geraldo's.
Put them together into the equation.
Yan's plus Geraldo's is equal to 21.
Substitute using the represented unknowns.
x + (x-3) = 21.
In solving, we can also rule out that:
x + x - 3 = 21
2 x - 3 = 21
2 x = 21 + 3
2 x = 24
x = 12
x - 3 = 9
Yan has 12 marbles
and Geraldo has 9 marbles.
Answer: X+(X-3)=21 or C
can someone help me answer this question please!!
Answer:
i think its A
Step-by-step explanation:
3y + 6x + 2x + 7y
simply the given expression
Answer:
so the answer is 8x+10y
Step-by-step explanation:
since we have to combine like terms like
3y+7y = 10y
and 6x + 2x= 8x
hope this helps!1
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Answer:
yes
Step-by-step explanation:
A= 20 square root of 2
B= 5
C=20
D=10
which represents the area of the figure
ASAP PLS
The Answer is B so pick it.
Answer:
What does a goat say?BBBBBBB
Step-by-step explanation:
Suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in its tank. When carrying 15 gallons of fuel, the airplane weighs 1984 pounds. When carrying 40 gallons of fuel, it weighs 2124 pounds. How much does the airplane weigh if it is carrying 50 gallons of fuel?
The equation 9 y minus 12 x = 36 is written in standard form. What is the first step when writing an equivalent equation which solves for y?
Answer:
9y-12x=36
9y=36+12x
y=(36+12x)÷9
Answer: y=8 and x=3
Example: Because 9*8=72 and 12*3=36
72-36=36
If y= 1-x+x²/1+x-x² than how about y'=?
This question is about derived function.
Answer:
as
[tex]\frac{d}{dx}\left(1-x+\frac{x^2}{1}+x-x^2\right)=0[/tex]
so
[tex]y'=0[/tex]
Step-by-step explanation:
Given the function
[tex]y=\:1-x+\frac{x^2}{1}+x-x^2[/tex]
Taking derivative
[tex]\frac{d}{dx}\left(1-x+\frac{x^2}{1}+x-x^2\right)[/tex]
[tex]\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'[/tex]
[tex]=\frac{d}{dx}\left(1\right)-\frac{d}{dx}\left(x\right)+\frac{d}{dx}\left(\frac{x^2}{1}\right)+\frac{d}{dx}\left(x\right)-\frac{d}{dx}\left(x^2\right)[/tex]
as
[tex]\frac{d}{dx}\left(1\right)=0[/tex] ∵ [tex]\mathrm{Derivative\:of\:a\:constant}:\quad \frac{d}{dx}\left(a\right)=0[/tex]
[tex]\frac{d}{dx}\left(x\right)=1[/tex] ∵ [tex]\mathrm{Apply\:the\:common\:derivative}:\quad \frac{d}{dx}\left(x\right)=1[/tex]
[tex]\frac{d}{dx}\left(\frac{x^2}{1}\right)=2x[/tex] ∵ [tex]\mathrm{Apply\:the\:Power\:Rule}:\quad \frac{d}{dx}\left(x^a\right)=a\cdot x^{a-1}[/tex]
[tex]\frac{d}{dx}\left(x\right)=1[/tex] ∵ [tex]\mathrm{Apply\:the\:common\:derivative}:\quad \frac{d}{dx}\left(x\right)=1[/tex]
[tex]\frac{d}{dx}\left(\frac{x^2}{1}\right)=2x[/tex] ∵ [tex]\mathrm{Apply\:the\:Power\:Rule}:\quad \frac{d}{dx}\left(x^a\right)=a\cdot x^{a-1}[/tex]
substituting all the values in the expression
[tex]=\frac{d}{dx}\left(1\right)-\frac{d}{dx}\left(x\right)+\frac{d}{dx}\left(\frac{x^2}{1}\right)+\frac{d}{dx}\left(x\right)-\frac{d}{dx}\left(x^2\right)[/tex]
[tex]=0-1+2x+1-2x[/tex]
[tex]=0[/tex]
Hence,
[tex]\frac{d}{dx}\left(1-x+\frac{x^2}{1}+x-x^2\right)=0[/tex]
Therefore,
[tex]y'=0[/tex]
help me out really fast pleaseee
Distributive because he changed the fractions to the way it would go.
Find the slope of the line through the
given points: (5,-4) & (-1,-4).
Answer:
m=0
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
Since -4-(-4)=0, we know that the slope has to be zero since the numerator is zero.
HTH :)
Will give brainliest!!!!
Explain how solving -7y > 161 is different from solving 7y > -161.
To solve -7y > 161, we divide both sides by -7 and we get y < -23. The inequality sign flipped because we divided both sides by a negative number.
To solve 7y > -161, we divide both sides by 7 and it leads to y > -23. The inequality sign does not flip in this case, because we are not dividing both sides by a negative number.
The similarities is that we end up with -23 on the right side, but the inequality signs are different.
What is the approximate value of x? Round to the nearest tenth
Answer:
10
Step-by-step explanation:
Two scuba divers are swimming below sea level. The locations of the divers can be represented by -30 feet and -42 feet. Which measure represents the location that is closest to sea level.
Answer:
-30 feet
Step-by-step explanation:
it is -30 feet because that one is closest to sea level because -42 feet is -12 feet more than -30 feet. plsss give me brainliest plssss
What is the answers help me please part A B C
Giving extra points
Correct answer
Answer:
A, 38, 40
Step-by-step explanation:
a. A has to be the first graph because it starts at $ 25 and it rises as more work needs to get done
b.if you go from 50 up until you get to the line, then look left at the axis is about $38
c. C=25+s*0.25, substitute c=35 and find s
35=25+s*0.25 subtreact 25 from both sides
35-25= s*0.25
10=s*0.25 divide both sides by 0.25
10/0.25=s
40=s
50 points, need help ASAP
Solve this system of equations, then determine what y equals.
x + 5y= 7
2x + 4y = -4
y=-18
y=3
y=8
y=-8
Answer: [tex]y = 3[/tex]
1. First, solve for unknown x.
[tex](x+5y=7)2[/tex]
2. Balance the equation.
[tex]2x+10y=14[/tex]
[tex]\mathrm {2x + 4y = -4}[/tex]
3. Now, we subtract.
[tex]6y = 18[/tex]
[tex]6[/tex] × [tex]3 = 18[/tex]
4. Finally, divide.
[tex]18/6=3[/tex]
6. The Awesome Bowl Factory makes two kinds of bowls. They produce a
basic bowl every 9 minutes and a gigantic bowl every 12 minutes. They
start at 8:00 A.M. At what time are the basic bowl and the gigantic bowl
first produced together?
Answer: 8.36 a.m
Step-by-step explanation:
To solve this, first we need to calculate the lowest common multiple of 9 and 12.
Multiples of 9 = 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108.
Multiples of 12 = 12, 24, 36, 48, 60, 72, 84, 96, 108, 120.
Here, the lowest common multiple = 36
Therefore, we will add 8.00am plus 36 minutes. This will be:
= 8:00 a.m + 36 minutes
= 8.36 am
The time that the basic bowl and the gigantic bowl are first produced together is 8.36 am.
Find the lcm for 96 and 24
Answer: 96
Step-by-step explanation:
Michael spent $210 on school supplies and books. This amount was 30% of his savings.
How much was his savings?
8x^(2)+16x=42 completeing the square
Brandon enters bike races.
He bikes 8 /2 miles every 1/2 hour.
How fast did he go
Answer:
He goes 8 miles an hour
Step-by-step explanation:
8/2 is equal to 4. If Brandon bikes 4 miles in half an hour and keeps a constant speed he ends up biking 8 miles in an hour since two halves of an hour make one.