Answer:
[tex] \displaystyle 8[/tex]
Step-by-step explanation:
we would like to compute the following limit
[tex] \displaystyle \lim_{x \to 16} \left( \frac{x - 16}{ \sqrt{x} - 4} \right) [/tex]
if we substitute 16 directly we'd end up
[tex] \displaystyle = \frac{16 - 16}{ \sqrt{16} - 4} [/tex]
[tex] \displaystyle = \frac{0}{ 0} [/tex]
which isn't a good answer now notice that we have a square root on the denominator so we can rationalise the denominator to do so multiply the expression by √x+4/√x+4 which yields:
[tex] \displaystyle \lim_{x \to 16} \left( \frac{x - 16}{ \sqrt{x} - 4} \times \frac{ \sqrt{x} + 4 }{ \sqrt{x} + 4 } \right) [/tex]
simplify which yields:
[tex] \displaystyle \lim_{x \to 16} \left( \frac{(x - 16)( \sqrt{x} + 4)}{ x - 16} \right) [/tex]
we can reduce fraction so that yields:
[tex] \displaystyle \lim_{x \to 16} \left( \frac{ \cancel{(x - 16)}( \sqrt{x} + 4)}{ \cancel{x - 16} } \right) [/tex]
[tex] \displaystyle \lim _{x \to 16} \left( \sqrt{x } + 4\right) [/tex]
now it's safe enough to substitute 16 thus
substitute:
[tex] \displaystyle = \sqrt{16} + 4[/tex]
simplify square root:
[tex] \displaystyle = 4 + 4[/tex]
simplify addition:
[tex] \displaystyle = 8[/tex]
hence,
[tex] \displaystyle \lim_{x \to 16} \left( \frac{x - 16}{ \sqrt{x} - 4} \right) = 8[/tex]
31. The volume in a water drum is halved every 2 days of a drought. If the volume of water
in the drum was initially 1,000,000 gallons, what was the approximate volume after 10
days?
Answer:
30'000 gallons approx
Step-by-step explanation:
day 2 - 500,000 gallons
day 4 - 250,000 gallons
day 6 - 125,000 gallons
day 8 - 62,500 gallons
day 10 - 31,250 gallons
A table tennis ball has a radius of 2 cm. There are 3 table tennis balls stacked on top of one another in a cylinder that has the same diameter as the table tennis balls. The table tennis balls reach the top and bottom of the cylinder. How much volume is left inside the cylinder when the container is full?
Answer:
Volume left = 16π cm³ or 50.265 cm³
Step-by-step explanation:
Let's first find the surface area of the tennis ball.
S.A = (4/3)πr³
Radius of a ball = 2 cm
Thus;
S.A = (4/3)π(2)³
S.A = 32π/3
Since there are 3 radius balls that will make the cylinder full, then;
Surface area of 3 balls = 3 × 32π/3 = 32π
Now, formula for volume of cylinder is;
V = πr²h
r = 2 cm
h = 4 × 3 = 12 (since diameter of tennis ball is 4 cm)
Thus;
V = π × 2² × 12
V = 48π
Thus;
Volume left = Volume of cylinder - surface area of 3 balls = 48π - 32π = 16π cm³ or 50.265 cm³
Can someone please help me with this it’s so confusing
Answer:
B and C
18-10 is 8
6 times 10 is 60
Help me please help me please help me please !!!!!!!!!!!!!
Answer: y = 1/4x - 1.
Step-by-step explanation: This line has a slope (rise over run) of 1/4, and a y-intercept of -1. Plugging those values into slope-intercept form (y = mx + b) gives you the answer.
Which expression is equivalent to
Answer:
8x^12 y^3
Step-by-step explanation:
8x^12 y^3
what additional information is needed to prove the triangles congruent by AAS
Answer:
pq=su
Step-by-step explanation:
its the only one that makes sense
The measures of the angles of a triangle are shown in the figure below. Solve for x.
Answer:
x = 39°
Step-by-step explanation:
51° + 90° = 141°
180° - 141° = x
x = 39°
They often don't label the 90° angle, so watch out for that in the future
which of the following is equal square root of 9 x 4
Answer:
You didn't list any "of the following"
Here are some possible answers
√( 9 x 4) = 3 * 2
√( 9 x 4) = 6
Help meeeee pleaseeeeeeeeeeeeeeeeeeee
Answer:
m<K = 146°
Step-by-step explanation:
From the above information given, we can conclude that ∆JKL is an isosceles triangle with two equal sides, KL and JK. Therefore, the angles opposite each side of KL and JK are congruent to each other. Which are:
<J and <L.
m<J = 17° (given)
Therefore,
m<L = m<J = 17° (base angles of the isosceles ∆)
m<L = 17°
m<K = 180° - (m<J + m<L)
m<K = 180° - (17 + 17)
m<K = 146°
what is 5 pi over three raidans in degrees
Answer:
300 degrees
Step-by-step explanation:
5 pi/3
To change radians to degrees, multiply by 180/pi
5 pi/3 * 180/pi
5/3 * 180
5 * 60
300 degrees
the expanded form of 6,398 is
Answer:
The expanded form of 6,398 is 6000 + 300 + 90 + 8
plsplspls help it's due today and is needed for reports. I'll brainlist you! just do the questions u know and leave the ones u don't idm I'll do it myself but at least do a few. it'll make my day:)
Answer:
[tex]x=10[/tex]
Step-by-step explanation:
For all right triangles, the Pythagorean Theorem states:
[tex]a^2+b^2=c^2[/tex], where [tex]c[/tex] is the hypotenuse, or the longest side, of the right triangle.
Therefore, we have (starting from the blanks):
[tex]x^2+576=676,\\x^2+576-676=676-676,\\x^2=100,\\x=\boxed{10}[/tex]
(−7,−6)y(9,10)(-7,-6)y(9,10)
Answer:
i need more information to answer this question
Step-by-step explanation:
Part A: Drag the factors of 45 and 75 into the correct boxes.
Part B: What is the greatest common factor of 45 and 75? Enter your answer in the box.
Answer:
3 x 5 is the gcf of 45 and 75. gcf(45,75) = 15.
Step-by-step explanation:
hope this helped! yw :}
HELP PLEASE ALSO NO LINKS THANK YOU
Answer:
21
Step-by-step explanation:
(base1+base2)2/ height
Which linear equation best fits the data ?
Answer:
[tex]{ \tt{slope = \frac{2 - 1.5}{40 - 60} }} \\ = - 0.025 \\ \\ { \tt{y = mx + c}} \\ 2 = ( - 0.025 \times 40) + c \\ c = 3 \\ { \bf{ y = - 0.025x + 3}}[/tex]
Tom and friends went to the movie the show started at 2:30pm and ended at 4:15 how long did the movie last Well the movie lasted 1 hour and 45 mins hope this help
Answer:
You are correct, it is 1 hr 45 minutes since 2:30+30 = 3:00 and 1:15 + 3:00 = 4:15. 1:15+30 = 1:45.
Step-by-step explanation:
An airplane took off at a constant angle of elevation. After the plane traveled for 25 miles, it reached an altitude of 5 miles. To the nearest tenth of a degree, what was the angle of elevation?
Answer:
11.5 degrees
Step-by-step explanation:
For future reference trianglecalculator.net is very helpful
The angle of elevation to the nearest tenth of a degree is 11.54°.
What is an angle of elevation?An angle of elevation is defined as the angle between the slant horizontal line of an eye and the object in relation to the baseline called the adjacent.
In trigonometry, the angle of elevation can be determined by using the sine rule.
[tex]\mathbf{sin \ \theta = \dfrac{opp}{hyp} }[/tex]
[tex]\mathbf{sin \ \theta = \dfrac{5}{25} }[/tex]
[tex]\mathbf{ \theta =sin^{-1} (0.2)}[/tex]
[tex]\mathbf{ \theta =11.54^0}[/tex]
Learn more about the angle of elevation here:
https://brainly.com/question/88158
Solve for in the diagram below.
(2x + 45°
7
RO
7 -
Answer:
45°
Step-by-step explanation:
The angles should add to 180°. so we can say 2x+45+x=180
3x+45=180
3x=135
X=45°
Answer:
x = 45°
Step-by-step explanation:
The sum of both angles should add up to 180°, because they are supplementary. Supplementary angles is just another way of saying two angles on a straight line. In order to find the value of x:
Given |
[tex]2x + 45 + x = 180[/tex]
2x + x
Combine like-terms. |
[tex]3x + 45 = 180[/tex]
180 - 45
Subtraction Property of Equality. |
[tex]3x = 135[/tex]
135 / 3
Division Property of Equality. |
[tex]x = 45[/tex]
simplify
x2 + 6 − (3x2 − 2x − 5)
Answer:
- 2x² + 2x + 11
Step-by-step explanation:
Given
x² + 6 - (3x² - 2x - 5) ← distribute parenthesis by - 1
= x² + 6 - 3x² + 2x + 5 ← collect like terms
= - 2x² + 2x + 11
Answer:
Step-by-step explanation:
The train departs from Paris at 2028 and the journey takes 9 hours 10 minutes. Find the the train arrives in Milan
Do the surface area plzzz and u get 25 points and if u Dk don’t answer and no links
Answer:
184
Step-by-step explanation:
A = 2(wl+hl+hw) = 2 · (6 · 2 + 10 · 2 + 10 · 6) = 184
Answer:
SA = 184 m²
Step-by-step explanation:
The opposite faces of the cuboid are congruent , then surface area (SA) is
SA = 2(2 × 6) + 2(6 × 10) + 2(2 × 10)
= 2(12) + 2(60) + 2(20)
= 24 + 120 + 40
= 184 m²
Help me please thank u
Answer:
your answer to this question is C.
The algebraic expression 6x² + 9x + 3 represents the area of a rectangle. What is the area of the
rectangle when x = 3 feet?
a. 51 square feet
b. 60 square feet
c. 66 square feet
d. 84 square feet
this is the easiest question
Answer: [tex]3\dfrac{2}{6}\ h[/tex]
Step-by-step explanation:
Given
Rami practices his saxophone for [tex]\frac{5}{6}[/tex] hour on 4 day each week
So, for a week she practices around
[tex]\Rightarrow \dfrac{5}{6}\times 4\\\\\Rightarrow \dfrac{20}{6}[/tex]
Converting it into mixed fraction
[tex]\Rightarrow \dfrac{20}{6}=\dfrac{18+2}{6}\\\\\Rightarrow 3\dfrac{2}{6}\ h[/tex]
Answer:
33/100
Step-by-step explanation:
The three planes given meet at a point. The planes are 3x+y-2z = 11, 4x-2y+z = -5, x+5y-4z = 33. The intersection is at what point? (Please explain.)
Answer:
(2, 7, 1)
Step-by-step explanation:
We have three equations, and using Gauss-Jordan Elimination, we can solve for x, y, and z
3x + y - 2z = 11
4x - 2y + z = -5
x + 5y - 4z = 33
We can start by taking out the z from all rows except one. To do this, we can work with the second row. I chose the second row because -5 is small and easy to add up with other numbers, and z has no coefficient in this row.
We can add 2 times the second row to the first row and 4 times the second row to the third row to get
11x - 3y = 1
4x - 2y + z = -5
17x -3y = 13
We then have the first and third rows having two variables. Since the y coefficients are the same, we can eliminate the y by adding the negative of the first row to the third row. Our result is then
11x - 3y = 1
4x - 2y + z = -5
6x = 12
From the third row, we can gather that x= 2. We can then plug that into the first row to get
22 -3y = 1
subtract 22 from both sides
-3y = -21
divide both sides by -3
y = 7
We can then plug our x and y values into the second row to get
4(2) - 2(7) + z = -5
8 - 14 + z = -5
-6 + z = -5
add 6 to both sides
z = 1
Our answer is thus (2, 7, 1)
John has 8 cards that spell the word H O M E W O R K. He shuffles them and then places them face down. Assume he returns the card on each occasion.
a) What is the probability that he will choose the letter O?
Answer:
1/4
Step-by-step explanation:
A card is chosen at random from a pack of playing cards. what is the probability that it is either a heart or the queen spades
Answer:
14/52=7/26
favorable outcomes = 14 (heart =13 queen of spades=1)
total outcomes = 52
hope it helps
find the slope of the line that contains 2,2 and -3, 4
Answer:
-2/5
Step-by-step explanation:
your answer is -2/5 because whenever you have two points you can go ahead and just do rise over run and the formula is y1-y2/x1-y1 now you can go ahead and label them so y1 is 2, y2 is 4, x1 is 2 and x2 is -3 and now plug everything in
2-4/2-(-3)
-2/5
Why would the answer be 3.?
Answer: Cause why not?
Step-by-step explanation:
[tex]3(4x-1)=-2x+19+8x-4[/tex]
First combine like terms:
[tex]3(4x-1)=(-2x+8x)+(19-4)\\\\3(4x-1)=6x+15[/tex]
Now distributive property
[tex](3)(4x)-(3)(1)=6x+15\\12x-3=15+6x[/tex]
Additive Property of Equality
[tex]12x-3+3=15+6x+3\\12x=18+6x[/tex]
Subtractive Property of Equality
[tex]12x-6x=18+6x-6x\\6x=18[/tex]
And finally Division Property of Equality
[tex]\frac{6x}{6} =\frac{18}{6} \\x=3[/tex]