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]
Please help with my math! Question number 2
Answer:
17.804
Step-by-step explanation:
Pythagorean theorem. 14^2 + 11^2 = c^2
Jacob wants to enlarge a 4 in. By 6 in. Photo so that the longer side will be 14 in. How long will the shorter side be? (MUST SHOW WORK) HINT: Refer to your notes on Scale Drawings.
Answer: 9.3 in.
Step-by-step explanation:
Jacob wants to enlarge the larger side of the photo which is the 6 in. part, to becomes 14 in.
This means that Jacob wants to increase the larger side by a scale factor of:
= Length of enlarged picture / Length of original
= 14 / 6
= 2.33
2.33 is therefore the scale factor.
The shorter side will also increase by this same scale factor:
= 4 * 2.33
= 9.3 in.
Out of 260 racers who started the marathon, 235 completed the race, 17 gave up, and 8 were disqualified. What percentage did not complete the marathon? Round your answer to the nearest tenth of a percent.
Answer:
9.6% or 9.7% did not finish
Step-by-step explanation:
You can solve this 2 different ways:
First way: 17+8=25, so 25 out of 260 did not complete. 25/260=0.096, or 9.6% did not finish.
Second way: 235 out of 260 finished. 235/260=0.903, or 90.3% finished. 100-90.3= 9.7, which is almost exactly equal to our first answer.
They can't be the same because 25/260 and 235/260 are very random decimals, so the answer is 9.6% to 9.7% :)
What is the total SURFACE AREA of a cylinder with a radius of 5 cm and a height of 7 cm?
Answer:
SA=376.9911184cm^2
Step-by-step explanation:
SA=2πrh+2πr^2
376.9911184cm^2=(2*π*5*7)+(2*π*5^2)
One year, the population of a city was 99,000. Several years later it was 82,170. Find the percent decrease.
PLEASE HELP DUE TONIGHT (W/ WORK IF POSSIBLE) THANK YOU
Cuanto interes ganara lesli si presta 5000 L a pagar en tres años con un interés simple anual de 5%
Answer:
Amount of simple interest in three year = 750
Step-by-step explanation:
Given:
Amount invested = 5,000
Number of year = 3 year
Rate of interest = 5% Annually
Find:
Amount of simple interest in three year
Computation:
Simple interest = (P){R)(T)
Amount of simple interest in three year = (5,000)(3)(5%)
Amount of simple interest in three year = (5,000)(3)(0.05)
Amount of simple interest in three year = (5,000)(0.15)
Amount of simple interest in three year = 750
What is the value of m in the equation {m-án=16, when n = 8?
A 20
B 32
C 44
D 48
Answer:
32
Step-by-step explanation:
m-án=16, when n = 8
which of the following is equivalent to 2cos^2(x) - cos(2x)? A. sin(2x) B. Sin^2(x) C. 1 D. 2
Answer:
C. 1
Step-by-step explanation:
2cos²(x) - cos(2x) = 1
Answer:
C
Step-by-step explanation:
Using the identity
cos2x = 2cos²x - 1 , then
2cos²x = cos2x + 1
Given
2cos²x - cos2x
= cos2x + 1 - cos2x
= 1 → C
PLEASE HELP ME PLS PLS!
i need help please i’m confused
find the length of each side of an equilateral triangle whose perimeter is 36m
Answer:
12m
Step-by-step explanation:
36÷3=12
Hope this helps! :)
Help plz I dont get it
How many times larger than
(15 + 10) is 8 x (15 + 10)?
Answer:
8 times larger
Step-by-step explanation:
(15+10) is the singular equation alone. Muiltiply it by 8, and it's 8 times larger then the initial singular expression. Therefore, the answer is 8 times larger.
Please help fast! The table shows the results of spinning a spinner several times
Out come A B C D E
frequency 2 4 3 1 2
What is the experimental probability of spinning a c or a d?
2/5
1/48
4/5
1/3
Answer:
2/5
hope it helps
Thank you
A(n) ___ expression is an expression that contains a radical symbol.
A.exponential
B.constant
C.polynomial
D.variable
F.radical
Answer:
radical
Step-by-step explanation:
What is the diameter?
Answer:
16 inches
Step-by-step explanation:
c = πd
50.26 = 3.14 * d
Divide both sides by 3.14
d = 16.0
16 inches
Answer:
The diameter is 16 inches
Nine split into four groups is two, with a ___ of one.
My mama got me doing freaking school work pls help me out
Answer:
x=50
Step-by-step explanation:
corresponding angles
Can 17, 9, and 11 be the side lengths of a triangle?
Answer:
No it cant
Step-by-step explanation:
You have to use the Pythagoras theorem which is a^2 + b^2 = c^2. So 9^2 + 11^2= 202. Then 17 is the hypotenuse so 17^2= 289. They are not equal so they are not.
Find the volume of the cylinder round your answer to the nearest tenth.
Answer:
V = 17362.9 ft^3 using 3.14 for the approximation
17371.8 ft^3 using the pi button
Step-by-step explanation:
V = pi r^2 h where r is the radius and h is the height
V = pi (12)^2 ( 38.4)
V =pi ( 144) 38.4
5529.6pi
Letting pi be 3.14
V = 5529.6 (3.14)
V =17362.944 ft^3
Rounding to the nearest tenth
V = 17362.9 ft^3
Letting pi = pi button
V =17371.75074 or to the nearest tenth 17371.8 ft^3
convert the decimal number 356 to a Quinary number
Answer : Yes the answer to your question is 2411.
Explanation : how I got the answer
To convert decimal number 356.625, we convert its integer and fraction part individually and then add them to get the equivalent quinary number, as below:
To convert integer 356 to quinary, follow these steps:
Divide 356 by 5 keeping notice of the quotient and the remainder. Continue dividing the quotient by 2 until you get a quotient of zero.
Then just write out the remainders in the reverse order to get the equivalent quinary number.
356 / 5 = 71 with remainder 1
71 / 5 = 14 with remainder 1
14 / 5 = 2 with remainder 4
2 / 5 = 0 with remainder 2
Here is the answer to 356 decimal to quinary number:
2411
What is the product?
(2y +3)(3y^2+ 4y +5)
Answer:
6y^3 + 17y^2 +22y + 15
Step-by-step explanation:
Multiply each term in the first expression by each term in the second expression and combine like terms.
Write the equations of two lines that are parallel to the line 3x+6y-5=0
Answer:
X+2Y=7 and 4X+8Y=19
Step-by-step explanation:
Step 1: Write the equations in the form y=mx+c, where m represents the gradient.
In this case, gradient is equal to -0.5
Step 2: Now fix arbitrary values on the equation, y=mx+c while maintaining the value of m as - 0.5
You can make endless equations
Mr. Mitchell deposited $4000 in a bank and earned simple intrest at 7% per annum for 2 years.
(i) Calculate the amount he will recive at the end of the 2 year period.(Hint find the simple intrest first...)
Answer:
interest per annum is 280
interest for 2 year is 560
Step-by-step explanation:
money deposited in bank = 4000
1persent of 4000 = 40
7 persent of 4000 = 280
interest for 2 year is 280 x 2 = 560
Mark me as Brainestcalculate the amount that will be in the bank after 4years if R3500 was invested at 9% p.a. simple interest
Answer:
4760
Step-by-step explanation:
Simple interest= principal× time ×rate/100
=3500×4×9/100
= 1260
Amount that will be in the bank after 4years= 3500+1260
=4760
if a recipe calls for 0.8 cups of water per cup of water per 5/8 cups of milk. What is the unit rate per cup of milk ( with correct labels )
Answer: 1.28 cups of water per cup of milk
Step-by-step explanation:
0.8 divided by 5/8 equals 1.28
verified by my teacher :)
square root of 64 by division method
hope you understand.....
Find the area of the shaded region
Answer:
Area of the shades region = 244.6 ft²
Step-by-step explanation:
Area of the shaded region = Area of the rectangle ABCD- Area of the right angle triangle DEC
Area of the rectangle = Length × width
= 29.8 × 13
= 387.4 ft²
By applying Pythagoras theorem in the right triangle DEC,
(Hypotenuse)² = (leg 1)² + (leg 2)²
CD² = DE² + EC²
(29.8)² = DE² + (28)²
888.04 = DE² + 784
DE² = 888.04 - 784
DE = 10.2 ft
Area of ΔDEC = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
= [tex]\frac{1}{2}(10.2)(28)[/tex]
= 142.8 ft²
Area of the shades region = 387.4 - 142.8
= 244.6 ft²
Solve ay+b = cx for y
Answer:
y=cx-b/a
Step-by-step explanation:
ay+b=cx
ay=cx-b
y=cx-b/a
Find the measure of arc CB
Answer:
Arc CB is equals to 160
Step-by-step explanation:
Add all of those numbers and subtracted by 360
Answer:
Step-by-step explanation:
Remark
Be very careful that you understand which arc you are asking for. Arc CB could be the arc made up of 53 + 79 + 68 = 200.
Somehow I get the idea that is not what you want. You want the arc that is not divided up so it is
Arc CB = 360 - Sum of the minor arcs
Arc CB = 360 -- 200
Arc CB = 160
