Answer:
Step-by-step explanation:
(1/3)*(3/5)*(5/7)*.......*(93/95) * (95/97) * (97/99)
The denominator of each fraction will cancel out the numerator of the next fraction.
Take a close look
Therefore the result is 1/99
HOPE IT HELPS!!
The product of the geometric series is 1/99.
The product is a geometric series with first term 1/3 and common ratio 2/3. The number of terms is 49. The sum of the series is 1/99.
Here's the explanation:
A geometric series is a series where each term is multiplied by a constant value to get the next term. The constant value is called the common ratio.
In this case, the first term is 1/3 and the common ratio is 2/3. This means that each term is multiplied by 2/3 to get the next term.
The number of terms in the series is 49. This means that there are 49 terms in the series, starting with 1/3 and ending with 97/99.
The sum of the series is 1/99. This can be found using the formula for the sum of a geometric series:
S = a × (1 - [tex]r^{n}[/tex]) / 1 - r
where a is the first term, r is the common ratio, and n is the number of terms.
In this case, a = 1/3, r = 2/3, and n = 49. Substituting these values into the formula, we get:
S = (1/3) × (1 - (2/3)49) / 1 - (2/3) = 1/99
Therefore, the product is 1/99.
Learn more about geometric series here: brainly.com/question/30264021
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I NEED HELP PLEASE ! I GIVE 5 STARS !
Answer:
2
Step-by-step explanation:
Remember, a radical is the same thing as an exponent, but as a fraction. Therefore, instead of taking the 12th of the root, you can put [tex]8^4[/tex] to the 12th power like this: [tex](8^4)^{\frac{1}{12} }[/tex]
The two exponents can multiply together, so now it'll be [tex]8^{\frac{4}{12} }[/tex] which is [tex]8^{\frac{1}{3} }[/tex] when reduced
[tex]8^{\frac{1}{3} }[/tex] is the same thing as [tex]\sqrt[3]{8}[/tex]
Now, think about which number, when multiplied by itself 3 times is equal to 8... that number is 2--your answer
Answer:
2
Step-by-step explanation:
make it simple.. use a scientific calculator.
= ¹²√8⁴
= ¹²√4096
= 2
help me with it please with steps
class 9 trigonometry
secA=√2
secA=sec45
A=45°
3cos²45+5tan²45/ 4tan²A-sin²45
= 3(1/√3)²+5(1)² / 4(1)²-(1/√2)²
=3/2+5/4-1/2
=13/7
Answer:
[tex]\frac{13}{7}[/tex]
Step-by-step explanation:
Using the identities
cos x =[tex]\frac{1}{secx}[/tex] , sin²x = 1 - cos²x
tan²x = sec²x - 1
Given
[tex]\frac{3cos^2A+5tan^2A}{4tan^2A-sin^2A}[/tex]
= [tex]\frac{3(\frac{1}{sec^2A}+5(sec^2A-1) }{4(sec^2A -(1-cos^2A)}[/tex]
= [tex]\frac{3.(\frac{1}{\sqrt{2})^2 } +5((\sqrt{2})^2-1) }{4((\sqrt{2})^2-1)-(1-(\frac{1}{\sqrt{2} })^2 }[/tex]
= [tex]\frac{\frac{3}{2}+5(2-1) }{4(2-1)-(1-\frac{1}{2} )}[/tex]
= [tex]\frac{\frac{3}{2} +5}{4-\frac{1}{2} }[/tex]
= [tex]\frac{\frac{13}{2} }{\frac{7}{2} }[/tex]
= [tex]\frac{13}{2}[/tex] × [tex]\frac{2}{7}[/tex]
= [tex]\frac{13}{7}[/tex]
Trigonometric ratios
class 9
please answer my questions
Step-by-step explanation:
Hi there!
Please see the answer in the picture.
Hope it helps!
1. Approach
One is given a trigonometric equation with and one is asked to prove that it is true. Using the attached image, combined with the knowledge of trigonometry, one can evaluate each trigonometric function. Then one can simplify each ratio to solve. To yield the most accurate result, one has to each of the ratios in a fractional form, rather than simplifying it into a decimal form. Remember the right angle trigonometric ratios, these ratios describe the relationship between the sides and angles in a right triangle. Such ratios are as follows,
[tex]sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}\\\\csc(\theta)=\frac{hypotenuse}{opposite}\\\\sec(\theta)=\frac{hypotenuse}{adjacent}\\\\cot(\theta)=\frac{adjacent}{opposite}[/tex]
Please note that the terms (opposite) and (adjacent) are relative to the angle uses in the ratio, however the term (hypotenuse) refers to the side opposite the right angle, this side never changes its name. Use these ratios to evaluate the trigonometric functions. Then simplify to prove the identity.
2. Problem (9)
[tex]\frac{sin(60)+cos(30)}{1+sin(30)+cos(60)}=sin(60)[/tex]
As per the attached image, the following statements regarding the value of each ratio can be made:
[tex]sin(60)=\frac{\sqrt{3}}{2}\\\\cos(30)=\frac{\sqrt{3}}{2}\\\\sin(30)=\frac{1}{2}\\\\cos(60)=\frac{1}{2}[/tex]
Substitute,
[tex]\frac{sin(60)+cos(30)}{1+sin(30)+cos(60)}=sin(60)[/tex]
[tex]\frac{\frac{\sqrt{3}}{2}+\frac{\sqrt{3}}{2}}{1+\frac{1}{2}+\frac{1}{2}}=\frac{\sqrt{3}}{2}[/tex]
Simplify,
[tex]\frac{\frac{\sqrt{3}}{2}+\frac{\sqrt{3}}{2}}{1+\frac{1}{2}+\frac{1}{2}}=\frac{\sqrt{3}}{2}[/tex]
[tex]\frac{\frac{2\sqrt{3}}{2}}{1+\frac{1}{2}+\frac{1}{2}}=\frac{\sqrt{3}}{2}[/tex]
[tex]\frac{\frac{2\sqrt{3}}{2}}{1+1}=\frac{\sqrt{3}}{2}[/tex]
[tex]\frac{\sqrt{3}}{1+1}=\frac{\sqrt{3}}{2}[/tex]
[tex]\frac{\sqrt{3}}{2}=\frac{\sqrt{3}}{2}[/tex]
Thus, this equation is true.
2. Problem (10)
Use a similar strategy to evaluate this equation,
[tex]\frac{1-cos(30)}{sin(30)}=\frac{1-cot(60)}{1+cot(60)}[/tex]
Use the attached image to evaluate the ratios.
[tex]cos(30)=\frac{\sqrt{3}}{2}\\\\sin(30)=\frac{1}{2}\\\\cot(60)=\frac{1}{\sqrt{3}}[/tex]
Substitute,
[tex]\frac{1-cos(30)}{sin(30)}=\frac{1-cot(60)}{1+cot(60)}[/tex]
[tex]\frac{1-\frac{\sqrt{3}}{2}}{\frac{1}{2}}=\frac{1-\frac{1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}[/tex]
Simplify,
[tex]\frac{1-\frac{\sqrt{3}}{2}}{\frac{1}{2}}=\frac{1-\frac{1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}[/tex]
[tex]\frac{\frac{2-\sqrt{3}}{2}}{\frac{1}{2}}=\frac{1-\frac{1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}[/tex]
[tex]\frac{\frac{2-\sqrt{3}}{2}}{\frac{1}{2}}=\frac{\frac{\sqrt{3}-1}{\sqrt{3}}}{1+\frac{1}{\sqrt{3}}}[/tex]
[tex]\frac{\frac{2-\sqrt{3}}{2}}{\frac{1}{2}}=\frac{\frac{\sqrt{3}-1}{\sqrt{3}}}{\frac{\sqrt{3}+1}{\sqrt{3}}}[/tex]
[tex]2-\sqrt{3}=\frac{\frac{\sqrt{3}-1}{\sqrt{3}}}{\frac{\sqrt{3}+1}{\sqrt{3}}}[/tex]
[tex]2-\sqrt{3}=\frac{\sqrt{3}-1}{\sqrt{3}}*\frac{\sqrt{3}}{\sqrt{3}+1}}[/tex]
[tex]2-\sqrt{3}=\frac{\sqrt{3}-1}{\sqrt{3}+1}[/tex]
Rationalize the denominator,
[tex]2-\sqrt{3}=\frac{\sqrt{3}-1}{\sqrt{3}+1}[/tex]
[tex]2-\sqrt{3}=\frac{\sqrt{3}-1}{\sqrt{3}+1}*\frac{\sqrt{3}-1}{\sqrt{3}-1}[/tex]
[tex]2-\sqrt{3}=\frac{(\sqrt{3}-1)^2}{3-1}[/tex]
[tex]2-\sqrt{3}=\frac{3-2\sqrt{3}+1}{2}[/tex]
[tex]2-\sqrt{3}=\frac{4-2\sqrt{3}}{2}[/tex]
[tex]2-\sqrt{3}=2-\sqrt{3}[/tex]
Therefore, this equation is also true.
a number y cubed plus x squared decreased by 7
Step-by-step explanation:
It is read thus Y^3+X^2-7
The equation form from the given statement would be Y^3 + X^2 - 7.
How to form mathematical expression from the given description?You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically.
For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4.
We have been given a statement as;
"A number y cubed plus x squared decreased by 7".
So, the equation form would be
Y^3 + X^2 - 7
Learn more about expression here;
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The complete question is
"A number y cubed plus x squared decreased by 7". write the expression.
Find tan a Picture included
Answer:
5/12
Step-by-step explanation:
We know its a right angled triangle because of phythogorean theorem,
h^2=p^2+b^2
Take angle A as reference,
13^2=12^2+5^2
or,169=144+25
169=169
Now,
We know,
Tanx=p/b
As we took angle A as reference,
p=5
b=12
h=13
Put that in tanx=p/b
We get,
tanx=p/b=5/12
Answer:
Step-by-step explanation:
[tex]tan \ A = \frac{opposite \ side}{adjacent \ side}\\\\tan \ A = \frac{5}{12}[/tex]
Find the approximate volume of this prism (Image down below)
Answer:
about 62m^3
Step-by-step explanation:
Is 6272 a perfect square? If not find the smallest number by which it must be divided so that the product becomes a perfect square.
Answer:
(2^7)*(7^2)
Step-by-step explanation:
2*2*2*2*2*2*2*7*7=6272where2 is the smallest number by which it becomes a perfect square
(algebra) grade 9
Do the ratios 2/1 and 4/8 form a proportion?
answers:
~yes~
or
~no~
Answer:
No
Step-by-step explanation:
Find a number you can multiply 2 by to get 4.
2
Okay, now to ensure the ratio stays the same, multiply by 2/2 (aka 1)
You'll get 4/2, 2hixh is NOT equal to 4/8. So no, these ratios aren't equal.
Hope this helps!
all integers are whole numbers?true or false
Answer:
that would be false
Step-by-step explanation:
all whole numbers are integers, but not all integers are whole numbers
Match the vocab word
Answer:
1). Algebraic expression - a letter or symbol used to represent an unknown.
2). Coefficient - a numerical value.
3). Constant - the constant preceding the variables in a product.
4). Expression - a mathematical expression containing one or more variables.
5). Variable - a mathematical phrase that cannot be determined true or false.
when would you write an x in an equation?)
Answer:
[tex]\Large \boxed{\mathrm{When \ a \ number \ is \ not \ known}}[/tex]
Step-by-step explanation:
For example, a sum of a number and 6 is 12.
The number is unknown.
Let the number be x.
x + 6 = 12We can solve for x (unknown number). Subtract 6 from both sides of the equation.
x = 6Simply. If the solution is not a real number enter not a real number rotate picture answer all 3 please
Answer:
13. [tex]\frac{\sqrt[5]{x^4} }{x}[/tex].
14. [tex]v = \pm3\sqrt{5}[/tex]
15. 2.
Step-by-step explanation:
13. [tex]x^{1/5} * x^{-2/5}[/tex]
= [tex]x^{1/5 + (-2/5)}[/tex]
= [tex]x^{1/5 - 2/5}[/tex]
= [tex]x^{-1/5}[/tex]
= [tex]\frac{1}{x^{1/5}}[/tex]
= [tex]\frac{x^{4/5}}{x^{1/5 + 4/5}}[/tex]
= [tex]\frac{x^{4/5}}{x}[/tex]
= [tex]\frac{\sqrt[5]{x^4} }{x}[/tex].
14. [tex]v^2 - 45 = 0[/tex]
[tex]v^2 = 45[/tex]
[tex]\sqrt{v^2} = \pm\sqrt{45}[/tex]
[tex]\sqrt{v^2} = \pm\sqrt{3^2 * 5}[/tex]
[tex]v = \pm3\sqrt{5}[/tex].
15. [tex]\sqrt[3]{2} * \sqrt[3]{4}[/tex]
= [tex]\sqrt[3]{2 * 4}[/tex]
= [tex]\sqrt[3]{2 * 2 * 2}[/tex]
= [tex]\sqrt[3]{2 ^3}[/tex]
= 2.
Hope this helps!
I need urgent help with the question. Can someone please give full working out of the attached question
Answer:
2x-2
Step-by-step explanation:
Being specifically asked to rationalise the denominator we focus on it as required.
To rationalise a term it has to be multiplied by its inverse.
The inverse of
[tex] \sqrt{x} - \sqrt{2 - x} [/tex]
is
[tex] \sqrt{x} + \sqrt{2 - x} [/tex]
Multiplying this two vives us a difference of two squares
[tex] {( \sqrt{x} })^{2} - {( \sqrt{2 - x} )}^{2} [/tex]
which gives us
x-(2-x)
=2x-2
What characteristics do similar triangles share? a They have the same sides and angles. b They have the same sides but different angles. c They have the same ratios for the sides. d They are the exact same.
Answer:
b. they have the same sides but different angles
Step-by-step explanation:
this answer makes the most sense
Answer:
C they have the same ratios for the sides
Step-by-step explanation:
Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion. In other words, similar triangles are the same shape, but not necessarily the same size. The triangles are congruent if, in addition to this, their corresponding sides are of equal length.
please answer if you can
Step-by-step explanation:
denominator
add numerator
the difference of two numbers is 24.if the smaller number is 38,find the greater one
Answer:
62
Step-by-step explanation:
add 24 to the smaller number to get the greater one
Answer:
62
Step-by-step explanation:
let, the greater number be 'x' and smaller number be 'y'
x-y=24 i.e. x-38=24
or, X=24+38
X= 62
Find the missing value can someone help me get this
Answer:
-3
Step-by-step explanation:
-5 = -8 - (- 3)
pls help with this question
Try this
(x^2 + x - 12) + (x^2 - 8x + 16)
2y - 1
√36
i wanted to help you! :)
Answer:
[tex]\frac{3}{3}[/tex] = 1 (everything basically cancels)
Step-by-step explanation:
find the lower quartile for the data {47.2, 33.8, 43, 62, 5.8, 9, 61.4, 30.8, 68.2, 51.6, 13.2, 17.4, 64.2, 50.6, 29.4, 40.4}
Answer:
The lower quartile is 23.4
Step-by-step explanation:
The given data are;
47.2, 33.8, 43, 62, 5.8, 9, 61.4, 30.8, 68.2, 51.6, 13.2, 17.4, 64.2, 50.6, 29.4, 40.4
Rearranging the data, we have;
5.8, 9, 13.2, 17.4, 29.4, 30.8, 33.8, 40.4, 43, 47.2, 50.6, 51.6, 61.4, 62, 64.2, 68.2
The lower quartile, Q₁, is the (n + 1)/4 th term which is (16 +1)/4 = 4.25th term
However since we have an even set of numbers, we place a separator at the middle and we look for the median of the left half as follows
5.8, 9, 13.2, 17.4, 29.4, 30.8, 33.8, 40.4║ 43, 47.2, 50.6, 51.6, 61.4, 62, 64.2, 68.2
We have two numbers (17.4 + 29.4) at the median of the left set of numbers, we find the average of the two numbers to get the lower quartile
The lower quartile is therefore = (17.4 + 29.4)/2 = 23.4.
The common difference of an ap is -2 find its sum of first term is hundred and last term is -10 with full solution
Answer:
2520
Step-by-step explanation:
The n th term of an AP is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference.
To find the number of terms given [tex]a_{n}[/tex] = - 10 , d = - 2 and a₁ = 100, then
100 - 2(n - 1) = - 10 ( subtract 100 from both sides )
- 2(n - 1) = - 110 ( divide both sides by - 2 )
n - 1 = 55 ( add 1 to both sides )
n = 56 ← number of terms
Given n, a₁ and a₅₆ , then the sun of the terms is
[tex]S_{56}[/tex] = [tex]\frac{n}{2}[/tex] (a₁ + a₅₆ )
= [tex]\frac{56}{2}[/tex] (100 - 10) = 28 × 90 = 2520
after allowing 20% discount an article is sold for rs.672 levying 12% VAT, find its market price
The market price is Rs. 750 which was obtained by creating a mathematical relationship from the given parameters.
PERCENTAGE DISCOUNT = 20%
VAT LEVIED= 12%
PRICE SOLD = 672
Let the MARKET PRICE = m
Hence,
market price * (1 - discount) * (1 + VAT) = price sold
m * (1 - 20%) * (1 + 12%) = 672
m * (1 - 0.2) * (1 + 0.12) = 672
m * 0.8 * 1.12 = 672
0.896m = 672
m = 672 / 0.896
m = Rs. 750
Learn more :
https://brainly.com/question/20418815
The Market Price of the product is RS. 750.
The Market Price is calculated by dividing the components associated to Discount, which is less than 1, and the Value Added Tax, which more than 1, to the Resulting Price.
[tex]c_{M} = \frac{c_{R}}{\left(1-\frac{r_{D}}{100} \right)\cdot \left(1+\frac{r_{T}}{100} \right)}[/tex] (1)
Where:
[tex]c_{M}[/tex] - Market price, in monetary units.
[tex]c_{R}[/tex] - Resulting price, in monetary units.
[tex]r_{D}[/tex] - Discount rate, in percentage.
[tex]r_{T}[/tex] - Tax rate, in percentage.
If we know that [tex]c_{R} = 672[/tex], [tex]r_{D} = 20[/tex] and [tex]r_{T} = 12[/tex], then the market price is:
[tex]c_{M} = \frac{672}{\left(1-\frac{20}{100} \right)\cdot \left(1+\frac{12}{100} \right)}[/tex]
[tex]c_{M} = 750[/tex]
The market price of the product is RS. 750.
Three identical squares are placed side by side to form a rectangle with a perimeter of 104 inches. What is the area, in square inches, of each square?
Answer:
13 inches
Step-by-step explanation:
I have done a Little draw because I don't know how i can explain you this exuse me
what is the x intercept for y=(2x(x-3))/(x-1). ?
my answer sheet says it is supposed to be -0.5
Answer:
( 0,0) and (3,0)
Step-by-step explanation:
y=(2x(x-3))/(x-1)
Set y = 0
0 =(2x(x-3))/(x-1)
Multiply each side by x-1, which makes x not equal to 1
0 =(2x(x-3))
Using the zero product property
2x=0 x-3 =0
x=0 x= 3
The x intercepts are x=0 x= 3
( 0,0) and (3,0)
Problem at the River-A girl with a fox ,a goose and a bag of corn wanted to cross a river she could only take one animal or object at a time the fox first,the goose if they were left alone together.if the girl took the fox first the goose would eat the corn . How did the girl get all there safely across the river?
This is a great riddle to get people thinking, because it's not an obvious answer!
River A, you have: a fox, a goose, and a bag of corn.
So, you've probably gone through this looking for some way to bring one of them over, but if she takes the cornmeal, the fox will eat the goose, if she takes the fox, the goose will eat the corn, and if she takes the goose, then the fox and the cornmeal will be left together (which isn't bad until you have to pick one of them to take over with the goose).
Let's start by picking one of the animals (or objects) to take over first. Because it takes two trips for things to get bad with the goose, will do it first.
We take the goose across river A, and come back to the fox and the cornmeal. Nothing bad has happened. Now we know that if we leave the goose with the fox or the cornmeal, the cornmeal or the goose will be eaten.
There is one other thing we can do! The girl can only take one thing back and forth, but she can bring something back when she takes one of them across!
This means that:
She can take the goose first and the cornmeal second, but when she takes the cormeal, she can grab the goose and bring it back with her, so now the cornmeal is across river A but the goose isn't! Then, she can drop off the gosse and grab the fox, because the fox won't do anything to the cornmeal, and then come back for the goose!
Just ask if you have an questions! :)
What is [tex]3^2*3^5[/tex]?
Answer:
[tex]3^7[/tex]
Step-by-step explanation:
[tex]3^2*3^5[/tex]
[tex]\text {Apply Product Rule: } a^b+a^c=a^{b+c}\\\\3^2*3^5=3^{2+5}=3^7[/tex]
Complete the sequence
8,27,64,125,.........
Just next letter
Answer:
216.
Step-by-step explanation:
These numbers are perfect cubes starting with 2^3.
2^3, 3^3, 4^3, 5^3 so the next one is 6^3, which is 216.
PLEASE HELP ME FAST...
I will mark you a BRAINLEST
Answer: Hi!
Row A: 7, 11, 15, 19, 23
Row B: 51, 42, 33, 24, 15
Row C: 4, 8, 16, 32, 64
Row D: 64, 32, 16, 8, 4
(If you notice, Row C and Row D are just swapped in order!)
Hope this helps!
Hi there! Hopefully this helps!
--------------------------------------------------------------------------------------------------------------
A's rule, add 4: 7, 11, 15, 19, 23
B's rule, Subtract 9: 51, 42, 33, 24, 15
C's rule, Multiply by 2: 4, 8, 16, 32, 64
D's rule, Divide by 2: 64, 32, 16, 8, 4
Can someone please do this for me please
Answer:
r=-11
Step-by-step explanation:
7r+2=5(r-4)
7r+2=5r-20
2r=-22
r=-11
find the positive square root of 26.77
Answer:5.173973328
Step-by-step explanation:
T. For a science experiment, Katie had
to cool one sample bacteria to -52°C.
She had to cool a second sample
bacterium to -79°C. What is the
difference in the two temperatures?
Please help me figure out the equation too.
Answer:
Step-by-step explanation:
A "difference" indicates subtraction is being used. The difference between these 2 numbers is found the same way we find the distance between 2 points on a number line. Since both the difference and the distance have to be positive numbers, the formula to find it is
|a - b| which is the absolute value of a - b.
If a = -52 and b = -79:
| -52 - (-79) | = | -52 + 79 | = 27 OR
If a = -79 and b = -52:
| -79 - (-52) | = | -79 + 52 | = | -27 | = 27