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3 years ago

Rani has a stamp collection which consists of Indian stamps and foreign stamps. The ratio of

Mathematics

1 answer:

Lostsunrise [7]3 years ago

8 0

Answer:

2/9

Step-by-step explanation:

2 + 7 = 9

There are two Indian stamps, and the total is 9 stamps.

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A triangle with three acute angles

kotegsom [21]

Answer:

An Acute triangle

Step-by-step explanation:

An acute triangle (or acute-angled triangle) is a triangle with three acute angles (less than 90°).

6 0

2 years ago

What value of t is the solution of the above equation?

mel-nik [20]

Answer:

15/4, or 3 3/4 is your answer.

Step-by-step explanation:

Isolate the variable, t. Note the equal sign, what you do to one side, you do to the other. Multiply 3/2 to both sides.

(3/2)(2/3)t = (5/2)(3/2)

t = (5/2)(3/2)

t = 15/4

15/4, or 3 3/4 is your answer.

7 0

3 years ago

What is the square root of m^6?

Nastasia [14]

Answer:
If m is nonnegative (ie not allowed to be negative), then the answer is m^3
If m is allowed to be negative, then the answer is either |m^3| or |m|^3

==============================

Explanation:

There are two ways to get this answer. The quickest is to simply divide the exponent 6 by 2 to get 6/2 = 3. This value of 3 is the final exponent over the base m. Why do we divide by 2? Because the square root is the same as having an exponent of 1/2 = 0.5, so
sqrt(m^6) = (m^6)^(1/2) = m^(6*1/2) = m^(6/2) = m^3
This assumes that m is nonnegative.

---------------------------

A slightly longer method is to break up the square root into factors of m^2 each and then apply the rule that sqrt(x^2) = x, where x is nonnegative

sqrt(m^6) = sqrt(m^2*m^2*m^2)
sqrt(m^6) = sqrt(m^2)*sqrt(m^2)*sqrt(m^2)
sqrt(m^6) = m*m*m
sqrt(m^6) = m^3
where m is nonnegative

------------------------------

If we allow m to be negative, then the final result would be either |m^3| or |m|^3.

The reason for the absolute value is to ensure that the expression m^3 is nonnegative. Keep in mind that m^6 is always nonnegative, so sqrt(m^6) is also always nonnegative. In order for sqrt(m^6) = m^3 to be true, the right side must be nonnegative.

Example: Let's say m = -2
m^6 = (-2)^6 = 64
sqrt(m^6) = sqrt(64) = 8
m^3 = (-2)^3 = -8
Without the absolute value, sqrt(m^6) = m^3 is false when m = -2

4 0

3 years ago

A dog chased after a dandelion for 0.5 km, stopped to take a rest, and continued to chase after the dandelion for 750 m. How man

Annette [7]

1.25km Is How Far The Dog Traveled (1,250m)

5 0

3 years ago

Read 2 more answers

Could someplease explain the whole problem? For the first part my the answer I got was x= .618, -.618, and <img src="https://tex

algol13

9514 1404 393

Answer:

a) x = (√5 -1)/2 ≈ 0.618034

b) 1/x = (√5 +1)/2 ≈ 1.618034

Step-by-step explanation:

Given:

x/(1 -x) = 1/x

Find:

Exactly, and as a decimal approximation, ...

a) x, using the quadratic formula

b) 1/x

Solution:

a) We can multiply the given equation by x(1 -x) to obtain ...

x² = 1 -x

x² +x -1 = 0 . . . . . . add x-1

The coefficients for use in the quadratic formula are a=1, b=1, c=-1. The solution using the quadratic formula is ...

$x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-1\pm\sqrt{1^2-4\cdot1\cdot(-1)}}{2\cdot1}=\dfrac{-1\pm\sqrt{5}}{2}$

We are only interested in the positive solution, which is ...

$\boxed{x=\dfrac{\sqrt{5}-1}{2}\approx0.618034}$

b) The quadratic we developed in the first part can be rearranged like this:

x² +x = 1 . . . . . . add 1 to both sides

x(x +1) = 1 . . . . . factor out x

x +1 = 1/x . . . . . .divide by x

Then to find the value of 1/x, we simply need to add 1 to the value of x we have:

$\dfrac{1}{x}=\dfrac{\sqrt{5}-1}{2}+1=\dfrac{\sqrt{5}-1}{2}+\dfrac{2}{2}=\dfrac{\sqrt{5}-1+2}{2}\\\\\boxed{\dfrac{1}{x}=\dfrac{\sqrt{5}+1}{2}\approx1.618034}$

5 0

2 years ago