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STALIN [3.7K]
2 years ago
8

Is anyone able to figure this out, I can't do this

Mathematics
2 answers:
Bond [772]2 years ago
6 0
The answer to your equation is C
katrin [286]2 years ago
5 0

Answer:

C. √2 - 1

Step-by-step explanation:

If we draw a square from the center of the large circle to the center of one of the small circles, we can see that the sides of the square are equal to the radius of the small circle (see attached diagram)

Let r = the radius of the small circle

Using Pythagoras' Theorem a^2+b^2=c^2

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

to find the diagonal of the square:

\implies r^2 + r^2 = c^2

\implies 2r^2 = c^2

\implies c=\sqrt{2r^2}

So the diagonal of the square = \sqrt{2r^2}

We are told that the radius of the large circle is 1:

⇒ Diagonal of square + r = 1

\implies \sqrt{2r^2}+r=1

\implies \sqrt{2r^2}=1-r

\implies 2r^2=(1-r)^2

\implies 2r^2=1-2r+r^2

\implies r^2+2r-1=0

Using the quadratic formula to calculate r:

\implies r=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}

\implies r=\dfrac{-2\pm\sqrt{2^2-4(1)(-1)}}{2(1)}

\implies r=\dfrac{-2\pm\sqrt{8}}{2}

\implies r=-1\pm\sqrt{2}

As distance is positive, r=-1+\sqrt{2}=\sqrt{2}-1  only

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3 years ago
How do<br> you<br> write 9.59 x 10^2 in a standard form?
Alexxandr [17]

Answer:

You get

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Explanation:

look at the power of 10:

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You get:

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3 years ago
Test the convergence of 011xx dx .
Slav-nsk [51]

Step-by-step explanation:

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6 0
3 years ago
Tamara paid $3.00 for cartons of milk. Teo paid $3.75 for a different number of cartons at the same store. How much is one carto
Rashid [163]
1- Price of each carton:
Since they both bought different number of cartons of milk from the same store, we can simply find the price of one carton from the difference between what they both paid.

Since Tamara paid 3$ and Toe paid 3.75$, we can simply say that one carton of milk costs 0.75$ and that Toe bought one carton more than Tamra.

2- How many cartons each bought:
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3 0
3 years ago
The base of a triangle exceeds the height by 7 centimeters. If the area is 400 square centimeters, find the length of the base a
zvonat [6]

Answer:

Base = 32 cm

Height = 25 cm

Step-by-step explanation:

Area of a triangle can be calculated as:

Area = \frac{1}{2}\times Base \times Height

We are given that the base of triangle exceeds the height by 7 cm. This can be expressed in an equation form as:

Base = Height + 7

Lets use B to represent base and H to represent height

B = H + 7

The equation of area can be stated as:

Area=\frac{1}{2}bh\\\\ Area=\frac{1}{2}(h+7)(h)\\\\ 400=\frac{1}{2}h(h+7)\\\\ 800=h^{2}+7h\\\\ h^{2}+7h-800=0

This is a quadratic equation which can be solved using a quadratic equation as shown below:

h=\frac{-7+-\sqrt{49-4(1)(-800)} }{2(1)} \\\\ h=\frac{-7+-57}{2}\\\\h=-32,25

Since the height cannot be negative, we'll consider the positive value only i.e height is equal to 25 cm.

Therefore, the length of base will be 25 + 7 = 32 cm.

8 0
3 years ago
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