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Bumek [7]
3 years ago
15

Find the smallest integer k such that 60k is aperfect square​

Mathematics
1 answer:
Travka [436]3 years ago
5 0

Answer:  k = 15

<u>Step-by-step explanation:</u>

60 times some number k must be a perfect square.

Factor 60 to see which values do not have a pair:

60 = 2 · 2 · 3 · 5   --> 60 =<u> 2 · 2</u> · 3 · 5

                                                        ↓

                                                     3 · 5   are not pairs

So,  you need to multiply 60 by 15 to make a perfect square

60 × 15 = 900      →          \sqrt{900}=30

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A blimp can be seen flying at an altitude of 5500 feet above a motor speedway during a race. The slanted distance directly to th
Vladimir [108]

Answer:

The expression of h as function of x is   h = \sqrt{(d + 5500) (d - 5500)}

Step-by-step explanation:

Given as :

The distance of blimp  (AB) = 5500 feet

The slanted distance to the pagoda (BC) = d feet

The horizontal distance (AC) = h

Let the angle made between slanted distance and horizontal distance be Ф

So , cos Ф = \frac{AC}{BC} = \frac{h}{d}

And sin Ф =  \frac{AB}{BC} = \frac{5500}{d}

∵, cos²Ф = 1 - sin²Ф

So, (\frac{h}{d})^{2} = 1 - (\frac{5500}{d})^{2}

Or, (\frac{h}{d})^{2} = (\frac{d^{2}- 5500^{2}}{d^{2}})

Or,                                     h² = d² - 5500²

∴                                        h = \sqrt{d^{2}- 5500^{2}}

Or,                                     h = \sqrt{(d + 5500) (d - 5500)}

Hence The expression of h as function of x is   h = \sqrt{(d + 5500) (d - 5500)}     Answer

3 0
3 years ago
Use pi=3<br> Calculate the area of a circle with a diameter of 10cm
GalinKa [24]
Area of a circle is 75 cm².

Area of a circle is computed by multiplying pi to the square of the radius.

A = πr²

diameter = 10 cm
radius = d/2 = 10/2 = 5 cm
pi = 3

A = 3(5cm²)
A = 3(25cm²)
A = 75 cm²
7 0
2 years ago
Which property is shown? 4/5+ -<br> 4/5=0
TEA [102]
This looks like the additive inverse property, because when you add something to its negative counterpart (or its additive inverse), you get 0 as a sum.

Another example would be 2+ (-2) = 0. -2 is the additive inverse for 2.
7 0
2 years ago
P: 2,012
Hunter-Best [27]

El volumen que queda entre la esfera y el cubo es:  30.49cm^3

<h3>¿Como calcular el volume sobrante?</h3>

El volumen sobrante será simplemente la diferencia entre el volumen del cubo y el volumen de la esfera.

Para el cubo que tiene una arista de 4cm, el volumen es:

V = (4cm)^3 = 64 cm^3

Para la esfera con un diametro de 4cm, el radio es:

R = 4cm/2 = 2cm

Y el volumen será:

V' = (4/3)*3.141592654*(2cm)^3 = 33.51 cm^3

El volumen que queda entre la esfera y el cubo es:

V - V' = 64 cm^3 - 33.51 cm^3 = 30.49cm^3

Sí quieres aprender más sobre volumenes:

brainly.com/question/1972490

#SPJ1

5 0
8 months ago
The perimeter of a rectangular field is 26 yards. The length is 4 more yards than twice the width. Find the length and width of
solong [7]

The formula for perimeter is P = 2length + 2width (P = 2L + 2W)

You know that the length is 4 more yards then twice the width. In equation form this would be:

length = 4 + 2w

Plug what you know into the perimeter formula:

26 = 2(4 + 2w) + 2w

First you must distribute the 2 to the numbers inside the parentheses, which would be 4 and 2w...

26 = (2 * 4) + (2 * 2w) + 2w

26 = 8 + 4w + 2w

Now you must combine like terms. This means that first numbers with  the same variables (w) must be combined...

26 = 8 + 4w + 2w

4w + 2w = 6w

26 = 8 + 6w

Now bring 8 to the left side by subtracting 8 to both sides (what you do on one side you must do to the other). Since 8 is being added on the right side, subtraction (the opposite of addition) will cancel it out (make it zero) from the right side and bring it over to the left side.

26 - 8 = 8 - 8 + 6w

18 = 0 + 6w

18 = 6w

To isolate w divide 6 to both sides

18 / 6 = 6w / 6

w = 3

We know that the width is 3 ft

Now you must find the length. To do this plug 3 where you see w in the equation:

length = 4 + 2w

l = 4 + 2(3)

l = 4 + 6

l = 10

We know that length is 10 ft

Letter B. is the correct answer

Hope this helped!

~Just a girl in love with Shawn Mendes

4 0
3 years ago
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