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2 years ago

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1 answer:

GalinKa [24]2 years ago

6 0

Answer:

36 votes

(2x7)-(3x1) Take each instruction separately, use brackets to separate their action More

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2.74 as a mix number

Inga [223]

Answer:

2 74/100

Step-by-step explanation:

6 0

2 years ago

Nicole bought six pounds of apples at $1.50 per pound. The store had a discount of $2 off her total purchase. Nicole and her fri

Andru [333]

Answer:

Step-by-step explanation:

Total amount of apples that Nicole bought was 6 pounds.

Each pound of apple cost $1.50

This means that the total cost of the 6 pounds of apple that Nicole bought would be

6 × 1.5 = $9

The store had a discount of $2 off her total purchase. This means that the amount that was paid is

9 - 2 = $7

If Nicole and her friend then divided the cost of the purchase evenly, let x represent the amount that each of them would pay. Therefore, the expression that can be used to determine how much Nicole and her friend each paid for the apples would be

x = 7/2

6 0

2 years ago

The point P = (-3, y) lies on the unit circle shown below. What is the value of y

alukav5142 [94]

The equation of the circle is given as (x-h)² + (y-k)² = r². Then the value of y will be ± √5/3.

<h3>What is an equation of a circle?</h3>

A circle can be characterized by its center's location and its radius's length.

Let the center of the considered circle be at (h, k) coordinate.

Let the radius of the circle be 'r' units.

Then, the equation of that circle would be:

(x-h)² + (y-k)² = r²

The equation of the circle has the center at the origin and the radius is one unit. Then we have

x² + y² = 1

The point P = (-2/3, y) lies on the unit circle. Then the value of y will be

(-2/3)² + y² = 1

y² = 1 - 4/9

y² = 5/9

y = ± √5 / 9

Learn more about the equation of a circle here:

brainly.com/question/10165274

#SPJ1

5 0

1 year ago

Find the length of the curve. R(t) = cos(8t) i + sin(8t) j + 8 ln cos t k, 0 ≤ t ≤ π/4

arsen [322]

we are given

$R(t)=cos(8t)i+sin(8t)j+8ln(cos(t))k$

now, we can find x , y and z components

$x=cos(8t),y=sin(8t),z=8ln(cos(t))$

Arc length calculation:

we can use formula

$L=\int\limits^a_b {\sqrt{(x')^2+(y')^2+(z')^2} } \, dt$

$x'=-8sin(8t),y=8cos(8t),z=-8tan(t)$

now, we can plug these values

$L=\int _0^{\frac{\pi }{4}}\sqrt{(-8sin(8t))^2+(8cos(8t))^2+(-8tan(t))^2} dt$

now, we can simplify it

$L=\int _0^{\frac{\pi }{4}}\sqrt{64+64tan^2(t)} dt$

$L=\int _0^{\frac{\pi }{4}}8\sqrt{1+tan^2(t)} dt$

$L=\int _0^{\frac{\pi }{4}}8\sqrt{sec^2(t)} dt$

$L=\int _0^{\frac{\pi }{4}}8sec(t) dt$

now, we can solve integral

$\int \:8\sec \left(t\right)dt$

$=8\ln \left|\tan \left(t\right)+\sec \left(t\right)\right|$

now, we can plug bounds

and we get

$=8\ln \left(\sqrt{2}+1\right)-0$

so,

$L=8\ln \left(1+\sqrt{2}\right)$ ..............Answer

5 0

2 years ago

An arched drainage culvert can be modelled by the function:

Zanzabum

Substitute 136.5 for y.

$136.5=\frac{x(191-x)}{60}$

$8190=x(191-x)$

$8190=191x-x^{2}$

$x^{2} -191x+8190=0$

Compare this equation with $ax^{2} +bx+c=0$

a = 1, b = - 191, c = 8190

$x=\frac{-b+\sqrt{b^{2}-4ac } }{2}$ or

$x=\frac{-b-\sqrt{b^{2}-4ac } }{2}$

$x=\frac{191+\sqrt{191^{2}-4(1)(8190) } }{2}$ or

$x=\frac{191-\sqrt{191^{2}-4(1)(8190) } }{2}$

$x=\frac{191+\sqrt{36481-32760 } }{2}$ or

$x=\frac{191-\sqrt{36481-32760 } }{2}$

$x=\frac{191+\sqrt{3721 } }{2}$ or

$x=\frac{191-\sqrt{3721 } }{2}$

$x=\frac{191+61}{2}$ or

$x=\frac{191-61}{2}$

$x=\frac{252}{2}$ or

$x=\frac{130}{2}$

x = 126 or x = 65

Hence, the points on the curve are (65, 136.5) and (126, 136.5).

The width of the air space is the distance between these points.

Width = $\sqrt{(x_{2}- x_{1})^{2} +( y_{2}- y_{1}) ^{2}$

= $\sqrt{(126- 65)^{2} +(136.5-136.5) ^{2}$

= 126 - 65

= 61

Hence, width of the air space is 61m.

5 0

2 years ago