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3 years ago

Which statement is true about the circumference of a circle?

Mathematics

1 answer:

PolarNik [594]3 years ago

5 0

Answer:

Step-by-step explanation:

yes it is found by multiplying phi with diameter of the circle

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A truck that is 11 feet tall and 7 feet wide is traveling under an arch. The arch can be modeled by:

Kryger [21]

Answer:

Yes

8 ft

Step-by-step explanation:

The equation of the arch is

$y=-0.0625x^2+1.25x+5.75$

Differentiating with respect to $x$ we get

$\dfrac{dy}{dx}=-2\times 0.0625x+1.25=-0.125x+1.25$

Equating with zero

$0=-0.125x+1.25\\\Rightarrow x=\dfrac{-1.25}{-0.125}\\\Rightarrow x=10$

Double derivative of the equation

$\dfrac{d^2y}{dx^2}=-0.125$

So, the function is maximum at $x=10$

$y=-0.0625x^2+1.25x+5.75=-0.0625\times 10^2+1.25\times 10+5.75\\\Rightarrow y=12$

The function is maximum at $(10,12)$

So, the truck's center should be below the point $(10,12)$ for maximum width to pass through.

Now truck is 11 feet tall so $y=11$

$11=-0.0625x^2+1.25x+5.75\\\Rightarrow -0.0625x^2+1.25x-5.25=0\\\Rightarrow x=\frac{-1.25\pm \sqrt{1.25^2-4\left(-0.0625\right)\left(-5.25\right)}}{2\left(-0.0625\right)}\\\Rightarrow x=6,14$

The maximum width of the truck can be $14-6=8\ \text{ft}$ if it is 11 feet tall.

So, the truck which has a width of 7 feet can fit under the arch.

5 0

2 years ago

What is the slope of the line that passes through the points (5,−4) and (7, -4) ?Write your answer in simplest form.

mihalych1998 [28]

Answer:

Undefined

Step-by-step explanation:

$\boxed{slope = \frac{y1 - y2}{x1 - x2} }$

☆ (x₁, y₁) is the first coordinate and (x₂, y₂) is the second coordinate.

Slope of the line

$=\frac{ - 4 - ( - 4)}{7 - 5} \\ =\frac{ - 4 + 4}{2} \\ = \frac{0}{2} \\ (undefined)$

Thus, the slope of the line is undefined.

(Since 2 cannot be divided by zero)

Notice that the two coordinates have the same y- coordinate of -4. This means that the line is a vertical line. Vertical lines have undefined slopes.

7 0

3 years ago

The total amount of deductions from an employee's gross pay is $83.20. If the gross pay is $378.18, what percent of their gross

sukhopar [10]

83.20/378.18=.22 *100= 22%

7 0

3 years ago

Read 2 more answers

PLEASE HURRY Aline has a slope of -1/2 and a y-intercept of -2. What is the x-intercept of the line?

DiKsa [7]

Answer:

x- intercept = - 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - $\frac{1}{2}$ and c = - 2 , then

y = - $\frac{1}{2}$ x - 2 ← equation of line

To find the x- intercept let y = 0

0 = - $\frac{1}{2}$ x - 2 ( add 2 to both sides )

2 = - $\frac{1}{2}$ x ( multiply both sides by - 2 to clear the fraction )

- 4 = x

The x- intercept is - 4

7 0

3 years ago

HALPPPPP PLZZZ I'll give Brainliest for the first answer CORRECT

ddd [48]

Answer:

Since it is area, it is most defined as base times height, so the larger rectangle would be 9x14 which is 126 and the smaller rectangle is 6x8 which is 48, and since they are together in one shape, you can add both areas which would give you an answer of 174

Step-by-step explanation:

7 0

3 years ago