55. A triangle has two angles measuring 46 and 14. Determine the measure of the third angle.

In a video game, a bird is flung on a sling shot and follows a parabolic path. The path of the bird can be modeled by the equati

Novay_Z [31]

Answer:

The bird will take 0.88 seconds to reach a height of 40 feet in the air for the first time

Step-by-step explanation:

we have

$h=-16t^2+55t+4$

This is a vertical parabola open downward

The vertex represent a maximum

where

h is the height of the bird

t is the amount of time, in seconds, the bird had been in the air

For h=40 ft

substitute in the quadratic equation

$40=-16t^2+55t+4$

$-16t^2+55t+4-40=0$

$-16t^2+55t-36=0$

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

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

in this problem we have

$-16t^2+55t-36=0$

so

$a=-16\\b=55\\c=-36$

substitute in the formula

$x=\frac{-55\pm\sqrt{55^{2}-4(-16)(-36)}} {2(-16)}$

$x=\frac{-55\pm\sqrt{721}} {-32}$

$x=\frac{-55+\sqrt{721}} {-32}=0.88\ sec$

$x=\frac{-55-\sqrt{721}} {-32}=2.56\ sec$

therefore

The bird will take 0.88 seconds to reach a height of 40 feet in the air for the first time

3 0

2 years ago

Find the measurements (the length L and the width W) of an inscribed rectangle under the line with the 1st quadrant of the x &am

Leni [432]

The question is incomplete. Here is the complete question.

Find the measurements (the lenght L and the width W) of an inscribed rectangle under the line y = - $\frac{3}{4}$ x + 3 with the 1st quadrant of the x & y coordinate system such that the area is maximum. Also, find that maximum area. To get full credit, you must draw the picture of the problem and label the length and the width in terms of x and y.

Answer: L = 1; W = 9/4; A = 2.25;

Step-by-step explanation: The rectangle is under a straight line. Area of a rectangle is given by A = L*W. To determine the maximum area:

A = x.y

A = x(- $\frac{3}{4}.x + 3$ )

A = - $\frac{3}{4}.x^{2} + 3x$

To maximize, we have to differentiate the equation:

$\frac{dA}{dx}$ = $\frac{d}{dx}$ (- $\frac{3}{4}.x^{2} + 3x$ )

$\frac{dA}{dx}$ = -3x + 3

The critical point is:

$\frac{dA}{dx}$ = 0

-3x + 3 = 0

x = 1

Substituing:

y = - $\frac{3}{4}$ x + 3

y = - $\frac{3}{4}$ .1 + 3

y = 9/4

So, the measurements are x = L = 1 and y = W = 9/4

The maximum area is:

A = 1 . 9/4

A = 9/4

A = 2.25

6 0

2 years ago

Directions: Study the thermometers and answer these questions.

Soloha48 [4]

Answer:

1. F:32 C:0

2. F:212 C:100

3. F:70 C:30

4. F: 97 C: 36.5

Step-by-step explanation:

4 0

2 years ago

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Neeeddddd HELP LOOKONG FOR ANSWERS!!

kaheart [24]

Answer:

a.) 13 students

b.) 53 members

Step-by-step explanation:

a.) In the given equation of y=4x+13, "x" represents how many years have gone by since the club had started. The number "13" in this equation represents the y-intercept, or the value of "y" when x = 0. Therefore, when "x" is 0 years, there were 13 students in the clubs, meaning that the original group that started the club contained 13 students.

b.) Since the question asks how many members that the club will have after their tenth year and you already know that "x" in the equation y=4x+13 represents the number of years since the club started, all you have to do is plug 10 in for "x" in the equation; so, the equation will now look like this: y=4(10)+13. Keeping PEMDAS in mind, you first multiply 4 and 10 to get 40, and then you add 13 to get an answer of 53 members after year 10.

7 0

2 years ago

3.225×100 is what again let see who gets it

Sonbull [250]

This would result in 322.5. you get this by moving the decimal place two to the right

6 0

2 years ago

Read 2 more answers