Please answer this correctly without making mistakes

(a) h(t) is quadratic, so we can complete the square to write

h(t) = 100 + 40 t - 5 t²

h(t) = 100 - 5 (t² - 8 t)

h(t) = 100 - 5 (t² - 8 t + 16 - 16)

h(t) = 100 + 80 - 5 (t² - 8 t + 16)

h(t) = 180 - 5 (t - 4)²

The squared quantity is always non-negative, which means h(t) has a maximum value of 180 m.

(b) First, find when the projectile hits the ground, which happens when h(t) = 0:

0 = 180 - 5 (t - 4)²

180 = 5 (t - 4)²

36 = (t - 4)²

± 6 = t - 4

t = -2   OR   t = 10

Omit the negative solution. The velocity of the ball at t = 10 s is equal to the derivative at the point, h' (10).

[tex]h'(10)=\displaystyle\lim_{t\to10}\frac{h(t)-h(10)}{t-10}[/tex]

[tex]h'(10)=\displaystyle\lim_{t\to10}\frac{(180-5(t-4)^2)-80}{t-10}[/tex]

[tex]h'(10)=\displaystyle\lim_{t\to10}\frac{100+40t-5t^2}{t-10}[/tex]

[tex]h'(10)=\displaystyle-5\lim_{t\to10}\frac{(t+2)(t-10)}{t-10}[/tex]

[tex]h'(10)=\displaystyle-5\lim_{t\to10}(t+2)=-60[/tex]

So the projectile has a downward velocity of 60 m/s at the moment it touches the ground.

Hello!

Find the maximum height by finding the maximum of the function, where the derivative switches from positive to negative. Find the derivative of the equation:

h(t) = 100 +40t -5t²

Power rule:

h'(t) = 40 - 10t

Set the equation equal to 0:

0 = 40 - 10t

-40 = -10t

t = 4

Test values on both sides of 4 to ensure that there is a maximum at this x value:

40 - 10(3) = 10

40 - 10(5) = -10

Therefore, the derivative switches from positive to negative. There is a maximum at t = 4. Find the height by plugging in this value for time into the original equation:

h(4) = 100 + 40(4) - 5(4)²

h(4) = 100 + 160 - 80

h(4) = 180 meters

Find the velocity when it hits the ground. Begin by finding the time necessary for the object to hit the ground:

0 = 100 + 40t - 5t²

Rearrange and factor:

0 = -5t² + 40t + 100

0 = (5t + 10)(-t + 10)

Set each factor equal to 0:

5t + 10 = 0

t = -2

-t + 10 = 0

t = 10

Therefore, the object takes 10 seconds to reach the ground. Plug this into the derivative of the equation (solved for earlier), which is the velocity:

h'(t) = 40 - 10t

h'(10) = 40 - 10(10)

h'(1) = -60 m/s. This is the *downward* velocity when the object hits the ground.

Answer:

Step-by-step explanation:

Required equation

Solving for x

Answer:

x=-2

Step-by-step explanation:

hope this helps

follow me

Answer:

-1

Step-by-step explanation:

-x + 2 = x+4

-x-x = 4-2

-2x = 2

x= 2/-2

x= -1

hope it will help......

Answer:

The Rate is 1,383!

Step-by-step explanation:

1st)32,555-18,725=13,830

2nd)13,830/10=1,383.

HOPE THIS HELPS!!!!!!!!!!!!!

Answer:

                                   0.32608696

Step-by-step explanation:

Answer:

The correct value of x will be "[tex]-\frac{19}{16}[/tex]". The further explanation is given below.

Step-by-step explanation:

The given equation is:

⇒  [tex]7x + 21 + 9x = 2[/tex]

⇒        [tex]16x+21=2[/tex]

On subtracting "21" from both sides, we get

⇒  [tex]16x+21-21=2-21[/tex]

⇒                [tex]16x=-19[/tex]

⇒                   [tex]x=-\frac{19}{16}[/tex]

Answer:

A polygon is a pentagon if and only if it has five sides."If this statement is true, then which of the follow… Get the ... The given statement is of the form

Step-by-step explanation:

hope it helps you

❤❤❤❤❤

Answer:

D.  If it is a pentagon, then it has five sides. If the polygon has five sides, then it is a pentagon

Step-by-step explanation:

Given statements;

      A polygon is a pentagon if and only if it has five sides.

Therefore, this bi-conditional statement is premised on two "if"s,

    If it is a pentagon then we are dealing with a body with 5 sides.

   And if such body has five sides, it is a polygon called pentagon

The correct option is D

Choice A, B and C are logically flawed.

A.  If it is a pentagon, then it has five sides. If it is a polygon, then it is a pentagon.

The emboldened part we do not know.

B.  If it is a pentagon, then it is a polygon. If it is a polygon, then it is a pentagon

 The emboldened part is flawed.

C. If it is a pentagon, then it is a polygon. If it is a polygon, then it has five sides.

We do not know if all pentagons have 5 sides.

Answer:

law of contrapositive

Step-by-step explanation:

Answer:

The answers D on Edg

Step-by-step explanation:

Just finished the test

The distance of the ship from the beginning  is 226.48 miles far apart.

A triangle is a flat geometric figure that has three sides and three angles. The sum of the interior angles of a triangle is equal to 180°. The exterior angles sum up to 360°.

For the given situation,

The diagram below shows the travelling of ship from A to C.

Let sides a = 30 miles, c = 200 miles,

The measure of angle B is [tex]\angle CBA = 180-30[/tex]   [∵ Supplementary angle]

⇒ [tex]\angle CBA = 150[/tex]

Here two sides and one angle of triangle are provided.

The other side of the triangle, that is the distance traveled by the ship can be found by using the law of cosines.

The formula of law of cosines,

[tex]b = \sqrt{a^{2}+c^{2}-2ac (cosB ) }[/tex]

On substituting the values,

⇒ [tex]b = \sqrt{30^{2}+200^{2}-2(30)(200) (cos150 ) }[/tex]

⇒ [tex]b = \sqrt{900+40000-12000(-0.8660 ) }[/tex]

⇒ [tex]b = \sqrt{40900+10392 }[/tex]

⇒ [tex]b = \sqrt{51292}[/tex]

⇒ [tex]b=226.477[/tex] ≈ [tex]226.48[/tex]

Hence we can conclude that the distance of the ship from the beginning  is 226.48 miles far apart.

Learn more about triangles here

https://brainly.com/question/8541181

#SPJ3

Answer:

Step-by-step explanation:

90 - 28  = 62  is the measure of 28° supplementary angle

Answer:

its 152

Step-by-step explanation:

Answer:

It is true.

Step-by-step explanation:

4*8 = 32, which is divisible by 4.

222*608 = 134 976, which is divisible by 4.

Answer:

x values

Step-by-step explanation:

Answer:the rate of change is 5

Step-by-step explanation:

Answer:

x=-14

Step-by-step explanation:

Multiply each term in  − x = 14  by  − 1

Answer:

-14

Step-by-step explanation:

Answer:

Step-by-step explanation:

The answer is b

Answer:

ratio bozo

Step-by-step explanation:

Problem 1

Answer: Yes a triangle can be formed with side lengths 5,5,3

--------------------

Explanation:

Take any two sides and add them up. If we get a sum larger than the third side, then a triangle is possible. This is the triangle inequality theorem.

5+5 = 10 is larger than 3

5+3 = 8 is larger than 5

This shows a triangle is possible. The triangle is isosceles because two sides are the same length.

==========================================================

Problem 2

Answer: Yes a triangle can be formed with side lengths 8,8,8

--------------------

Explanation:

This triangle is equilateral because all sides are the same length.

Take any two sides, add them up, and you'll find the sum is larger than the third side.

==========================================================

Problem 3

Answer: No a triangle cannot be formed with sides 7,8,15

--------------------

Explanation:

Yes it is true that

8+15 = 23 is larger than 7

7+15 = 22 is larger than 8

but

7+8 = 15 is not larger than 15

So this means a triangle is not possible.

Imagine you had 3 strips of paper that were 7 inches, 8 inches and 15 inches long. The 7 and 8 inch strips add to 15 inches, but those two smaller strips only form a straight line. We cannot pull them so a triangle forms. If we did, then the third side would be smaller than 15 inches. This is one way to get hands on to see why the triangle inequality theorem works.

==========================================================

Problem 4

Answer: Yes a triangle is possible with side lengths 5,6,10

--------------------

Explanation:

Same idea as before. We can take any two sides, add them, and get a sum larger than the third side. A triangle is possible.

Answer

3/2

Step-by-step explanation:

(y2-y1)/(x2-x1)=(-4-5)/(-2-4)=-9/-6=3/2

Answer:

The C=intercept of the regression line

Step-by-step explanation:

The slope of the regression line has a logical interpretation as the average rate of change in collar size for a 1cm increase in height.

A linear regression is represented as [tex]^\wedge y = mx + c[/tex]

The option that has no logical interpretation is: E The c-intercept of the regression line

From the question, we have:

[tex]^\wedge c = 94 + 0.9h[/tex]

Using the above representation of a regression line [tex]\wedge y = mx + c[/tex]

[tex]m \to[/tex] the slope

[tex]c \to[/tex] the y-intercept

By comparing [tex]\wedge y = mx + c[/tex] to  [tex]^\wedge c = 94 + 0.9h[/tex]

[tex]0.9 \to[/tex] slope

[tex]94 \to[/tex] the y-intercept

While [tex]^ \wedge c[/tex] and [tex]h[/tex] are the variables (i.e. collar size and height)

From the list of given options (see attachment), the option that has no logical interpretation is:

E. The c-intercept of the regression line

This is because c does not represent the intercept of [tex]^\wedge c = 94 + 0.9h[/tex]

Read more about linear regression at:

https://brainly.com/question/18405415

Answer:

C

Step-by-step explanation:

y-intercept is 3 down and slope is the same

Answer:

The unit price per cup of blue paint would be $8

Step-by-step explanation:

because 6x8=48 soo each cup would be 8 dollars. 

Answer:

The slope of side w is: ¼

The slope of side z is: -4

The slope of side x is: ¼

The slope y is : -4

Step-by-step explanation:

Slope of w between (-1, 5) and (-5, 4):

[tex] slope(m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 - 5}{-5 -(-1)} = \frac{-1}{-4} = \frac{1}{4} [/tex]

Slope of x between (-3, -4) and (1, -3):

[tex] slope(m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-3 -(-4)}{1 -(-3)} = \frac{1}{4} = [/tex]

Slope of y between (-3, -4) and (-5, 4):

[tex] slope(m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 -(-4)}{-5 -(-3)} = \frac{8}{-2} = -4 [/tex]

Slope of z between (1, -3) and (-1, 5)):

[tex] slope(m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 -(-3)}{-1 - 1} = \frac{8}{-2} = -4 [/tex]

The slope of side w is

1/4

The slope of side z is

-4

The slope of side x is

1/4

The slope of side y is

-4

Step-by-step explanation:

it just is

Answer:

[tex]Max = 18\ mins[/tex]

[tex]Min = 12\ mins[/tex]

Step-by-step explanation:

Given

[tex]Time = 15\ mins[/tex]

[tex]Variation = 3\ mins[/tex]

Required

Determine the max and min values

The max value is calculated as thus:

[tex]Max = Time + Variation[/tex]

[tex]Max = 15\ mins + 3\ mins[/tex]

[tex]Max = 18\ mins[/tex]

The min value is calculated as thus:

[tex]Min = Time - Variation[/tex]

[tex]Min = 15\ mins - 3\ mins[/tex]

[tex]Min = 12\ mins[/tex]