The function f(t) = −5t 2 + 20t + 60 models the approximate height of an objectt seconds after it is launched. How many seconds does it take the object to hit the
ground?

Answers

Answer 1

Answer:

Answer:

6 seconds.

Step-by-step explanation:

We have been given a function formula $f(t)=-5t^2+20t+60$ that models the approximate height of an object t seconds after it is launched.

To find the number of seconds it will take the object to hit the ground, we need to find the zeros of our given function.

$-5t^2+20t+60=0$

Upon dividing our equation by -5 we will get,

$t^2-4t-12=0$

We will factor our given equation by splitting the middle term as:

$t^2-6t+2t-12=0$

$t(t-6)+2(t-6)=0$

$(t-6)(t+2)=0$

$(t-6)=0\text{ or }(t+2)=0$

$t=6\text{ or }t=-2$

Since time cannot be negative, therefore, it will take the object 6 seconds to hit the ground.

Answer 2

Answer: f(t) = -5t^2 + 20t + 60
-5(t^2 - 4t - 12)
-5(t + 2) (t - 6)
t = -2 or t = 6

6 seconds

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Based on the graph below, what is the total number of solutions to the equation f(x) = g(x)?graph of function f of x equals negative 11 by 3 multiplied by x plus 11 by 3 and graph of function g of x equals x cubed plus 2 multiplied by x squared minus x minus 2

One
Two
Three
Four

Answers

Answer:

The total number of solutions is one

Step-by-step explanation:

we have

$f(x)=-(11)/(3)x+ (11)/(3)$

$g(x)=x^(3)+2x^(2)-x-2$

To solve the system of equations equate f(x) and g(x)

$f(x)=g(x)$

The solution of the system of equations is the intersection points both graphs

Using a graphing tool

see the attached figure

The solution of x

$x=1$

There is only one point of intersection both graphs

therefore

The total number of solutions is one

Answer:

the answer is One

Step-by-step explanation:

A solution is where the two lines intersect on the graph, and as you can see, in the picture above, the two lines only intersect once

Name the property for the given statement. (4 6)(3) = (4)(3) (6)(3)

Answers

DISTRIBUTIVE PROPERTY IS THE PROPERTY USED IN THE GIVEN STATEMENT...

Answer:

distributive property because you must distribute the numbers in parenthesis

Step-by-step explanation:

What is 5 to the power of negative two

Answers

the answer is 3 best negative two is -2 so u have 5 - 2 and 3 is your answer

simplify the expression.Exact Form:125/125Decimal Form:0.04

What is the distance between point A and point B? Round to nearest tenth.

Answers

Answer:

$d \approx 12.6$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra II

Distance Formula: $d = √((x_2-x_1)^2+(y_2-y_1)^2)$

Step-by-step explanation:

Step 1: Define

Find points from graph.

Point A (-4, 2)

Point B (8, 6)

Step 2: Find distance d

Simply plug in the 2 coordinates into the distance formula to find distance d.

Substitute [DF]: $d = √((8+4)^2+(6-2)^2)$
Add/Subtract: $d = √((12)^2+(4)^2)$
Exponents: $d = √(144+16)$
Add: $d = √(160)$
Simplify: $d = 4√(10)$
Evaluate: $d = 12.6491$
Round: $d \approx 12.6$

Evaluate the limit as x approaches 0 of (1 - x^(sin(x)))/(x*log(x))aka: $(1-x^(sin(x)))/(x*log(x))$

Please include steps/explanation.

Answers

$sin~ x \approx x ~ ~\sf{as}~~ x \rightarrow 0$

We can replace sin x with x anywhere in the limit as long as x approaches 0.

Also,

$\large \lim_( x \to 0 ) ~ x^x = 1$

I will make the assumption that log(x)=ln(x).

The limit result can be proven if the base of log(x) is 10.

$\large \lim_(x \to 0^(+)) (1- x^(\sin x) )/(x \log x ) \n~\n \large = \lim_(x \to 0^(+)) (1- x^(\sin x) )/( \log( x^x) ) \n~\n \large = \lim_(x \to 0^(+)) (1- x^(x) )/( \log( x^x) ) ~~ \normalsize{\text{ substituting x for sin x } } \n~\n \large = (\lim_(x \to 0^(+)) (1) - \lim_(x \to 0^(+)) \left( x^(x)\right) )/( \log( \lim_(x \to 0^(+))x^x) ) = (1-1)/(\log(1)) = (0)/(0)$

We get the indeterminate form 0/0, so we have to use Lhopitals rule

$\large \lim_(x \to 0^(+)) (1- x^(x) )/( \log( x^x) ) =_(LH) \lim_(x \to 0^(+)) (0 -x^x( 1 + \log (x)) )/(1 + \log (x) ) \n = \large \lim_(x \to 0^(+)) (-x^x) = \large - \lim_(x \to 0^(+)) (x^x) = -1$

Therefore,

$\large \lim_(x \to 0^(+)) (1- x^(\sin x) )/(x \log x ) =\boxed{ -1}$

Amy ran 3/4 mile write the distance amy ran as a decimal

Answers

we just need to perform the indicated division:
3/4 = 0.75
that is the solution as decimal, they are equivalent

Solutions

To convert fraction to decimal divide the numerator by denominator.

3 ÷ 4 = 0.75

0.75 is decimal

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The function f(t) = −5t 2 + 20t + 60 models the approximate height of an objectt seconds after it is launched. How many seconds does it take the object to hit the ground?

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The function f(t) = −5t 2 + 20t + 60 models the approximate height of an objectt seconds after it is launched. How many seconds does it take the object to hit the
ground?