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lisabon 2012 [21]

3 years ago

13

Solve. ln (x+1) ^3 = 3

1 answer:

Anastaziya [24]3 years ago

6 0

Answer:

x = <em>e-1</em>

Step-by-step explanation:

ln((x+1)³) = 3

3ln(x+1) = 3

ln(x+1) = 1

x+1 = e

x = <em>e</em>-1

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A batter strikes a baseball. the equation y = -0.005^2 +0.7x + 3.5 models its path, where x is the horizontal distance, in feet,

hram777 [196]

Answer:

(D)144.8 feet

Step-by-step explanation:

Given the equation which models the path of the baseball

$y = -0.005x^2 +0.7x + 3.5$

where x is the horizontal distance, in feet, the ball travels and y is the height, in feet, of the ball.

To determine how far from the batter the ball will land, we determine the distance x at which the height, y=0.

$y = -0.005x^2 +0.7x + 3.5=0$

$-0.005x^2 +0.7x + 3.5=0$

We use the quadratic formula to solve.

In the quadratic equation above, a=-0.005, b=0.7, c=3.5

$x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a} \\=\dfrac{-0.7\pm\sqrt{0.7^2-4(-0.005*3.5)} }{2*-0.005} \\=\dfrac{-0.7\pm\sqrt{0.49+0.07} }{-0.01}\\=\dfrac{-0.7\pm\sqrt{0.56} }{-0.01}\\x=\dfrac{-0.7+\sqrt{0.56} }{-0.01} \: or\: x=\dfrac{-0.7-\sqrt{0.56} }{-0.01}\\x=-4.83 \: or\: x=144.83$

Since x cannot be negative, x=144.8 feet to the nearest tenth of a foot.

<u>The correct option is D.</u>

6 0

3 years ago

Change each mixed number into an equal improper fraction a. 1 7/16, b. 11 5/9, c. 30 5/9, d. 10 10/13, e. 24 3/5, f. 129 1/2

elixir [45]

Answer:

a)

$\dfrac{23}{16}$

b)

$\dfrac{104}{9}$

c)

$\dfrac{275}{9}$

d)

$\dfrac{140}{13}$

e)

$\dfrac{103}{5}$

f)

$\dfrac{259}{2}$

Step-by-step explanation:

<em>" A fraction in which the numerator is greater than the denominator "</em>

We have to change each of the mixed fraction into improper fraction:

We know that the mixed fraction is converted into fraction as:

$a\frac{b}{c}=\dfrac{a\times c+b}{c}$

a)

$1\frac{7}{16}$ could be written as:

$=\dfrac{1\times 16+7}{16}\\\\=\dfrac{16+7}{16}\\\\=\dfrac{23}{16}$

b)

$11\frac{5}{9}$

$=\dfrac{11\times 9+5}{9}\\\\=\dfrac{99+5}{9}\\\\=\dfrac{104}{9}$

c)

$30\frac{5}{9}$

$\dfrac{30\times 9+5}{9}\\\\=\dfrac{270+5}{9}\\\\=\dfrac{275}{9}$

d)

$10\frac{10}{13}$

$\dfrac{10\times 13+10}{13}\\\\=\dfrac{130+10}{13}\\\\=\dfrac{140}{13}$

e)

$24\frac{3}{5}\\\\=\dfrac{24\times 5+3}{5}\\\\=\dfrac{100+3}{5}\\\\\dfrac{103}{5}$

f)

$129\frac{1}{2}\\\\\\=\dfrac{19\times 2+1}{2}\\\\=\dfrac{258+1}{2}\\\\=\dfrac{259}{2}$

8 0

3 years ago

Read 2 more answers

Im giving 100 Points to anyone who could solve this for me please.

myrzilka [38]

Answer:

AB = 27.2

BC = 33.5

AC = 50.4

∠A = 38°

∠ABC = 112°

Step-by-step explanation:

<u>Trigonometric ratios</u>

$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$

where:

$\theta$ is the angle
O is the side opposite the angle
A is the side adjacent the angle
H is the hypotenuse (the side opposite the right angle)

$\implies \sf \cos(30^{\circ})=\dfrac{29}{BC}$

$\implies \sf BC=\dfrac{29}{\cos(30^{\circ})}$

$\implies \sf BC=\dfrac{58\sqrt{3}}{3}=33.5\:(nearest\:tenth)$

$\implies \sf \tan(30^{\circ})=\dfrac{BD}{29}$

$\implies \sf BD=29\tan(30^{\circ})$

$\implies \sf BD=\dfrac{29\sqrt{3}}{3}$

$\implies \sf \sin(38^{\circ})=\dfrac{BD}{AB}$

$\implies \sf AB=\dfrac{\dfrac{29\sqrt{3}}{3}}{\sin(38^{\circ})}$

$\implies \sf AB=27.2\:(nearest\:tenth)$

$\implies \sf \tan(38^{\circ})=\dfrac{BD}{AD}$

$\implies \sf AD=\dfrac{\dfrac{29\sqrt{3}}{3}}{\tan(38^{\circ})}$

$\implies \sf AD=21.4\:(nearest\:tenth)$

$\implies \sf AC=AD+DC=21.4+29=50.4$

The interior angles of a triangle sum to 180°

⇒ ∠A + 52° + 90° = 180°

⇒ ∠A = 180° - 90° - 52°

⇒ ∠A = 38°

⇒ ∠ABC + 38° + 30° = 180°

⇒ ∠ABC = 180° - 38° - 30°

⇒ ∠ABC = 112°

**I have checked the measures using a graphing programme - see attached**

8 0

2 years ago

77 students is what percent of 87 students

Natali [406]

Answer:

0.89%

Step-by-step explanation:

77/87=0.89%

4 0

3 years ago

Read 2 more answers

A number plus itself, plus twice itself, plus 4 times itself is equal to -104

NARA [144]

The scenario will will be represented by: $x+x+2x+4x=-104$

The number will be -13

Step-by-step explanation:

We have to convert the given situation into the mathematical form

Let x be the number

Then

"a number plus itself"

x+x

"plus twice itself"

x+x+2x

"plus 4 times itself"

x+x+2x+4x

"is equal to -104"

$x+x+2x+4x=-104$

This can also be written as:

$x+x+2x+4x=-104\\8x=-104\\Dividing\ both\ sides\ by\ 8\\\frac{8x}{8}=\frac{-104}{8}\\x=-13$

Keywords: Linear Equation

Learn more about linear equation at:

#LearnwithBrainly

7 0

3 years ago