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KengaRu [80]
3 years ago
11

You hammer a nail into a tree trunk 10 ft above the ground (and the tree is currently 20 ft tall). The tree grows taller at a ra

te of 2 feet per year. How far above ground level will the nail be in 10 years
Mathematics
1 answer:
AnnZ [28]3 years ago
3 0

Answer:

The nail would be 30 feet above the ground in 10 years.    

Step-by-step explanation:

We are given the following in the question:

Height of nail = 10 feet.

The tree grows taller at a rate of 2 feet per year.

Thus, the height of nail can be represented by a linear function:

h(t) = 10 + 2t

where t is the number of years.

We have to find the height of nail in 10 years.

Putting t = 10, we get,

h(10) = 10 + 2(10)\\h(10) = 30

Thus, the nail would be 30 feet above the ground in 10 years.

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Write an equation (a) in slope-intercept form and (b) in standard form for the line passing through (-3,5) and parallel to x + 4
Dmitry [639]

Answer:

  • \boxed{\sf Standard-form :x + 4y -17=0 }\\

  • \boxed{\sf Slope-intercept\ form :y =\dfrac{-1}{4}x +\dfrac{17}{4}}

Step-by-step explanation:

Here a equation of the line is given to us and we need to find out the equation of line which passes through the given point and parallel to the given line , the given equation is ,

\longrightarrow x + 4y = 7\\

Firstly convert it into <em>s</em><em>l</em><em>o</em><em>p</em><em>e</em><em> </em><em>i</em><em>n</em><em>t</em><em>e</em><em>r</em><em>c</em><em>e</em><em>p</em><em>t</em><em> </em><em>f</em><em>o</em><em>r</em><em>m</em><em> </em>of the line which is <u>y</u><u> </u><u>=</u><u> </u><u>m</u><u>x</u><u> </u><u>+</u><u> </u><u>x</u><u> </u>, as ;

\longrightarrow 4y = -x + 7  \\

\longrightarrow y =\dfrac{-x}{4}+\dfrac{7}{4}\\

On comparing it to <em>y</em><em> </em><em>=</em><em> </em><em>m</em><em>x</em><em> </em><em>+</em><em> </em><em>c</em><em> </em>, we have ,

\longrightarrow m =\dfrac{-1}{4}\\

\longrightarrow c =\dfrac{7}{4}\\

Now as we know that the <em>s</em><em>l</em><em>o</em><em>p</em><em>e</em><em> </em><em>o</em><em>f</em><em> </em><em>t</em><em>w</em><em>o</em><em> </em><em>p</em><em>a</em><em>r</em><em>a</em><em>l</em><em>l</em><em>e</em><em>l</em><em> </em><em>l</em><em>i</em><em>n</em><em>e</em><em>s</em><em> </em><em>i</em><em>s</em><em> </em><em>s</em><em>a</em><em>m</em><em>e</em><em> </em>. Therefore the slope of the parallel line will be ,

\longrightarrow m_{||)}=\dfrac{-1}{4}\\

Now we may use <em>p</em><em>o</em><em>i</em><em>n</em><em>t</em><em> </em><em>s</em><em>l</em><em>o</em><em>p</em><em>e</em><em> </em><em>f</em><em>o</em><em>r</em><em>m</em><em> </em>of the line as ,

\longrightarrow y - y_1 = m(x-x_1) \\

On substituting the respective values ,

\longrightarrow y - 5 =\dfrac{-1}{4}\{ x -(-3)\}\\

\longrightarrow y -5=\dfrac{-1}{4}(x+3)\\

\longrightarrow 4(y -5 ) =-1(x +3) \\

\longrightarrow 4y -20 = - x -3 \\

\longrightarrow x + 4y -20+3=0\\

\longrightarrow \underset{Standard \ Form }{\underbrace{\underline{\underline{ x + 4y -17=0}}}} \\

Again the equation can be rewritten as ,

\longrightarrow y - 5 = \dfrac{-1}{4}(x +3) \\

\longrightarrow y = \dfrac{-1}{4}x -\dfrac{3}{4}+5  \\

\longrightarrow y = \dfrac{-1}{4}x -\dfrac{20-3}{4}  \\

\longrightarrow \underset{Slope-Intercept\ form }{\underbrace{\underline{\underline{  y =\dfrac{-1}{4}x +\dfrac{17}{4}}}}}\\

6 0
2 years ago
Solve for x<br> (1/x) -2/3 = (4x)
Vadim26 [7]

The value of x is x=\frac{-1+\sqrt{37}}{12} and x=\frac{-1-\sqrt{37}}{12}

Step-by-step explanation:

The equation is \frac{1}{x}-\frac{2}{3}=4 x

Subtracting by 4x on both sides,

\frac{1}{x}-\frac{2}{3}-4 x=0

Taking LCM,

\frac{3-12 x^{2}-2 x}{3 x}=0

Multiplying by 3x on both sides,

-12 x^{2}-2 x+3=0

Dividing by (-) on both sides,

12 x^{2}+2 x-3=0

Using quadratic formula, we can solve for x.

\begin{aligned}x &=\frac{-2 \pm \sqrt{2^{2}-4 \cdot 12 \cdot(-3)}}{2 \cdot 12} \\&=\frac{-2 \pm \sqrt{4+144}}{2 \cdot 144} \\&=\frac{-2 \pm \sqrt{148}}{24} \\&=\frac{-2 \pm 2 \sqrt{37}}{24}\end{aligned}

Taking out common term 2, we get,

\begin{array}{l}{x=\frac{-2(1 \pm \sqrt{37})}{24}} \\{x=\frac{-1 \pm \sqrt{37}}{12}}\end{array}

Thus, the value of x is  x=\frac{-1+\sqrt{37}}{12} and x=\frac{-1-\sqrt{37}}{12}

4 0
3 years ago
PLZ HELP E!!!!!!! WILL MARK BRAINLIEST
vitfil [10]

Answer:

1

+

sec

2

(

x

)

sin

2

(

x

)

=

sec

2

(

x

)

Start on the left side.

1

+

sec

2

(

x

)

sin

2

(

x

)

Convert to sines and cosines.

Tap for more steps...

1

+

1

cos

2

(

x

)

sin

2

(

x

)

Write  

sin

2

(

x

)

as a fraction with denominator  

1

.

1

+

1

cos

2

(

x

)

⋅

sin

2

(

x

)

1

Combine.

1

+

1

sin

2

(

x

)

cos

2

(

x

)

⋅

1

Multiply  

sin

(

x

)

2

by  

1

.

1

+

sin

2

(

x

)

cos

2

(

x

)

⋅

1

Multiply  

cos

(

x

)

2

by  

1

.

1

+

sin

2

(

x

)

cos

2

(

x

)

Apply Pythagorean identity in reverse.

1

+

1

−

cos

2

(

x

)

cos

2

(

x

)

Simplify.

Tap for more steps...

1

cos

2

(

x

)

Now consider the right side of the equation.

sec

2

(

x

)

Convert to sines and cosines.

Tap for more steps...

1

2

cos

2

(

x

)

One to any power is one.

1

cos

2

(

x

)

Because the two sides have been shown to be equivalent, the equation is an identity.

1

+

sec

2

(

x

)

sin

2

(

x

)

=

sec

2

(

x

)

is an identity

Step-by-step explanation:

7 0
3 years ago
Is 1+4(3x-10)-12x equivalent to-9
Ymorist [56]

Answer:

no

Step-by-step explanation:

Given

1 + 4(3x - 10) - 12x ← distribute the parenthesis

= 1 + 12x - 40 - 12x ← collect like terms

= 1 - 40

= - 39 ≠ - 9

5 0
3 years ago
The difference of the quotient m and 9 and the quotient of n and 30
Zanzabum
Answer: (30m-9n)/270

First we start with m/9-n/30.

We multiply the denominators to get 270.

Then we multiply the numerators by the original denominators to get (30m-9n).

To check, we can use m=2, and n=4

2/9-4/30=4/45

(30*2-9*4)/270=24/270=4/45
5 0
3 years ago
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