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3 years ago

Can anyone help me out on this

Mathematics

1 answer:

Rashid [163]3 years ago

4 0

Answer: y=x+60

So y=mx+b is slope intercept form

y=x+60

m=1/1 because we go equally up as we go right so just put x

b=60 because we start at 60

Hope this helps

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Given the function y = x^4- 8x² + 16.

nevsk [136]

Answer:

Step-by-step explanation:

Recall that we use the first derivative to discover where a function is increasing or decreasing; it's increasing where the first derivative is + and decreasing where the first derivative is -.

The derivative of y = x^4 - 8x^2 + 16 is dy/dx = 4x^3 - 16x, or 4x(x^2 - 4).

This can be factored further: 4x(x - 2)(x + 2).

Set this equal to zero and solve for the three critical values:

{-2, 0, 2}.

Set up a total of four intervals: (-∞, -2), (-2, 0), (0, 2), (2, ∞).

Now choose a test point within each interval: {-3, -1, 1, 3}.

Evaluate the first derivative, dy/dx, at each of these four test points. Rule: if the first derivative is +, we know the function is increasing on that interval; if -, the function is decreasing.

At x = -3, dy/dx = 4x(x - 2)(x + 2) becomes (-)(-)(-), which is -, so we know that the function is decreasing on interval (∞, -2).

At x = -1, dy/dx is (-)(-)(+), which is +, so we know that the function is increasing on (-2, 0).

At x = 1, dy/dx is (+)(-)(+), which is -, so we know that the function is decreasing on (0, 2).

Finally: at x = 3, dy/dx is (+)(+)(+), so we know that the function is increasing on (2, ∞ ).

5 0

4 years ago

Help me now I need the answer on pepar

olga2289 [7]

Using the given information, the height of the shorter cone is 6.81 cm

<h3>Calculating volume of a cone </h3>

From the question, we are to determine the height of the shorter cone.

First, we will calculate the volume of the first cone

Using the formula for calculating the volume of a cone,

$V = \frac{1}{3}\pi r^{2}h$

Where V is the volume

r is the radius

and h is the height

From the given information,

r = 8.5 cm

h = 10 cm

Then,

$V = \frac{1}{3}\pi \times 8.5^{2}\times 10$

$V = \frac{1}{3}\pi \times 72.25\times 10$

$V = \frac{722.5}{3}\pi$ cm³

Now, for the shorter cone

r = 10.3 cm

Since the two cones have the exact same volume, we can write that

$\frac{722.5}{3}\pi= \frac{1}{3}\pi \times 10.3^{2} \times h$

$722.5= 106.09 \times h$

$h = \frac{722.5}{106.09}$

h = 6.81 cm

Hence, the height of the shorter cone is 6.81 cm.

Learn more on Calculating volume of a cone here: brainly.com/question/12004994

#SPJ1

4 0

2 years ago

Solve the following equation: 3(2x - 8) + 4x = -2(12 - 7x) - 4x

dezoksy [38]

Answer:

Step-by-step explanation:

3(2x - 8) + 4x = -2(12 - 7x) - 4x

6x - 24 + 4x = - 24 + 14x - 4x

10x + 24 = 24 + 10 x

6 0

4 years ago

Z varies directly with x and inversely with y. When x=6 and y=2, .z=15. Write function that models variation. Then, find z when

tester [92]

$\bf \begin{array}{cccccclllll}
\textit{direct proportional variation}\\\\\textit{something}&&\textit{varies directly to}&&\textit{something else}\\ \quad \\
\textit{something}&=&{{ \textit{some value}}}&\cdot &\textit{something else}\\ \quad \\
y&=&{{ k}}&\cdot&x
\\
&& y={{ k }}x
\end{array}\\ \quad \\$

$\bf \textit{inverse proportional variation}\\\\
\begin{array}{llllll}
\textit{something}&&\textit{varies inversely to}&\textit{something else}\\ \quad \\
\textit{something}&=&\cfrac{{{\textit{some value}}}}{}&\cfrac{}{\textit{something else}}\\ \quad \\
y&=&\cfrac{{{\textit{k}}}}{}&\cfrac{}{x}
\\
&&y=\cfrac{{{ k}}}{x}
\end{array}$

$\bf \\\\
-------------------------------\\\\
\textit{z varies directly with x}\implies z=kx
\\\\
\textit{and inversely with y}\implies z=\cfrac{kx}{y}
\\\\\\
\textit{we also know that}\quad 
\begin{cases}
x=6\\
y=2\\
z=15
\end{cases}\implies 15=\cfrac{k\cdot 6}{2}\implies 30=6k$

$\bf \cfrac{30}{6}=k\implies \boxed{5=k}\impliedby \textit{constant of variation}
\\\\\\
thus\implies z=\cfrac{5x}{y}\\\\
-------------------------------\\\\
\textit{what's "z" when }
\begin{cases}
x=4\\
y=9
\end{cases}\implies z=\cfrac{5\cdot 4}{9}$

4 0

4 years ago

Please help!! i’ll mark you as brainliest!!

PtichkaEL [24]

Answer:

For Triangle 1

a. Hypothenus = 4

b. Adjacent = 2√3

For Triangle 2:

a. Hypothenus = 2√2

b. Adjacent = 2

Step-by-step explanation:

For Triangle 1

NOTE: We shall be using angle 30°.

a. Determination of the Hypothenus.

Opposite = 2

Angle (θ) = 30°

Hypothenus =?

Sine θ = Opposite /Hypothenus

Sine 30 = 2 / Hypo

0.5 = 2 / Hypo

Cross multiply

0.5 × Hypo = 2

Divide both side by 0.5

Hypo = 2 / 0.5

Hypothenus = 4

b. Determination of the Adjacent

NOTE: We shall be using angle 30°.

Opposite = 2

Angle (θ) = 30°

Adjacent =?

Tan θ = Opposite / Adjacent

Tan 30 = 2 / Adj

1 / √3 = 2 / Adj

Cross multiply

1 × Adj = 2 × √3

Adjacent = 2√3

For Triangle 2:

a. Determination of the Hypothenus.

Opposite = 2

Angle (θ) = 45°

Hypothenus =?

Sine θ = Opposite /Hypothenus

Sine 45 = 2 / Hypo

1 / √2 = 2 / Hypo

Cross multiply

1 × Hypo = 2 × √2

Hypothenus = 2√2

b. Determination of the Adjacent

Opposite = 2

Angle (θ) = 45°

Adjacent =?

Tan θ = Opposite / Adjacent

Tan 45 = 2 / Adj

1 = 2 / Adj

Cross multiply

1 × Adj = 2

Adjacent = 2

5 0

3 years ago