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3 years ago

The graph y=x^2 is vertically stretched by a factor of 9 and the resulting graph is reflected across the x-axis

Mathematics

1 answer:

SpyIntel [72]3 years ago

7 0

Y=-9(x^2)
y=a(x-h)+k
K either goes up or down
While h Goes right or left. a either shrinks or stretches

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The period 7 (in seconds) of a pendulum is given by T = 2pi√( L divided by 32) where L stands for the length (in feet) of the pe

oksano4ka [1.4K]

Answer:

128 feet

Step-by-step explanation:

$t = 2\pi \sqrt{\frac{l}{32} }$

So now we will substitute the values of T and π into the equation.

$12.56 = 2 \times 3.14 \sqrt{ \frac{l}{32} }$

$12.56 = 6.28 \sqrt{ \frac{l}{32} }$

Divide both sides by 6.28

$2 = \sqrt{ \frac{l}{32} }$

Square both sides.

$4 = \frac{l}{32}$

Multiply both sides by 32

$l = 4 \times 32 \\ l = 128 \: feets$

5 0

1 year ago

The height of the tunnel at the center is 35ft, and the vertical clearance must be 21 ft at a point of 8ft from the center. Find

Zinaida [17]

Answer:

y=-0.215x^2+35

Step by Step:

Let, $h=0$ , $k=35$ , $x=8$ , $y=21$

We know that, the general equation of the parabola.

$y-k = a(x-h)^2$

$\Rightarrow y=a(x-h)^2+k .........(i)$

Substitute the value of $h, k, x, y$ in equation $(i)$ and find the value of $a.$

$21=a(8-0)^2+35$

$\Rightarrow 21=a\times 8^2+35$

$\Rightarrow 21=64a+35$

$\Rightarrow 64a=21-35$

$\Rightarrow 64a=-14$

$\Rightarrow a=\frac{-14}{65}$

$\Rightarrow a=-0.215$

Hence, the equation of the parabola is:

$y=-0.215x^2+35$

8 0

3 years ago

PLEASE HELP I WILL GIVE BRAINIEST!

marshall27 [118]

The distance is (0, 1.3)

7 0

3 years ago

Atown uses positive numbers to track increases in population and negative numbers to track decreases in population.

amid [387]

Answer:

Step-by-step explanation:

-60

Step-by-step explanation:

Increase in population is given by positive sign

Change in population in 5 years = -300

Decrease in population is represented by negative sign

Change in population in 1 year = -300\5

= -60

Town's population faces a decrease of 60 residents each year.

4 0

3 years ago

A manufacturer of running shoes knows that the average lifetime for a particular model of shoes is 15 months. Someone in the res

Alexus [3.1K]

Answer:

Step-by-step explanation:

Hello!

So you have a new type of shoe that lasts presumably longer than the ones that are on the market. So your study variable is:

X: "Lifetime of one shoe pair of the new model"

Applying CLT:

X[bar]≈N(μ;σ²/n)

Known values:

n= 30 shoe pairs

x[bar]: 17 months

S= 5.5 months

Since you have to prove whether the new shoes last more or less than the old ones your statistical hypothesis are:

H₀:μ=15

H₁:μ≠15

The significance level for the test is given: α: 0.05

Your critical region will be two-tailed:

$Z_{\alpha /2} = Z_{0.025}= -1.96$

$Z_{1-\alpha /2} = Z_{0.975}= 1.96$

So you'll reject the null Hypothesis if your calculated value is ≤-1.96 or if it is ≥1.96

Now you calculate your observed Z-value

Z=<u>x[bar]-μ</u> ⇒ Z=<u> 17-15 </u> = 1.99

σ/√n 5.5/√30

Since this value is greater than the right critical value, i.e. Zobs(1.99)>1.96 you reject the null Hypothesis. So the average durability of the new shoe model is different than 15 months.

I hope you have a SUPER day!

5 0

3 years ago