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3 years ago

The value of y varies directly with x, and y=28 when x=7. Find y when x=4 by first finding k.

1 answer:

7 0

Direct proportionality is the type of proportionality where an increase in one quantity or variable causes a corresponding increase in another quantity.
Therefore; y varies directly as x
Hence; y α x
y =k x where k is a constant
if y= 28 and x = 7 , then k = 28/4 =4
hence, y = 4 k
when x = 4, then y= 16

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3 years ago

Simplify the expression -2(p+4)^2-3+5p.What is the simplified expression in standard form?

Leokris [45]

Answer: -2x²-11x-35

Step-by-step explanation:

-2(p+4)²-3+5p

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-2x²-11x-35

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3 years ago

What expressions has a value equal to 28 divided by 4

nordsb [41]

Answer:

28/4=28/7

Step-by-step explanation:

when you divide 28 by 4 you get seven so if you use 7 instead of 4 to divide it's an equal value.

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3 years ago

A lighthouse is located on a small island 5 km away from the nearest point P on a straight shoreline and its light makes seven r

Vaselesa [24]

Answer:

Light is moving at the speed = 77.78 km/min

Step-by-step explanation:

Given:

Distance between island and point P = 5 km

Moving along the the shoreline when it is 1 km from P.

So, x = 1

From the above statement light makes seven revolutions per minute.

Therefore,

$\frac{d\theta}{dt}=\frac{7\times 2\pi\ rad}{1\ min} = 14\pi\ rad/min$

Solution:

From the given figure.

$tan\theta=\frac{x}{5}$

Substitute x = 1

$tan\theta=\frac{1}{5}$ -------------------(1)

Now, first we differentiate both side with respect to t.

$\frac{d(tan\theta)}{dt} = \frac{d}{dt}.(\frac{x}{3})$

Using chain rule.

$\frac{d(tan\theta)}{dt}.\frac{d\theta}{dt} = (\frac{1}{5})\frac{dx}{dt}$

$sec^{2} \theta.\frac{d\theta}{dt} = \frac{1}{5}.\frac{dx}{dt}$

$(1+tan^{2} \theta).\frac{d\theta}{dt} = \frac{1}{5}.\frac{dx}{dt}$

Substitute $tan\theta=\frac{1}{5}$ from equation 1.

$(1+(\frac{1}{3})^{2} ).\frac{d\theta}{dt} = \frac{1}{5}.\frac{dx}{dt}$

$(1+\frac{1}{9}).\frac{d\theta}{dt} = \frac{1}{5}.\frac{dx}{dt}$

Substitute $\frac{d\theta}{dt}=14\pi$

$\frac{10}{9}.14\pi = \frac{1}{5}.\frac{dx}{dt}$

Applying cross multiplication rule.

$\frac{dx}{dt}= \frac{700\pi }{9}$

$\frac{dx}{dt}= 77.78\pi$

Therefore, light is moving along the shore at the speed of 77.78 km/min

6 0

3 years ago

On a test with a population mean of 75 and standard deviation equal to 16, if the scores are normally distributed, what percenta

sashaice [31]

Answer:

Percentage of scores that fall between 70 and 80 = 24.34%

Step-by-step explanation:

We are given a test with a population mean of 75 and standard deviation equal to 16.

Let X = Percentage of scores

Since, X ~ N( $\mu,\sigma^{2}$ )

The z probability is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1) where, $\mu$ = 75 and $\sigma$ = 16

So, P(70 < X < 80) = P(X < 80) - P(X <= 70)

P(X < 80) = P( $\frac{X-\mu}{\sigma}$ < $\frac{80-75}{16}$ ) = P(Z < 0.31) = 0.62172

P(X <= 70) = P( $\frac{X-\mu}{\sigma}$ < $\frac{70-75}{16}$ ) = P(Z < -0.31) = 1 - P(Z <= 0.31)

= 1 - 0.62172 = 0.37828

Therefore, P(70 < X < 80) = 0.62172 - 0.37828 = 0.24344 or 24.34%

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3 years ago