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Dvinal [7]
3 years ago
11

For what point on the curve of y=8x^2 - 3x is the slope of a tangent line equal to -67

Mathematics
1 answer:
AleksandrR [38]3 years ago
3 0

The point on the curve is (–4, 140)

Solution:

Given y=8x^2-3x and slope is –67.

slope = –67

$\frac{dy}{dx}=-67$  – – – – (1)

Now calculate \frac{dy}{dx} for the given curve y=8x^2-3x.

Using differential rule:

$\frac{d}{dx}(x^n)=nx^{n-1}

$\frac{dy}{dx}=\frac{d}{dx}(8x^2-3x)

    $=\frac{d}{dx}(8x^2)-\frac{d}{dx}(3x)

    $=(8\times2x^{2-1})-(3\times1x^{1-1})

    $=16x^1-3x^0

    $=16x-3

$\frac{dy}{dx}=16x-3 – – – – (2)

Equate (1) and (2).

16x-3=-67

16x=-67+3

16x=-64

⇒ x = –4

Substitute x = –4 in y.

⇒ y=8(-4)^2-3(-4)

⇒    =8(16)+12

⇒ y = 140

Hence, the point on the curve given is (–4, 140).

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At least 75% of these commuting times are between 30 and 110 minutes

Step-by-step explanation:

Chebyshev Theorem

The Chebyshev Theorem can also be applied to non-normal distribution. It states that:

At least 75% of the measures are within 2 standard deviations of the mean.

At least 89% of the measures are within 3 standard deviations of the mean.

An in general terms, the percentage of measures within k standard deviations of the mean is given by 100(1 - \frac{1}{k^{2}}).

In this question:

Mean of 70 minutes, standard deviation of 20 minutes.

Since nothing is known about the distribution, we use Chebyshev's Theorem.

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THis means that 30 and 110 minutes is within 2 standard deviations of the mean, which means that at least 75% of these commuting times are between 30 and 110 minutes

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3 years ago
Which label on the cone below represents the height?<br> *<br> A<br> B<br> C<br> D
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Answer:

The answer is B.

Step-by-step explanation:

Let us go through each of the points one by one:

The label A represents the radius of the base of the cone.

The label B represents the height of the cone.

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The label D represents the vertex of the cone (where the cone ends).  

So it is choice B that represents the height of the cone.

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Answer:

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Step-by-step explanation:

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In which Q(t) is the population in t years after 1980, in billions, Q(0) is the initial population and r is the growth rate.

The world population at the beginning of 1980 was 4.5 billion. Assuming that the population continued to grow at the rate of approximately 1.3%/year.

This means that Q(0) = 4.5, r = 0.013

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