You should be able to multiply 91 by 8 to get the sum of the first 8 tests, then add the score on the 9th test. Then to get the average of the sum of the 9 tests you need to divide it by 9.
((91*8)+78)/9=89.555555555555.... So, 90%

3 0

4 years ago

The line L is a tangent to the curve with equation y= 4x^2 +1 . The line L cuts the y axis at (0,8) and has a positive gradient.

sergeinik [125]

A generic point on the graph of the curve has coordinates

$(x, 4x^2+1)$

The derivative gives us the slope of the tangent line at a given point:

$f(x) = 4x^2+1 \implies f'(x) = 8x$

Let k be a generic x-coordinate. The tangent line to the curve at this point will pass through $(k, 4k^2+1)$ and have slope $8k$

So, we can write its equation using the point-slope formula: a line with slope m passing through $(x_0, y_0)$ has equation

$y-y_0 = m(x-x_0)$

In this case, $(x_0, y_0)=(k, 4k^2+1)$ and $m=8k$ , so the equation becomes

$y-4k^2-1 = 8k(x-k)$

We can rewrite the equation as follows:

$y-4k^2-1 = 8k(x-k) \iff y = 8kx - 8k^2+4k^2+1 \iff y = 8kx-4k^2+1$

We know that this function must give 0 when evaluated at x=0:

$f(x) = 8kx-4k^2+1 \implies f(0) = -4k^2+1 = 8 \iff -4k^2 = 7 \iff k^2 = -\dfrac{7}{4}$

This equation has no real solution, so the problem looks impossible.

5 0

3 years ago

Judy has $10 to buy watermelons and grapes. Judy plans to buy two watermelons that cost $6 and as many pounds of grapes as she c

lawyer [7]

Judy can buy at least 5 pounds of grapes.

4 0

4 years ago

Explain how you can tell that 31\33 is in simplest form

Sindrei [870]

Because there is no whole number that you can divide into both the numerator and the denominator to get a proper fraction.

3 0

3 years ago

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