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3 years ago

Can someone please help with the answer!!! Thank you :)

Mathematics

1 answer:

Lelechka [254]3 years ago

4 0

Answer:

This sequence is a geometric sequence.

The common ratio of the sequence is

3/9 = 1/3

Hope this helps

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Find a number C such that the polynomial p(x)= -x+4x^2+Cx^3-8x^4

Ksenya-84 [330]

Answer:

C = 2

Step-by-step explanation:

$p(x)= -x+4x^2+Cx^3-8x^4 \\ \\ \because \: given \: polynmial \: has \: zero \: at \: \\x = \frac{1}{4} \\ \\ \implies \: p\bigg(\frac{1}{4} \bigg) = 0...(1) \\ \\ plug \: x = \frac{1}{4} \: in \: p(x) \: we \: find \\ \\ p \bigg(\frac{1}{4} \bigg) = - \frac{1}{4} + 4 {\bigg(\frac{1}{4} \bigg)}^{2} + c {\bigg(\frac{1}{4} \bigg)}^{3} - 8 {\bigg(\frac{1}{4} \bigg)}^{4} \\ \\ 0 = - \frac{1}{4} + \cancel 4 \times {\frac{1}{\cancel{16} } } + c {\bigg(\frac{1}{64} \bigg)} - \cancel 8 \times \frac{1}{\cancel{256} } \\ \\0 =\cancel{ - \frac{1}{4}} + \cancel {{\frac{1}{4} }} + c {\bigg(\frac{1}{64} \bigg)} - \times \frac{1}{32} \\ \\0 = c {\bigg(\frac{1}{64} \bigg)} - \frac{1}{32} \\ \\c {\bigg(\frac{1}{64} \bigg)} = \frac{1}{32} \\ \\ c = \frac{1}{32} \times 64 \\ \\ c = 2$

5 0

3 years ago

Write the linear equation in slope intercept form 1,3 and -3,-5

oksian1 [2.3K]

For this case we have that by definition, the equation of the line of the slope-intersection form is given by:

$y = mx + b$

Where:

m: It's the slope

b: It is the cut-off point with the y axis

We have two points through which the line passes:

$(x_ {1}, y_ {1}) :( 1,3)\\(x_ {2}, y_ {2}): (- 3, -5)$

We found the slope:

$m = \frac{y_ {2} -y_ {1}} {x_ {2} -x_ {1}}$

Substituting we have:

$m = \frac {-5-3} {- 3-1} = \frac {-8} {- 4} = 2$

Thus, the equation is of the form:

$y = 2x + b$

We substitute one of the points and find the cut-off point:

$3 = 2 (1) + b\\3 = 2 + b\\3-2 = b\\b = 1$

Finally, the equation is:

$y = 2x + 1$

ANswer:

$y = 2x + 1$

3 0

3 years ago

If you help out can you please explain it so I can understand?

rjkz [21]

Simplify just means put together everything into one big thing. In this case that is just adding. To add a fraction and a decimal we have to convert the fraction into a decimal as well. The decimal form of 1/4 is 0.25, and as such, 3/4 is .75. This means we have -0.75+1.5. Adding a positive to a negative is the same thing as simply subtracting the first number from the second, or 1.5-0.75. This is .75. The answer is C.

8 0

2 years ago

You are a lifeguard and spot a drowning child 60 meters along the shore and 40 meters from the shore to the child. You run along

sukhopar [10]

Answer:

The lifeguard should run across the shore a distance of 48.074 m before jumpng into the water in order to minimize the time to reach the child.

Step-by-step explanation:

This is a problem of optimization.

We have to minimize the time it takes for the lifeguard to reach the child.

The time can be calculated by dividing the distance by the speed for each section.

The distance in the shore and in the water depends on when the lifeguard gets in the water. We use the variable x to model this, as seen in the picture attached.

Then, the distance in the shore is d_b=x and the distance swimming can be calculated using the Pithagorean theorem:

$d_s^2=(60-x)^2+40^2=60^2-120x+x^2+40^2=x^2-120x+5200\\\\d_s=\sqrt{x^2-120x+5200}$

Then, the time (speed divided by distance) is:

$t=d_b/v_b+d_s/v_s\\\\t=x/4+\sqrt{x^2-120x+5200}/1.1$

To optimize this function we have to derive and equal to zero:

$\dfrac{dt}{dx}=\dfrac{1}{4}+\dfrac{1}{1.1}(\dfrac{1}{2})\dfrac{2x-120}{\sqrt{x^2-120x+5200}} \\\\\\\dfrac{dt}{dx}=\dfrac{1}{4} +\dfrac{1}{1.1} \dfrac{x-60}{\sqrt{x^2-120x+5200}} =0\\\\\\ \dfrac{x-60}{\sqrt{x^2-120x+5200}} =\dfrac{1.1}{4}=\dfrac{2}{7}\\\\\\ x-60=\dfrac{2}{7}\sqrt{x^2-120x+5200}\\\\\\(x-60)^2=\dfrac{2^2}{7^2}(x^2-120x+5200)\\\\\\(x-60)^2=\dfrac{4}{49}[(x-60)^2+40^2]\\\\\\(1-4/49)(x-60)^2=4*40^2/49=6400/49\\\\(45/49)(x-60)^2=6400/49\\\\45(x-60)^2=6400\\\\$

$x$

As $d_b=x$ , the lifeguard should run across the shore a distance of 48.074 m before jumpng into the water in order to minimize the time to reach the child.

7 0

3 years ago

3. Lucas bought grapes to bring to his class party. After the party,

Paul [167]

Answer: 4.2 lbs

Step-by-step explanation:

Amount of grapes he had (in pounds) = 1.9 + 2.3 pounds

Amount of grapes he had (in pounds) = 4.2 pounds

4 0

2 years ago