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2 years ago

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Ms. Mor ris has 35 tests to grade this weekend. Mrs. Cook has 80% more tests than that to grade this weekend. How many tests doe

s Mrs. Cook have to grade?

1 answer:

Serga [27]2 years ago

8 0

Answer:

Mrs. Cook has to grade 63 tests.

Step-by-step explanation:

In order to find the answer, first you have to calculate 80% of the number of tests Ms. Morris has:

35*80%= 28

Then, you have to add the number that represents 80% to the number of tests Ms. Morris has to grade:

35+28=63

According to this, the answer is that Mrs. Cook has to grade 63 tests.

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How do you simply 2x+8=-6

photoshop1234 [79]

To simplify <span>2x + 8 = -6, the easiest way is to manipulate the equation one step at a time:

</span>2x + 8 = <span>-6
</span>2x = <span>-14 (subtract 8 from both sides)
</span>x = -7 (divide both sides by 2)

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3 years ago

Find the values of y = p(x) = √x for<br> x = 0, 1.44, 2.25, 3.24, 4.41, 5.29

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P(x) = √x

for x = 0 → √0 = 0 and p(0) = 0
for x = 1.44 → √1.44 =1.2 and p(1.44) = 1.2
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for x = 3.24 → √3.24 = 1.8 and p(3.24) = 1.8
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3 years ago

What is the slope of the line?

postnew [5]

Answer: $\frac{3}{10}$

Step-by-step explanation:

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2 years ago

How do i solve that question?

yawa3891 [41]

a) The solution of this <em>ordinary</em> differential equation is $y =\sqrt[3]{-\frac{2}{\frac{3\cdot t}{8}-\frac{\sin 2t}{4}+\frac{\sin 4t}{32}-2 } }$ .

b) The integrating factor for the <em>ordinary</em> differential equation is $-\frac{1}{x}$ .

The <em>particular</em> solution of the <em>ordinary</em> differential equation is $y = \frac{x^{3}}{2}+x^{2}-\frac{5}{2}$ .

<h3>How to solve ordinary differential equations</h3>

a) In this case we need to separate each variable ( $y, t$ ) in each side of the identity:

$6\cdot \frac{dy}{dt} = y^{4}\cdot \sin^{4} t$ (1)

$6\int {\frac{dy}{y^{4}} } = \int {\sin^{4}t} \, dt + C$

Where $C$ is the integration constant.

By table of integrals we find the solution for each integral:

$-\frac{2}{y^{3}} = \frac{3\cdot t}{8}-\frac{\sin 2t}{4}+\frac{\sin 4t}{32} + C$

If we know that $x = 0$ and $y = 1$ <em>, </em>then the integration constant is $C = -2$ .

The solution of this <em>ordinary</em> differential equation is $y =\sqrt[3]{-\frac{2}{\frac{3\cdot t}{8}-\frac{\sin 2t}{4}+\frac{\sin 4t}{32}-2 } }$ . $\blacksquare$

b) In this case we need to solve a first order ordinary differential equation of the following form:

$\frac{dy}{dx} + p(x) \cdot y = q(x)$ (2)

Where:

$p(x)$ - Integrating factor
$q(x)$ - Particular function

Hence, the ordinary differential equation is equivalent to this form:

$\frac{dy}{dx} -\frac{1}{x}\cdot y = x^{2}+\frac{1}{x}$ (3)

The integrating factor for the <em>ordinary</em> differential equation is $-\frac{1}{x}$ . $\blacksquare$

The solution for (2) is presented below:

$y = e^{-\int {p(x)} \, dx }\cdot \int {e^{\int {p(x)} \, dx }}\cdot q(x) \, dx + C$ (4)

Where $C$ is the integration constant.

If we know that $p(x) = -\frac{1}{x}$ and $q(x) = x^{2} + \frac{1}{x}$ , then the solution of the ordinary differential equation is:

$y = x \int {x^{-1}\cdot \left(x^{2}+\frac{1}{x} \right)} \, dx + C$

$y = x\int {x} \, dx + x\int\, dx + C$

$y = \frac{x^{3}}{2}+x^{2}+C$

If we know that $x = 1$ and $y = -1$ , then the particular solution is:

$y = \frac{x^{3}}{2}+x^{2}-\frac{5}{2}$

The <em>particular</em> solution of the <em>ordinary</em> differential equation is $y = \frac{x^{3}}{2}+x^{2}-\frac{5}{2}$ . $\blacksquare$

To learn more on ordinary differential equations, we kindly invite to check this verified question: brainly.com/question/25731911

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2 years ago

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Zarrin [17]

Using proportions, according to the ratio of the partition, it is found that the location of point g is at 3.

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A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, point g partitions the directed line segment from d to f into a 5:4 ratio, hence:

$g - d = \frac{5}{9}(f - d)$

We have that d = -2 and f = 7, hence:

$g - d = \frac{5}{9}(f - d)$

$g + 2 = \frac{5}{9}(7 + 2)$

g + 2 = 5.

g = 3.

More can be learned about proportions at brainly.com/question/24372153

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2 years ago