How much gigameters is 93 million miles

ValentinkaMS [17]

Because none of the points on the number line are above 0, we know that the points will be negative.
This eliminates the second and third choices, as they contain positive numbers.
The first point, A, is a number less than -0.5 or -1/2
The first choice matches A with -5/16, which is less than -0.5 or -1/2
Therefore, the fourth choice must be the correct answer.

5 0

3 years ago

4x^2 y+8xy'+y=x, y(1)= 9, y'(1)=25

jarptica [38.1K]

Answer with explanation:

$\rightarrow 4x^2y+8x y'+y=x\\\\\rightarrow 8xy'+y(1+4x^2)=x\\\\\rightarrow y'+y\times\frac{1+4x^2}{8x}=\frac{1}{8}$

--------------------------------------------------------Dividing both sides by 8 x

This Integration is of the form ⇒y'+p y=q,which is Linear differential equation.

Integrating Factor

$=e^{\int \frac{1+4x^2}{8x} dx}\\\\e^{\log x^{\frac{1}{8}+\frac{x^2}{2}}\\\\=x^{\frac{1}{8}}\times e^{\frac{x^2}{2}}$

Multiplying both sides by Integrating Factor

$x^{\frac{1}{8}}\times e^{\frac{x^2}{2}}\times [y'+y\times\frac{1+4x^2}{8x}]=\frac{1}{8}\times x^{\frac{1}{8}}\times e^{\frac{x^2}{2}}\\\\ \text{Integrating both sides}\\\\y\times x^{\frac{1}{8}}\times e^{\frac{x^2}{2}}=\frac{1}{8}\int {x^{\frac{1}{8}}\times e^{\frac{x^2}{2}}} \, dx \\\\8y\times x^{\frac{1}{8}}\times e^{\frac{x^2}{2}}=\int {x^{\frac{1}{8}}\times e^{\frac{x^2}{2}}} \, dx\\\\8y\times x^{\frac{1}{8}}\times e^{\frac{x^2}{2}}=-[x^{\frac{9}{8}}]\times\frac{ \Gamma(0.5625, -x^2)}{(-x^2)^{\frac{9}{16}}}\\\\8y\times x^{\frac{1}{8}}\times e^{\frac{x^2}{2}}=(-1)^{\frac{-1}{8}}[ \Gamma(0.5625, -x^2)]+C-----(1)$

When , x=1, gives , y=9.

Evaluate the value of C and substitute in the equation 1.

6 0

3 years ago

Alex scored 98,72, and 87 on his first three math test. What must he score on the next test to have an average of at least 86 (P

ss7ja [257]

Answer:

$\huge\boxed{\text{At least an } 87\%}$

Step-by-step explanation:

In order to find what score Alex must earn to have an average of 86 on all his tests, we need to first note what the formula to find the average of a data set is.

$\displaystyle \frac{x_1+x_2+...x_n}{n}$

What the formula means is that we have to add up all the values then divide by the total number of values.

Let's represent our unknown number as $x$ .

$\displaystyle \frac{98+72+87+x}{4} \geq 86$ (since we want AT LEAST an 86).

Let's solve this inequality for x.

$\frac{98+72+87+x}{4} \cdot 4 \geq 86 \cdot 4$
$98+72+87+x \geq 344$
$257 + x \geq 344$
$257 + x - 257 \geq 344 - 257$
$x \geq 87$

So, Alex must score at least an 87% on his next quiz to have an average of 86%.

Hope this helped!

8 0

3 years ago

the weight of 1m^3 of air is approximately 1.3×10^3g. suppose that the volume of air inside of a building is 3×10^6 m^3. How muc

Afina-wow [57]

82 X 10-6 glm3of pollutants in the air. ... The weight of 1m3 of air is approximately 1.3 X 103g.Suppose that the volume of air inside of a building is 3 x 106 m3.

3 0

3 years ago

The Jayden family eats at a restaurant that is having a 15% discount promotion. Their meal costs $78.72 before the discount, and

Scorpion4ik [409]

If I’m not mistaking it is either 80.29 or 80.30 after rounding,I’m not sure.

4 0

3 years ago

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