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3 years ago

What equation can be solved to find the time when the pumpkin is 10 feet from the ground

1 answer:

4 0

H(t)=h0+vt-(at^2)/2 we can assume that this problem is near to the earth's surface so a≈32ft/s^2

h(t)=h0+vt-16t^2 now you need to plug in the initial velocity where v is and the initial height where h0 is...

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Order the fractions, decimals, and percents from least to greatest. ( If you get it right I will mark you Brainliest.

alex41 [277]

Step-by-step explanation:

Convert all into decimals:

0.14, 4/8=0.5,0.33

Answer:

0.14, 0.33, 0.5

0.14, 3/9, 4/8

5 0

3 years ago

an verage person has 6x10^2 times as many red bloods cells as white blood cells. A small sample of blood has 7x10^3 white blood

m_a_m_a [10]

Answer:

4.2 x 10⁶

Step-by-step explanation:

The problem says that there are 6x 10² times as many red blood cells as white blood cells. This means that you will need to multiply the given number of white blood cells, which is 7 x 10³ by 6x 10².

To do this, first you multiply the coefficients:

7 x 6 = 42

Next you combine the exponents of the 10s, because their bases are the same, we just add the exponents when you multiply them and copy the base:

10² x 10³ = 10⁵

So the result would be:

42 x 10⁵

However the following the form of scientific notation, you need to move the decimal one more time so that means you add one more to the exponent of 10.

4.2 x 10⁶

7 0

3 years ago

Solve the following equations: (a) x^11=13 mod 35 (b) x^5=3 mod 64

tino4ka555 [31]

$x^{11}=13\pmod{35}\implies\begin{cases}x^{11}\equiv13\equiv3\pmod5\\x^{11}\equiv13\equiv6\pmod7\end{cases}$

By Fermat's little theorem, we have

$x^{11}\equiv (x^5)^2x\equiv x^3\equiv3\pmod5$

$x^{11}\equiv x^7x^4\equiv x^5\equiv6\pmod 7$

5 and 7 are both prime, so $\varphi(5)=4$ and $\varphi(7)=6$ . By Euler's theorem, we get

$x^4\equiv1\pmod5\implies x\equiv3^{-1}\equiv2\pmod5$

$x^6\equiv1\pmod7\impleis x\equiv6^{-1}\equiv6\pmod7$

Now we can use the Chinese remainder theorem to solve for $x$ . Start with

$x=2\cdot7+5\cdot6$

Taken mod 5, the second term vanishes and $14\equiv4\pmod5$ . Multiply by the inverse of 4 mod 5 (4), then by 2.

$x=2\cdot7\cdot4\cdot2+5\cdot6$

Taken mod 7, the first term vanishes and $30\equiv2\pmod7$ . Multiply by the inverse of 2 mod 7 (4), then by 6.

$x=2\cdot7\cdot4\cdot2+5\cdot6\cdot4\cdot6$

$\implies x\equiv832\pmod{5\cdot7}\implies\boxed{x\equiv27\pmod{35}}$

$x^5\equiv3\pmod{64}$

We have $\varphi(64)=32$ , so by Euler's theorem,

$x^{32}\equiv1\pmod{64}$

Now, raising both sides of the original congruence to the power of 6 gives

$x^{30}\equiv3^6\equiv729\equiv25\pmod{64}$

Then multiplying both sides by $x^2$ gives

$x^{32}\equiv25x^2\equiv1\pmod{64}$

so that $x^2$ is the inverse of 25 mod 64. To find this inverse, solve for $y$ in $25y\equiv1\pmod{64}$ . Using the Euclidean algorithm, we have

64 = 2*25 + 14

25 = 1*14 + 11

14 = 1*11 + 3

11 = 3*3 + 2

3 = 1*2 + 1

=> 1 = 9*64 - 23*25

so that $(-23)\cdot25\equiv1\pmod{64}\implies y=25^{-1}\equiv-23\equiv41\pmod{64}$ .

So we know

$25x^2\equiv1\pmod{64}\implies x^2\equiv41\pmod{64}$

Squaring both sides of this gives

$x^4\equiv1681\equiv17\pmod{64}$

and multiplying both sides by $x$ tells us

$x^5\equiv17x\equiv3\pmod{64}$

Use the Euclidean algorithm to solve for $x$ .

64 = 3*17 + 13

17 = 1*13 + 4

13 = 3*4 + 1

=> 1 = 4*64 - 15*17

so that $(-15)\cdot17\equiv1\pmod{64}\implies17^{-1}\equiv-15\equiv49\pmod{64}$ , and so $x\equiv147\pmod{64}\implies\boxed{x\equiv19\pmod{64}}$

5 0

3 years ago

A suitcase measures 24 inches long and the dialogue is 30 inches long. How much material is needed to cover one side of the suit

borishaifa [10]

Answer:

432 in.^2

Step-by-step explanation:

The side of the suitcase is a rectangle. One length is 24 inches. The diagonal of the rectangle is 30 inches long. The diagonal is a hypotenuse of a right triangle. The length is a leg. We need to find the other leg.

We use the Pythagorean theorem,

a^2 + b^2 = c^2

(24 in.)^2 + b^2 = (30 in.)^2

576 in.^2 + b^2 = 900 in.^2

b^2 = 324 in.^2

b = sqrt(324 in^2)

b = 18 in

area of rectangle = length * width

A = 24 in. * 18 in.

A = 432 in.^2

6 0

3 years ago

The circular mirror hanging on Belle's wall has a diameter of 18 inches. What is the

just olya [345]

Answer:

56.52 inches

Step-by-step explanation:

The circumference of a circle can be found using:

$c=\pi d$

We know the diameter is 18, and $\pi$ is being rounded to 3.14, so we can substitute them in.

c=3.14*18 <em>Multiply</em>

c=56.52

So, the circumference is 56.52 inches

7 0

3 years ago