Find the exact value of tan (arcsin (2/5)). For full credit, explain your reasoning.

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Answer 1

Answer: Since arcsin(2/5)=x, sin x=2/5

Here we go $=sinx/(sqrt(1-sin^2x)) =(2/5)/(sqrt(1-4/5))$
$tan x = sinx/cosx$
More than one way possible :
$tan(arcsin(2/5)) =(2/5)/ (sqrt(21)/5)=2/sqrt(21)$

y = 0.25x + 150

y = total height after x days

x = total of days

since the rasio of difference in y (Δy) and difference in x (Δx) is constant, therefore it is applicable to linear function

Answer:

1) $\boxed{\rm{l = 150 + 0.25n}}$

where,

l is the length of the sunflower
n is the number of days.

2) The initial length of sunflower is 150 cm and it grows about 0.25 cm per day. It means it has grown 0.25 cm on the first day, then 0.25 × 2 = 0.5 cm on the second day, 0.25 × 3 = 0.75 cm on the third day and so on.. The total increase = 0.25 × n where n is the number of days. Now add the increase to the initial length of the sunflower to get the final length of the sunflower $.$

Grandma’s Bakery sells single-crust apple pies for $6.99 and double crust cherry pies for $10.99. The total number of pies sold on a busy Friday was 36. If the amount collected for all the pies that day was $331.64, how many of each type were sold?

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Answer:

15 single-crust apple pies were sold and 21 double-crust cherry pies were sold.

Step-by-step explanation:

Let a be the number of single-crust apple pies sold

Let c be the number of double-crust cherry pies sold

Please someone answer this question as quick as possible please

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Answer: 1/5 is the answer :)

Solve the system of equations using cramer's rule -x+y-3z=-4 3x-2y+8z=14 2x-2y+5z=7

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System of Equations
$-1x + 1y - 3z = -4 \n3x - 2y + 8z = 14 \n2x - 2y + 5z = 7$

Coefficient Matrix's Determinant
$D = \left[\begin{array}{ccc}-1&1&-3\n3&-2&8\n2&-2&5\end{array}\right]$

Answer Column
$\left[\begin{array}{ccc}-4\n14\n7\end{array}\right]$

Dx: Coefficient Determinant with Answer-Column values in X-Column
$D_(x) = \left[\begin{array}{ccc}-4&1&-3\n14&-2&8\n7&-2&5\end{array}\right]$

Dy: Coefficient Determinant with Answer-Column Values in Y-Column
$D_(y) = \left[\begin{array}{ccc}-1&-4&-3\n3&14&8\n2&7&5\end{array}\right]$

Dz: Coefficient Determinant with Answer-Column Values in Z-Column
$D_(z) = \left[\begin{array}{ccc}-1&1&-4\n3&-2&14\n2&-2&7\end{array}\right]$

Evaluating each Determinant
$D= \left[\begin{array}{ccc}-1&1&-3\n3&-2&8\n2&-2&5\end{array}\right] \nD = (-1 * (-2) * 5) + (1 * 8 * 2) + (-3 * 3 * (-2)) - (2 * (-2) * (-3)) - (-2 * 8 * (-1)) - (5 * 3 * 1) \nD = (10) + (16) + (18) - (12) - (16) - (15) \nD = 10 + 16 + 18 - 12 - 16 - 15 \nD = 26 + 18 - 12 - 16 - 15 \nD = 44 - 12 - 16 - 15 \nD = 32 - 16 - 15 \nD = 16 - 15 \nD = 1$

$D_(x) = \left[\begin{array}{ccc}-4&1&-3\n14&-2&8\n7&-2&5\end{array}\right] \nD_(x) = (-4 * (-2) * 5) + (1 * 8 * 7) + (-3 * 14 * (-2)) - (7 * (-2) * (-3)) - (-2 * 8 * (-4)) - (5 * 14 * 1)) \nD_(x) = (40) + (56) + (84) - (42) - (64) - (70) \nD_(x) = 40 + 56 + 84 - 42 - 64 - 70 \nD_(x) = 96 + 84 - 42 - 64 - 70 \nD_(x) = 180 - 42 - 64 - 70 \nD_(x) = 138 - 64 - 70 \nD_(x) = 74 - 70 \nD_(x) = 4$

$D_(y) = \left[\begin{array}{ccc}-1&-4&-3\n3&14&8\n2&7&5\end{array}\right] \nD_(y) = (-1 * 14 * 5) + (-4 * 8 * 2) + (-3 * 3 * 7) - (2 * 14 * (-3)) - (7 * 8 * (-1)) * (5 * 3 * (-4)) \nD_(y) = (-70)+ (-64) + (-63) - (-84) - (-56) - (-60) \nD_(y) = -70 - 64 - 63 + 84 + 56 + 60 \nD_(y) = -134 - 63 + 84 + 56 + 60 \nD_(y) = -197 + 84 + 56 + 60 \nD_(y) = -113 + 56 + 60 \nD_(y) = -57 + 60 \nD_(y) = 3$

$D_(z) = \left[\begin{array}{ccc}-1&1&-4\n3&-2&14\n2&-2&7\end{array}\right] \nD_(z) = (-1 * (-2) * 7) + (1 * 14 * 2) + (-4 * 3 * (-2)) - (2 * (-2) * (-4)) - (-2 * 14 * (-1)) - (7 * 3 * 1) \nD_(z) = (14) + (28) + (24) - (16) - (28) - (21) \nD_(z) = 14 + 28 + 24 - 16 - 28 - 24 \nD_(z) = 42 + 24 - 16 - 28 - 21 \nD_(z) = 66 - 16 - 28 - 21 \nD_(z) = 50 - 28 - 21 \nD_(z) = 22 - 21 \nD_(z) = 1$

$x = (D_(x))/(D) = (4)/(1) = 4 \ny = (D_(y))/(D) = (3)/(1) = 3 \nz = (D_(x))/(D) = (1)/(1) = 1 \n(x, y, z) = (4, 3, 1)$

Charlie runs ata speed of 3 yards per second. about how many miles per hour does charlie run?

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(3 yard/sec) x (3,600 sec/hr) x (1 mile / 1,760 yard) =

(3 x 3,600 / 1,760) (mile/hour) = 6.136... mph (rounded)

Adam runs 4 miles in 20 minutes. How many miles does he run in 1 hour?

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Answer: Adam will run 12 miles in 1 hour.

Step-by-step explanation:

Ok, so we know 4 miles in 20 minutes, correct?

Multiply 20x2. You will get 40. Then, multiply 4x2. That is 8. So in 40 minutes he ran 8 miles. So if we multiply 20x3, we would get 60 minutes which is an hour. So we need to multiply 4 by 3–12.

Answer: 12 miles

Step-by-step explanation:

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Find the exact value of tan (arcsin (2/5)). For full credit, explain your reasoning.

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y = 0.25x + 150

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